Review Article Passive Microwave Component Design Using...

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Hindawi Publishing Corporation International Journal of Antennas and Propagation Volume 2013, Article ID 761278, 10 pages http://dx.doi.org/10.1155/2013/761278 Review Article Passive Microwave Component Design Using Inverse Scattering: Theory and Applications Israel Arnedo, Iván Arregui, Magdalena Chudzik, Fernando Teberio, Aintzane Lujambio, David Benito, Txema Lopetegi, and Miguel A. G. Laso Electrical and Electronic Engineering Department, Public University of Navarre, Navarre 31006 Pamplona, Spain Correspondence should be addressed to Israel Arnedo; [email protected] Received 15 March 2013; Accepted 22 May 2013 Academic Editor: Rocco Pierri Copyright © 2013 Israel Arnedo et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We briefly review different synthesis techniques for the design of passive microwave components with arbitrary frequency response, developed by our group during the last decade. We provide the theoretical foundations based on inverse scattering and coupled- mode theory as well as several applications where the devices designed following those techniques have been successfully tested. e main characteristics of these synthesis methods are as follows. (a) ey are direct, because it is not necessary to use lumped- element circuit models; just the target frequency response is the starting point. (b) ey are exact, as there is neither spurious bands nor degradation in the frequency response; hence, there is no bandwidth limitation. (c) ey are flexible, because they are valid for any causal, stable, and passive transfer function; only inviolable physical principles must be guaranteed. A myriad of examples has been presented by our group in many different technologies for very relevant applications such as harmonic control of amplifiers, directional coupler with enhanced directivity and coupling, transmission-type dispersive delay lines for phase engineering, compact design of high-power spurious free low-pass waveguide filters for satellite payloads, pulse shapers for advanced UWB radar and communications and for novel breast cancer detection systems, transmission-type Nth-order differentiators for tunable pulse generation, and a robust filter design tool. 1. Introduction e rigorous study of nonuniform microwave structures has been the starting point of the novel synthesis tech- niques of passive microwave components presented in this paper. e theoretical background rests on the knowledge of the coupled-mode theory, the field of periodic structures (PS), the electromagnetic band-gap (EBG) concepts, and the one-dimensional (1D) inverse scattering (IS) principles. e advantage of our proposals comes from the inherent properties of our synthesis approach and from the good per- formance achieved by structures with smooth (nonabrupt) profiles in terms of flexibility in the design [1], robustness in the implementation [2], spurious-multimode-excitation avoidance [3], and high-power handling capability [4]. Although the frequency response of PS [5] and EBG structures [6] feature a wide and deep rejected band (yielding to novel devices that have been found very promising applica- tions, including the implementation of filters and resonators, improvement of the efficiency and radiation pattern of anten- nas, harmonic tuning in power amplifiers, oscillators and mixers, and suppression of spurious bands in filters [7]), they also exhibit characteristics that may be detrimental in other applications. Fortunately, some modifications on those structures [8] substantially ameliorate their behaviour. Windowing techniques [9] were reported to improve the out-of-band behaviour and chirping techniques [10] were used to enhance the bandwidth performance, while oversized structures were proposed to accomplish very high rejection levels over wide bandwidths [11]. Very useful to enrich the variety of target frequency responses attainable was the well-known Fourier transform relationship [12]. Unfortunately, this is only accurate enough for devices with very low reflectivity. Hence, using this rela- tionship, the synthesis of a device with an arbitrary frequency response is only done in a first approximation. To surpass these difficulties, 1D-IS principles play a fundamental role. In this paper, an exact and analytical relationship between

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Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2013 Article ID 761278 10 pageshttpdxdoiorg1011552013761278

Review ArticlePassive Microwave Component Design Using Inverse ScatteringTheory and Applications

Israel Arnedo Ivaacuten Arregui Magdalena Chudzik Fernando Teberio Aintzane LujambioDavid Benito Txema Lopetegi and Miguel A G Laso

Electrical and Electronic Engineering Department Public University of Navarre Navarre 31006 Pamplona Spain

Correspondence should be addressed to Israel Arnedo israelarnedounavarraes

Received 15 March 2013 Accepted 22 May 2013

Academic Editor Rocco Pierri

Copyright copy 2013 Israel Arnedo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We briefly review different synthesis techniques for the design of passivemicrowave components with arbitrary frequency responsedeveloped by our group during the last decade We provide the theoretical foundations based on inverse scattering and coupled-mode theory as well as several applications where the devices designed following those techniques have been successfully testedThe main characteristics of these synthesis methods are as follows (a) They are direct because it is not necessary to use lumped-element circuit models just the target frequency response is the starting point (b)They are exact as there is neither spurious bandsnor degradation in the frequency response hence there is no bandwidth limitation (c)They are flexible because they are valid forany causal stable and passive transfer function only inviolable physical principles must be guaranteed A myriad of examples hasbeen presented by our group in many different technologies for very relevant applications such as harmonic control of amplifiersdirectional couplerwith enhanced directivity and coupling transmission-type dispersive delay lines for phase engineering compactdesign of high-power spurious free low-pass waveguide filters for satellite payloads pulse shapers for advanced UWB radar andcommunications and for novel breast cancer detection systems transmission-type Nth-order differentiators for tunable pulsegeneration and a robust filter design tool

1 Introduction

The rigorous study of nonuniform microwave structureshas been the starting point of the novel synthesis tech-niques of passive microwave components presented in thispaper The theoretical background rests on the knowledgeof the coupled-mode theory the field of periodic structures(PS) the electromagnetic band-gap (EBG) concepts andthe one-dimensional (1D) inverse scattering (IS) principlesThe advantage of our proposals comes from the inherentproperties of our synthesis approach and from the good per-formance achieved by structures with smooth (nonabrupt)profiles in terms of flexibility in the design [1] robustnessin the implementation [2] spurious-multimode-excitationavoidance [3] and high-power handling capability [4]

Although the frequency response of PS [5] and EBGstructures [6] feature a wide and deep rejected band (yieldingto novel devices that have been found very promising applica-tions including the implementation of filters and resonators

improvement of the efficiency and radiation pattern of anten-nas harmonic tuning in power amplifiers oscillators andmixers and suppression of spurious bands in filters [7])they also exhibit characteristics that may be detrimentalin other applications Fortunately some modifications onthose structures [8] substantially ameliorate their behaviourWindowing techniques [9] were reported to improve theout-of-band behaviour and chirping techniques [10] wereused to enhance the bandwidth performance while oversizedstructures were proposed to accomplish very high rejectionlevels over wide bandwidths [11]

Very useful to enrich the variety of target frequencyresponses attainable was the well-known Fourier transformrelationship [12] Unfortunately this is only accurate enoughfor devices with very low reflectivity Hence using this rela-tionship the synthesis of a device with an arbitrary frequencyresponse is only done in a first approximation To surpassthese difficulties 1D-IS principles play a fundamental roleIn this paper an exact and analytical relationship between

2 International Journal of Antennas and Propagation

a generic frequency response and the physical dimensions ofa device in the form of an infinite series is shown Moreoveranother exact and automatic alternative validwhen the targetspecifications can be expressed in terms of an arbitraryrational function is proposed

Four different synthesis approaches are sketched in Sec-tions 2 and 3 while some devices synthesized following thosemethods are described in Section 4

2 Coupled-Mode Theory in Microwaves

In order to deal with nonuniform microwave structures it isessential to formulate an accurate coupled-mode theory suit-able for microwave devices where the crosssection methodwill be employed The basic idea of this method is that theelectromagnetic fields in an arbitrary nonuniformwaveguidecrosssection can be represented as a superposition of thedifferent modes (including their forward and backward trav-eling waves) corresponding to a uniform auxiliary waveguidethat has the same crosssection with identical distributionof 120576 and 120583 [13 14] It is important to note that in most ofthe cases in the design of microwave devices the problemcan be greatly simplified by introducing several reasonableapproximations thatwill lead to single-mode operationThusthe devices can be characterized by the following coupled-mode system of equations

119889119886+

119889119911

= minus119895 sdot 120573 sdot 119886+

+ 119870 sdot 119886minus

(1a)

119889119886minus

119889119911

= 119870 sdot 119886+

+ 119895 sdot 120573 sdot 119886minus

(1b)

where

= 119886

+

sdot +

+ 119886minus

sdot minus

(2a)

= 119886

+

sdot +

+ 119886minus

sdot minus

(2b)

119873+

= ∬

119878

+

times +

sdot 119889 119878 = minus119873minus

= minus∬

119878

minus

times minus

sdot 119889 119878

119870 =

minus1

2119873+

119878

(+

times

120597minus

120597119911

+

120597+

120597119911

times minus

) 119889 119878

minus

1

2119873+

sdot

119889119873minus

119889119911

(3)

being

the total electric and magnetic field present in thestructure + + minus and

minus the vectormode patterns of theforward (+) and backward (minus) traveling waves correspondingto the mode of operation in the auxiliary uniform waveguideassociated with the crosssection of interest 119873

+ 119873minus the

normalizations taken for the fields of the mode 120573 the phaseconstant of the mode 119870 the coupling coefficient betweenthe forward and backward traveling waves 119911 the directionof propagation and 119886

+ 119886minus the complex amplitudes of the

forward (+) and backward (minus) traveling waves along thenonuniform waveguide

Moreover the physical dimensions of the device alongthe propagation direction can be easily deduced from thecoupling coefficient once we choose a particular technologyof implementation [13]

3 Novel Synthesis Techniques

The aim of all the synthesis methods presented here is toobtain the coupling coefficient of the device (or equivalentlyits physical dimensions once the technology is chosen) start-ing from some given frequency specifications Depending onthe strategy used four kinds of methods arise

31 Synthesis of Optimum Periodic Structures If the structureis periodic along the propagation axis 119911 with period Λ thenthe 119870(119911) produced by the perturbation is also periodic withthe same period and hence it can be expanded in a Fourierseries as follows

119870 (119911) =

119899=infin

sum

119899=minusinfin

119870119899

sdot 119890119895sdot(2sdot120587Λ)sdot119899sdot119911

119870119899

=

1

Λ

sdot int

Λ

119870 (119911) sdot 119890minus119895sdot(2sdot120587Λ)sdot119899sdot119911

119889119911

(4)

For the system in (1a) and (1b) analytical expressions canbe obtained for the central frequency 119891

0119899 rejection level

|11987821

|min119899 return loss level |11987811

|max119899 and bandwidth betweenzeros 119861119882

119899 of the 119899th stopband produced by the two-port

structure For the case of planar structures (see [8]) we havethe following

1198910119899

=

119888 sdot 119899

2 sdot Λ sdot radic120576eff

100381610038161003816100381611987821

1003816100381610038161003816min119899 = sech (

1003816100381610038161003816119870119899

1003816100381610038161003816sdot 119871)

100381610038161003816100381611987811

1003816100381610038161003816max119899 = tanh (

1003816100381610038161003816119870119899

1003816100381610038161003816sdot 119871)

119861119882119899

=

119888 sdot1003816100381610038161003816119870119899

1003816100381610038161003816

120587 sdot radic120576effsdot radic1 + (

120587

1003816100381610038161003816119870119899

1003816100381610038161003816sdot 119871

)

2

(5)

where 119888 is the speed of light in vacuum 119871 is the device lengthand 120576eff is the mean value of 120576eff(119911) in a period calculated as120576eff = (1Λ sdot int

Λ

radic120576eff(119911) sdot 119889119911)

2These expressions can be used for the synthesis of

microwave structures with ad hoc rejected bands where wehave independent control of their frequency rejection levelandor bandwidth Of particular remarkable interest is thestructure with spurious-free frequency response Examining

International Journal of Antennas and Propagation 3

(5) the 119899th coefficient of the Fourier series 119870119899 is univocally

associated with the 119899th stopband and therefore to obtainan spurious-free EBG structure that features only the fun-damental stopband all the coefficients must be equal to zeroexcept for119870

plusmn1This results in a sinusoidal coupling coefficient

following the generic expression

119870 (119911) = 119860 sdot cos(

2 sdot 120587

Λ

sdot 119911 + 120579) (6)

where 119860 is the amplitude of the coupling coefficient and 120579 thephase that fixes its value at the origin

32 Synthesis of Quasi-Periodic Structures WindowedChirped and Oversized Structures In order to enrich thepanel of frequency responses that can be satisfied by the syn-thesized structures the purely periodic structure of sinus-oidal coupling coefficient (6) can be windowed (by makingthe amplitude a smooth function of 119911 [9 15 16]) or chirped(by making the period variable with 119911 [10 17]) Finally if theamplitude is high enough a transversal resonance can beachieved providing new degrees of freedom to the designer[11 18]

33 General Microwave Synthesis Technique for an ArbitraryFrequency Response as a Solution of the Gelrsquofand-Levitan-Marchenko 1D Inverse Scattering Problem In order to synthe-size a physical device with an arbitrary frequency response(just limited by causality stability and passivity) we startfrom the simplified system of coupled mode equations givenin (1a) and (1b) This system can be rewritten as a Zakharov-Shabat system of quantum mechanics [19] for which an

analytical solution can be found using the so-called Gelrsquofand-Levitan-Marchenko coupled integral equations valid for |119911| gt

120591 [19]

1198601

(119911 120591) + int

119911

minus120591

119860lowast

2(119911 119910) sdot 119865 (119910 + 120591) sdot 119889119910 = 0 (7a)

1198602

(119911 120591) + 119865 (119911 + 120591) + int

119911

minus120591

119860lowast

1(119911 119910) sdot 119865 (119910 + 120591) sdot 119889119910 = 0

(7b)

where 1198601(119911 120591) and 119860

2(119911 120591) are auxiliary functions to be

found and 119865(120591) is the inverse Fourier transform of the 11987811

(120573)

parameter (starting specifications)

119865 (120591) =

1

2120587

int

+infin

minusinfin

11987811

(120573) sdot 119890119895sdot120573sdot120591

sdot 119889120573 (8)

Thus applying the Fourier Transform to (1a) and (1b) andusing causality considerations the coupling coefficient can becalculated as follows [19]

119870 (119911) = 2 sdot 1198602

(119911 119911minus

) (9)

Now a series solution for 1198602(119911 120591) can be found by

alternating approximations of 1198601(119911 120591) and 119860

2(119911 120591) in (7a)

and (7b) in the following way We start by neglecting theintegral term in (7b) and the first approximation for 119860

2(119911 120591)

is achieved Introducing this result in (7a)1198601(119911 120591) is updated

and a new approximation of 1198602(119911 120591) is obtained Iterating

and taking finally into account that 119865(120591) will be real fora physical device we arrive at the exact analytical seriessolution for the coupling coefficient given in (10) shown atthe end of this subsection where 119909

1015840

119894= 119909119894+ 119909119894minus1

minus 2119911 for 119894 gt 1that can be efficiently implemented with a computer see [20]

119870 (119911) = minus2119865 (2119911) minus 2 int

2119911

0

1198891199091119865 (1199091) int

1199091

0

1198891199091015840

2119865 (1199091015840

2) 119865 (119909

1015840

2minus 1199091

+ 2119911) minus 2 int

2119911

0

1198891199091119865 (1199091) int

1199091

0

1198891199091015840

2119865 (1199091015840

2)

times int

1199092

0

1198891199091015840

3119865 (1199091015840

3) int

1199093

0

1198891199091015840

4119865 (1199091015840

4) 119865 (119909

1015840

4minus 1199093

+ 2119911) minus sdot sdot sdot minus 2 int

2119911

0

1198891199091119865 (1199091) int

1199091

0

1198891199091015840

2119865 (1199091015840

2)

times int

1199092

0

sdot sdot sdot int

1199092119873minus1

0

1198891199091015840

2119873119865 (1199091015840

2119873) 119865 (119909

1015840

2119873minus 1199092119873minus1

+ 2119911) minus sdot sdot sdot

(10)

34 General Microwave Synthesis Technique for RationalFrequency Responses by Means of the 1D Inverse ScatteringProblem in the Laplace Domain In the case that the targetfrequency response can be expressed as a rational function afast synthesismethod can be derived [21]Wewill assume that11987811

(119904) is a rational function that can be written as a quotientof polynomials as follows

11987811

(119904) =

119899 (119904)

119889 (119904)

=

1199030

sdot prod119872

119899=1(119904 minus 119888119899)

prod119873

119899=1(119904 minus 119901

119899)

(11)

being 119888119899the zeros and 119901

119899the poles of 119878

11(119904) 119872 the number

of zeros and 119873 the number of poles where it is satisfied that

119873 ge 119872 + 1 (11987811

(119904 = 119895120573) is a band limited function that tendsto zero when frequency goes to infinity) andR119890119901

119899 lt 0 (all

the polesmust be in the left-half 119904 plane to be a stable system)Finally 119903

0is a constant thatmust be adjusted to satisfy |119878

11(119904 =

119895120573)| lt 1 (passive system)Hence the 119878

21parameter of the device arises univocally

from the 11987811

parameter for our case of interest of reciprocaland lossless two-port networks Specifically the magnitudecan be calculated for each frequency (or equivalently 120573) asfollows [22]

100381610038161003816100381611987821

(119904 = 119895120573)1003816100381610038161003816

2

= 1 minus100381610038161003816100381611987811

(119904 = 119895120573)1003816100381610038161003816

2 (12)

4 International Journal of Antennas and Propagation

yielding to the following

11987821

(119904) =

prod119873

119899=1(119904 minus 119896

119899)

prod119873

119899=1(119904 minus 119901

119899)

(13)

being 119896119899the zeros and 119901

119899the poles of 119878

21(119904) whereR119890119896

119899 lt

0 (all the zeros are in the left-half 119904 plane because 11987821

(119904) isa minimum-phase function) and R119890119901

119899 lt 0 (all the poles

must be in the left-half 119904 plane to be a stable system)Appling the Laplace transform to (9) the coupling coef-

ficient can be calculated as follows [21]

119870 (119911) = minus2 sdot lim119904rarrminusinfin

(119890119904sdot119911

sdot 119904 sdot 1198862

(119911 119904)) (14)

By inspecting (14) it can be seen that the couplingcoefficient 119870(119911) necessary to implement a given frequencyresponse can be calculated analytically by obtaining first ananalytical solution for 119886

2(119911 119904) To do it we need to assume

that the 119873 poles of 11987811

(119904) and 11987821

(119904) 1199011 1199012 119901

119873 are

distinct that the 119873 zeros of 11987821

(119904) 1198961 1198962 119896

119873 are distinct

and that the119872 zeros of 11987811

(119904) 1198881 1198882 119888

119872 are different from

the conjugated poles with opposite sign minus119901lowast

1 minus119901lowast

2 minus119901

lowast

119873

Then 1198861(119911 119904) and 119886

2(119911 119904) can be expressed as a linear

combination of entire functions [21] and thus the soughtanalytical closed-form expression for the coupling coefficient119870(119911) of the microwave structure that satisfies the targetfrequency response is obtained [21]

119870 (119911) = 2 sdot

119873

sum

119899=1

1198892119899

(119911) sdot 119890119896119899sdot119911

minus 119889lowast

1119899(119911) sdot 119890

minus119896lowast

119899sdot119911

sdot 11987811

(minus119896lowast

119899)

(15)

where 1198891119899

(119911) and 1198892119899

(119911) are the solutions of the followinglinear system of 2 sdot 119873 equations [21]

119873

sum

119899=1

1

11987811

(119896119899)

sdot

119890minus119896119899sdot119911

119901119894minus 119896119899

sdot [

1198891119899

(119911)

1198892119899

(119911)] minus

119890119896lowast

119899sdot119911

119901119894+ 119896lowast

119899

sdot [

119889lowast

2119899(119911)

119889lowast

1119899(119911)

]

= [

0

1]

(16)

4 Applications of the Synthesis Techniques

Several devices have been designed following the above-mentioned synthesis methods in different technologiesTheyare classified by their intended application

41 Harmonic Control in Amplifier Applications To checkthe efficiency of an amplifier it is necessary to detect verytiny frequency spurious harmonics usually masked by thefundamental carrier power By using Section 31 a two-portspurious-free notch-filter can be designed [8] see Figures 1and 2

42 Directional Coupler with Enhanced Directivity and Cou-pling Manymicrowave systems demanddirectional couplerswith high directivity and coupling A fully planar device

Figure 1 Photograph of the fabricated prototype in microstriptechnology top view of the metallic strip and bottom view of theunaltered ground plane

0 2 4 6 8 10 12

0

Frequency (GHz)

minus5

minus10

minus15

minus20

minus25

minus30

|S11||S21|

(dB)

Figure 2 Measured |11987821

| (black line) and |11987811

| (grey line) parameterof the designed two-port EBG microstrip structure in Figure 1

1 2

43

Figure 3 Photograph of the fabricated EBG microstrip directionalcoupler with high directivity and coupling The ground plane isunaltered

where coupling level and frequency can be obtained followingthe method Section 31 for a four-port structure [23] seeFigures 3 and 4

43 Transmission-Type Dispersive Delay Lines for Phase-Engineering Application Phase engineering in microwaveshas drawn very much attention in the last years [24] Itis devoted to the development of analog signal processingsystems in the microwave frequency range with fundamentalbuilding blocks such as Dispersive Delay Lines of differentkinds Following the ideas of chirping and windowing inSection 32 a new transmission-type dispersive delay line canbe proposedwith closed formulas for the dispersion slope andbandwidth of operation [25] see Figures 5 6 7 and 8

International Journal of Antennas and Propagation 5

8 9 10 11 12

0

20

40

60

Frequency (GHz)

Dire

ctiv

ity an

d co

uplin

g (d

B)

minus20

Figure 4 Measured directivity (black line) and coupling (grey line)of the designed EBG microstrip directional coupler in Figure 3

Input

Output

1 2

43

Figure 5 Photograph of the fabricated prototype of transmission-type dispersive delay line indicating the input and output ports Azoom-in is included to show a detail of the deviceThe ground planeis unaltered

0 2 4 6 8 10 12Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

|S11||S31|

(dB)

Figure 6 Simulations (thin line) and measurements (thick line) of|11987811

| (grey line) and |11987831

| (black line) in the dispersive delay line ofFigure 5

44 Compact Design of High-Power Spurious-Free Low-Pass Waveguide Filters for Satellite Payloads High-powerspurious-free low-pass rectangular waveguide filters are keycomponents at the output of a satellite Output Multiplexer(OMUX) [26] As stated in Section 32 if the amplitudeof the sinusoidal coupling coefficient is high enough each

0 2 4 6 8 10 120

1

2

3

4

Frequency (GHz)

Gro

up d

elay

ofS

31

(ns)

Figure 7 Simulation (thin line) and measurement (thick line) ofthe group delay of the 119878

31parameter in the dispersive delay line of

Figure 5

0 2 4 6 8 10 12Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

|S21||S41|

(dB)

Figure 8 Simulations (thin line) and measurements (thick line) of|11987821

| (grey line) and |11987841

| (black line) in the dispersive delay line ofFigure 5

corrugation behaves like an individual bandstop elementwhose height is around 120582

1198924 being 120582

119892the guide wavelength

of the fundamental TE10mode at the frequency to be rejected

[11] see Figure 9The resulting device for a passband between 107GHz

and 127 GHz with return losses around 20 dB and a 60 dBrejection level for frequencies over 1375GHz and up to thethird harmonic (around 40GHz) has been manufactured incopper by electroforming The photograph of the fabricatedprototype is given in Figure 10(a) and in Figure 10(b) weshow the simulations using CSTMicrowave Studio (grey line)and the measurements (black line) that have been performedby means of an Agilent 8722 Vector Network Analyzerproper waveguide-to-coaxial transitions and Maury 7005Ecalibration kits

6 International Journal of Antennas and Propagation

l

h

L

zgmin0

A B C

(a)

Interpolatingfunction

hmin

hmax

z0

A B C

gmin 2

(b)

z0

A B C

(c)

Windowingfunction

Windowingfunction

z0

(d)

Figure 9 Schematics showing the design process of novel high-power spurious-free low-pass waveguide filters (a) sketch showing the finalfilter profile and its physical parameters (b) shaping of section 119861 (119892min ℎmin and ℎmax) (c) new bandstop elements added to define sections119860 and 119862 and (d) windowing applied to sections 119860 and 119862

45 Pulse Shapers for Advanced UWB Radar and Communi-cations and for Novel Breast Cancer Detection Systems Anewstrategy for generating customized pulse shapes intendedfor use in wideband applications has been proposed anddemonstrated [27] The strategy employs the exact analyticalseries solution proposed in Section 33 [19] Time-domainmeasurements are performed demonstrating the generationof two pulse shapes using microstrip technology The firstone satisfies the preestablished UWB mask requirements foradvanced radar and ultrafast communication systems [28]see Figures 11 12 and 13 The second one improves a time-domain microwave breast imaging system [29] see Figures14 and 15

46 Transmission-Type Nth-Order Differentiators for TunablePulse Generation 119873th-order differentiators are very promis-ing devices for temporal analog processing and for the designof advanced tunable pulse generators [30] Their generalmathematical expression is

119873(119891) = (2120587 sdot 119895 sdot 119891)

119873 where 119895 =

radicminus1 Here a 4th-order differentiator has been designed for

a frequency range from 31 to 74GHz which gives a goodtradeoff between energy efficiency andmaximum bandwidthfor UWB signals 119867

4(119891)

Following the synthesis procedure detailed in Section 33the required coupling coefficient 119870(119911) is calculated for thetarget frequency response 119867

4(119891) using (10) The device

will be implemented in coupled lines to work effectively intransmission and therefore the even and odd characteristicimpedance 119885

0119890(119911) and 119885

0119900(119911) need to be separated and

windowed to keep the ports matched Since microstriptechnology will be used to implement the resulting devicethe even and oddmodes will propagate at different velocitiesmaking the necessary to apply a compensation algorithm[30]

The resulting characteristic impedances together withthe photograph of the fabricated prototype are shown inFigure 16 Figure 17 shows a very good agreement betweenthe simulation using Agilent ADS Momentum (grey dottedline) and measurement results for the magnitude and phaseof the 119878

31(119891) parameter (grey solid line) compared with

International Journal of Antennas and Propagation 7

(a)

10 15 20 25 30 35 40

0

Frequency (GHz)

minus20

minus40

minus60

minus80

minus100

|S11||S21|

(dB)

(b)

Figure 10 (a) Photograph of the fabricated prototype and (b)simulations (grey line) and measurements (black line) of the novelcompact highpower spurious-free low-pass waveguide filter |119878

11| in

dashed line and |11987821

| in solid line Frequency specifications for |11987811

|

and |11987821

| are also given in dotted line

Figure 11 Photograph of a microstrip pulse shaper for UWB radarand communication systems

0 02 04 06 08

0

05

1

Pulse

1

(au

)

minus05

minus1

Time t (ns)

Figure 12 Performance of the pulse shaper for UWB radar andcommunications Sinusoidal waveform windowed by a squaredcosine the target pulse (thin line) and themeasurement (thick line)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

|Pul

se1|

(dB)

(a)

0 2 4 6 8 10 12

0

200

Frequency (GHz)

minus200

minus400

minus600

Phas

e of p

ulse

1(∘)

(b)

Figure 13 Spectrum (a)magnitude and (b) phase of the target signal(thin line) and Fourier-transformed measurement (thick line) ofthe pulse generated in the pulse shaper intended for UWB radarcommunications The FCC UWBmask is also shown in grey

the target specifications for the 4th-order differentiator (blackdashed line) Moreover the |119878

11| parameter (not shown)

is below minus20 dB in the entire frequency range of interestensuring a good matching at the input port

47 Robust Filter Design Tool A Cauer Filter Example Thesynthesis technique presented in Section 34 is incorporatedin an exact robust filter design tool The method is validatedwith an example in rectangular waveguide technology withWR-90 standard portsThe specifications are passbands from8GHz to 114GHz and from 189GHz up to 225GHz withreturn losses better than 20 dB and a rejected band from13GHz to 163 GHz with a rejection level higher than 60 dBA bandpass frequency response following a Cauer (Elliptic)approximation [21 31] will be used for the 119878

11parameter (a

bandstop frequency response will result for the 11987821

parame-ter)The order necessary for the approximationwill be 14 and

8 International Journal of Antennas and Propagation

(a) (b)

Figure 14 Two photographs of the heterogeneous breast phantoms (a) exterior view of the realistically shaped breast phantom and (b)coronal view of the 2mm skin layer and the conical gland structures embedded inside the phantom

minus80

minus60

minus40

minus20

0

20

40

60

80

minus50 0 50y (mm)

z(m

m)

Figure 15 A coronal slice of the reconstructed 3D image of therealistically shaped adipose breast phantomusing the designed pulseshaperThe dark red indicates higher intensity values correspondingto stronger EM scatterersThe ldquolowastrdquo denotes the global maximum andthe ldquoordquo represents the approximate tumour location based on theinsertion of the tumour into the breast phantom

the passband will extend from 131 GHz up to 162GHz witha passband ripple of 10

minus9 dB and a rejected band rippleof 25 dB From the magnitude of the 119878

11parameter the

magnitude of the 11987821

can be immediately obtained by using(12) and a bandstop frequency response results for the 119878

21

parameter with a rejected band attenuation of 67 dBFollowing the expressions in Section 34 a prototype is

designed and fabricated see Figure 18 As it can be seenin Figure 19 the target simulated using CST MicrowaveStudio and measured frequency responses are in a very goodagreement satisfying the frequency requirements mentionedabove and confirming the accuracy and flexibility of thesynthesis method proposed

0 2 4 6 8 10 12 14 1630

40

50

60

70

80

Z0eZ

0o(Ω

)

Propagation direction z (cm)

(a)

1 2

43

(b)

Figure 16 (a) Even (black line) and odd (grey line) characteristicimpedance of the 4th-order differentiator after the compensationprocess and (b) the corresponding photograph of the prototype inmicrostrip technology for the given characteristic impedance

5 Conclusion

Newdevices inmicrostrip technology rectangular waveguidetechnology and microstrip coupled line technology havebeen successfully designed easily fabricated and accuratelytested for very different applications A palate of InverseScattering microwave synthesis methods have been surveyedalong the paper highlighting their advantages and disad-vantages and confirming that all the techniques togetherrepresent a powerful tool for the design of passive microwavecomponents for the new emerging applications in the wire-less radar biomedical engineering and satellite worlds

International Journal of Antennas and Propagation 9

0 2 4 6 8 10 12

0

Frequency (GHz)

|H4|

and|S31|

(dB)

minus10

minus20

minus30

minus40

minus50

(a)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus1000

minus2000

minus3000

minus4000

minus5000

Phas

e ofH

4an

dS 3

1(∘)

(b)

Figure 17 Target (black dashed line) simulated (dark grey dotted line) and measured (light grey solid line) magnitude (a) and phase (b) ofthe frequency response of the 4th-order differentiator

Figure 18 Photograph of the fabricated filter prototype in rectan-gular waveguide technology Standard WR-90 ports are used

82 10 12 14 16 18 20 22

0

Frequency (GHz)

|S11||S21|

(dB)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Figure 19Magnitude of the 11987811-parameter (grey line) and of the 119878

21-

parameter (black line) for the final synthesized filter in waveguidetechnology in Figure 18 The target (thin solid line) simulated(dotted line) and measured (thick solid line) frequency responsesare given

Acknowledgments

This work has been supported by the Spanish Ministerio deCiencia e Innovacion through the Project TEC2011-28664-C02-01 Magdalena Chudzik would like also to acknowledgeSpanish Ministerio de Educacion for its FPU Grant

References

[1] D C Youla ldquoAnalysis and synthesis of arbitrarily terminatedlossless nonuniform linesrdquo IEEE Transactions on CircuitTheoryvol CT-11 pp 363ndash372 1964

[2] R W Klopfenstein ldquoA transmission-line taper of improveddesignrdquo Proceedings of the IRE vol 44 pp 31ndash35 1956

[3] M D Abouzahra and L Lewin ldquoRadiation from microstripdiscontinuitiesrdquo IEEE Transactions on Microwave Theory andTechniques vol MTT-27 no 8 pp 722ndash723 1979

[4] I Arregui I Arnedo T Lopetegi M A G Laso and AMarcotegui ldquoLow-pass filter for electromagnetic signalsrdquo U SPatent 20100308938 European Patent 2 244 330 January 212008

[5] C Elachi ldquoWaves in active and passive periodic structures areviewrdquo Proceedings of the IEEE vol 64 no 12 pp 1666ndash16981976

[6] Y Qian V Radisic and T Itoh ldquoSimulation and experiment ofphotonic band-gap structures for microstrip circuitsrdquo in Pro-ceedings of the 1997 Asia-Pacific Microwave Conference (APMCrsquo97) pp 585ndash588 Hong Kong December 1997

[7] F Yang R Coccioll Y Qian and T Itoh ldquoPlanar peg structuresbasic properties and applicationsrdquo IEICE Transactions on Elec-tronics vol E83-C no 5 pp 687ndash696 2000

[8] I ArnedoM Chudzik J D Schwartz et al ldquoAnalytical solutionfor the design of planar electromagnetic bandgap structureswith spurious-free frequency responserdquoMicrowave and OpticalTechnology Letters vol 54 no 4 pp 956ndash960 2012

[9] T Lopetegi M A G Laso R Gonzalo et al ldquoElectromagneticcrystals in microstrip technologyrdquo Optical and Quantum Elec-tronics vol 34 no 1ndash3 pp 279ndash295 2002

[10] M A G Laso T Lopetegi M J Erro et al ldquoReal-time spec-trum analysis in microstrip technologyrdquo IEEE Transactions onMicrowave Theory and Techniques vol 51 no 3 pp 705ndash7172003

[11] I Arregui I Arnedo A Lujambio et al ldquoA compact designof high-power spurious-free low-pass waveguide filterrdquo IEEE

10 International Journal of Antennas and Propagation

Microwave and Wireless Components Letters vol 20 no 11 pp595ndash597 2010

[12] E F Bolinder ldquoThe relationship of physical applications offourier transforms in various fields of wave theory and cir-cuitryrdquo IEEE Transactions onMicrowaveTheory and Techniquespp 153ndash158 1957

[13] B Z Katsenelenbaum L Mercader M Pereyaslavets MSorolla and M Thumm Theory of Nonuniform WaveguidesThe Cross-Section Method vol 44 of IEE Electromagnetic WavesSeries IET London UK 1998

[14] F Sporleder andHGUngerWaveguide Tapers Transitions andCouplers Peter Peregrinus London UK 1979

[15] I Arnedo J Gil N Ortiz et al ldquoKu-band high-power lowpassfilter with spurious rejectionrdquo Electronics Letters vol 42 no 25pp 1460ndash1461 2006

[16] I Arregui I Arnedo A Lujambio et al ldquoDesign method forsatellite output multiplexer low-pass filters exhibiting spurious-free frequency behavior and high-power operationrdquoMicrowaveand Optical Technology Letters vol 52 no 8 pp 1724ndash17282010

[17] J D Schwartz I Arnedo M A G Laso T Lopetegi J Azanaand D Plant ldquoAn electronic UWB continuously tunable time-delay system with nanosecond delaysrdquo IEEE Microwave andWireless Components Letters vol 18 no 2 pp 103ndash105 2008

[18] I Arregui F Teberio I Arnedo et al ldquoHigh-power low-passharmonic waveguide filter with TEn0-mode suppressionrdquo IEEEMicrowave and Wireless Components Letters vol 22 no 7 pp339ndash341 2012

[19] I Arnedo M A G Laso F Falcone D Benito and T LopetegildquoA series solution for the single-mode synthesis problem basedon the coupled-mode theoryrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 56 no 2 pp 457ndash466 2008

[20] M Chudzik I Arnedo I Arregui et al ldquoNovel synthesis tech-nique for microwave circuits based on inverse scattering effi-cient algorithm implementation and applicationrdquo InternationalJournal of RF and Microwave Computer-Aided Engineering vol21 no 2 pp 164ndash173 2011

[21] I Arnedo I Arregui A Lujambio M Chudzik M A GLaso and T Lopetegi ldquoSynthesis of microwave filters by inversescattering using a closed-form expression valid for rationalfrequency responsesrdquo IEEE Transactions on Microwave Theoryand Techniques vol 60 no 5 pp 1244ndash1257 2012

[22] M J Erro I Arnedo M A G Laso T Lopetegi and MA Muriel ldquoPhase-reconstruction in photonic crystals from S-parameter magnitude in microstrip technologyrdquo Optical andQuantum Electronics vol 39 no 4ndash6 pp 321ndash331 2007

[23] M Chudzik I Arnedo A Lujambio et al ldquoMicrostrip coupled-line directional coupler with enhanced coupling based on EBGconceptrdquo Electronics Letters vol 47 no 23 pp 1284ndash1286 2011

[24] C Caloz ldquoMetamaterial dispersion engineering concepts andapplicationsrdquo Proceedings of the IEEE vol 99 no 10 pp 1711ndash1719 2011

[25] A Lujambio I Arnedo M Chudzik I Arregui T Lopetegiand M A G Laso ldquoDispersive delay line with effectivetransmission-type operation in coupled-line technologyrdquo IEEEMicrowave and Wireless Components Letters vol 21 no 9 pp459ndash461 2011

[26] P Fortescue and J Stark Spacecraft Systems Engineering WileyChichester UK 1995

[27] Part 15 Rules for Unlicensed RF Devices Federal Communica-tions Commission (FCC) September 2007 httpwwwfccgovoetinforules

[28] I Amedo J D Schwartz M A G Laso T Lopetegi D V Plantand J Azana ldquoPassive microwave planar circuits for arbitraryUWBpulse shapingrdquo IEEEMicrowave andWireless ComponentsLetters vol 18 no 7 pp 452ndash454 2008

[29] A Santorelli M Chudzik E Kirshin et al ldquoExperimentaldemonstration of pulse shaping for time-domain microwavebrest imagingrdquo Progress in Electromagnetics Research vol 133pp 309ndash329 2013

[30] M Chudzik I Arnedo A Lujambio et al ldquoDesign of trans-mission-type Nth-order differentiators in planar microwavetechnologyrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 60 no 11 pp 3384ndash3394 2012

[31] I Arnedo A Lujambio T Lopetegi andM A G Laso ldquoDesignof microwave filters with arbitrary frequency response basedon digital methodsrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 634ndash636 2007

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Chemical EngineeringInternational Journal of Antennas and

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International Journal of

Page 2: Review Article Passive Microwave Component Design Using ...downloads.hindawi.com/journals/ijap/2013/761278.pdf · InternationalJournal of Antennas and Propagation a generic frequency

2 International Journal of Antennas and Propagation

a generic frequency response and the physical dimensions ofa device in the form of an infinite series is shown Moreoveranother exact and automatic alternative validwhen the targetspecifications can be expressed in terms of an arbitraryrational function is proposed

Four different synthesis approaches are sketched in Sec-tions 2 and 3 while some devices synthesized following thosemethods are described in Section 4

2 Coupled-Mode Theory in Microwaves

In order to deal with nonuniform microwave structures it isessential to formulate an accurate coupled-mode theory suit-able for microwave devices where the crosssection methodwill be employed The basic idea of this method is that theelectromagnetic fields in an arbitrary nonuniformwaveguidecrosssection can be represented as a superposition of thedifferent modes (including their forward and backward trav-eling waves) corresponding to a uniform auxiliary waveguidethat has the same crosssection with identical distributionof 120576 and 120583 [13 14] It is important to note that in most ofthe cases in the design of microwave devices the problemcan be greatly simplified by introducing several reasonableapproximations thatwill lead to single-mode operationThusthe devices can be characterized by the following coupled-mode system of equations

119889119886+

119889119911

= minus119895 sdot 120573 sdot 119886+

+ 119870 sdot 119886minus

(1a)

119889119886minus

119889119911

= 119870 sdot 119886+

+ 119895 sdot 120573 sdot 119886minus

(1b)

where

= 119886

+

sdot +

+ 119886minus

sdot minus

(2a)

= 119886

+

sdot +

+ 119886minus

sdot minus

(2b)

119873+

= ∬

119878

+

times +

sdot 119889 119878 = minus119873minus

= minus∬

119878

minus

times minus

sdot 119889 119878

119870 =

minus1

2119873+

119878

(+

times

120597minus

120597119911

+

120597+

120597119911

times minus

) 119889 119878

minus

1

2119873+

sdot

119889119873minus

119889119911

(3)

being

the total electric and magnetic field present in thestructure + + minus and

minus the vectormode patterns of theforward (+) and backward (minus) traveling waves correspondingto the mode of operation in the auxiliary uniform waveguideassociated with the crosssection of interest 119873

+ 119873minus the

normalizations taken for the fields of the mode 120573 the phaseconstant of the mode 119870 the coupling coefficient betweenthe forward and backward traveling waves 119911 the directionof propagation and 119886

+ 119886minus the complex amplitudes of the

forward (+) and backward (minus) traveling waves along thenonuniform waveguide

Moreover the physical dimensions of the device alongthe propagation direction can be easily deduced from thecoupling coefficient once we choose a particular technologyof implementation [13]

3 Novel Synthesis Techniques

The aim of all the synthesis methods presented here is toobtain the coupling coefficient of the device (or equivalentlyits physical dimensions once the technology is chosen) start-ing from some given frequency specifications Depending onthe strategy used four kinds of methods arise

31 Synthesis of Optimum Periodic Structures If the structureis periodic along the propagation axis 119911 with period Λ thenthe 119870(119911) produced by the perturbation is also periodic withthe same period and hence it can be expanded in a Fourierseries as follows

119870 (119911) =

119899=infin

sum

119899=minusinfin

119870119899

sdot 119890119895sdot(2sdot120587Λ)sdot119899sdot119911

119870119899

=

1

Λ

sdot int

Λ

119870 (119911) sdot 119890minus119895sdot(2sdot120587Λ)sdot119899sdot119911

119889119911

(4)

For the system in (1a) and (1b) analytical expressions canbe obtained for the central frequency 119891

0119899 rejection level

|11987821

|min119899 return loss level |11987811

|max119899 and bandwidth betweenzeros 119861119882

119899 of the 119899th stopband produced by the two-port

structure For the case of planar structures (see [8]) we havethe following

1198910119899

=

119888 sdot 119899

2 sdot Λ sdot radic120576eff

100381610038161003816100381611987821

1003816100381610038161003816min119899 = sech (

1003816100381610038161003816119870119899

1003816100381610038161003816sdot 119871)

100381610038161003816100381611987811

1003816100381610038161003816max119899 = tanh (

1003816100381610038161003816119870119899

1003816100381610038161003816sdot 119871)

119861119882119899

=

119888 sdot1003816100381610038161003816119870119899

1003816100381610038161003816

120587 sdot radic120576effsdot radic1 + (

120587

1003816100381610038161003816119870119899

1003816100381610038161003816sdot 119871

)

2

(5)

where 119888 is the speed of light in vacuum 119871 is the device lengthand 120576eff is the mean value of 120576eff(119911) in a period calculated as120576eff = (1Λ sdot int

Λ

radic120576eff(119911) sdot 119889119911)

2These expressions can be used for the synthesis of

microwave structures with ad hoc rejected bands where wehave independent control of their frequency rejection levelandor bandwidth Of particular remarkable interest is thestructure with spurious-free frequency response Examining

International Journal of Antennas and Propagation 3

(5) the 119899th coefficient of the Fourier series 119870119899 is univocally

associated with the 119899th stopband and therefore to obtainan spurious-free EBG structure that features only the fun-damental stopband all the coefficients must be equal to zeroexcept for119870

plusmn1This results in a sinusoidal coupling coefficient

following the generic expression

119870 (119911) = 119860 sdot cos(

2 sdot 120587

Λ

sdot 119911 + 120579) (6)

where 119860 is the amplitude of the coupling coefficient and 120579 thephase that fixes its value at the origin

32 Synthesis of Quasi-Periodic Structures WindowedChirped and Oversized Structures In order to enrich thepanel of frequency responses that can be satisfied by the syn-thesized structures the purely periodic structure of sinus-oidal coupling coefficient (6) can be windowed (by makingthe amplitude a smooth function of 119911 [9 15 16]) or chirped(by making the period variable with 119911 [10 17]) Finally if theamplitude is high enough a transversal resonance can beachieved providing new degrees of freedom to the designer[11 18]

33 General Microwave Synthesis Technique for an ArbitraryFrequency Response as a Solution of the Gelrsquofand-Levitan-Marchenko 1D Inverse Scattering Problem In order to synthe-size a physical device with an arbitrary frequency response(just limited by causality stability and passivity) we startfrom the simplified system of coupled mode equations givenin (1a) and (1b) This system can be rewritten as a Zakharov-Shabat system of quantum mechanics [19] for which an

analytical solution can be found using the so-called Gelrsquofand-Levitan-Marchenko coupled integral equations valid for |119911| gt

120591 [19]

1198601

(119911 120591) + int

119911

minus120591

119860lowast

2(119911 119910) sdot 119865 (119910 + 120591) sdot 119889119910 = 0 (7a)

1198602

(119911 120591) + 119865 (119911 + 120591) + int

119911

minus120591

119860lowast

1(119911 119910) sdot 119865 (119910 + 120591) sdot 119889119910 = 0

(7b)

where 1198601(119911 120591) and 119860

2(119911 120591) are auxiliary functions to be

found and 119865(120591) is the inverse Fourier transform of the 11987811

(120573)

parameter (starting specifications)

119865 (120591) =

1

2120587

int

+infin

minusinfin

11987811

(120573) sdot 119890119895sdot120573sdot120591

sdot 119889120573 (8)

Thus applying the Fourier Transform to (1a) and (1b) andusing causality considerations the coupling coefficient can becalculated as follows [19]

119870 (119911) = 2 sdot 1198602

(119911 119911minus

) (9)

Now a series solution for 1198602(119911 120591) can be found by

alternating approximations of 1198601(119911 120591) and 119860

2(119911 120591) in (7a)

and (7b) in the following way We start by neglecting theintegral term in (7b) and the first approximation for 119860

2(119911 120591)

is achieved Introducing this result in (7a)1198601(119911 120591) is updated

and a new approximation of 1198602(119911 120591) is obtained Iterating

and taking finally into account that 119865(120591) will be real fora physical device we arrive at the exact analytical seriessolution for the coupling coefficient given in (10) shown atthe end of this subsection where 119909

1015840

119894= 119909119894+ 119909119894minus1

minus 2119911 for 119894 gt 1that can be efficiently implemented with a computer see [20]

119870 (119911) = minus2119865 (2119911) minus 2 int

2119911

0

1198891199091119865 (1199091) int

1199091

0

1198891199091015840

2119865 (1199091015840

2) 119865 (119909

1015840

2minus 1199091

+ 2119911) minus 2 int

2119911

0

1198891199091119865 (1199091) int

1199091

0

1198891199091015840

2119865 (1199091015840

2)

times int

1199092

0

1198891199091015840

3119865 (1199091015840

3) int

1199093

0

1198891199091015840

4119865 (1199091015840

4) 119865 (119909

1015840

4minus 1199093

+ 2119911) minus sdot sdot sdot minus 2 int

2119911

0

1198891199091119865 (1199091) int

1199091

0

1198891199091015840

2119865 (1199091015840

2)

times int

1199092

0

sdot sdot sdot int

1199092119873minus1

0

1198891199091015840

2119873119865 (1199091015840

2119873) 119865 (119909

1015840

2119873minus 1199092119873minus1

+ 2119911) minus sdot sdot sdot

(10)

34 General Microwave Synthesis Technique for RationalFrequency Responses by Means of the 1D Inverse ScatteringProblem in the Laplace Domain In the case that the targetfrequency response can be expressed as a rational function afast synthesismethod can be derived [21]Wewill assume that11987811

(119904) is a rational function that can be written as a quotientof polynomials as follows

11987811

(119904) =

119899 (119904)

119889 (119904)

=

1199030

sdot prod119872

119899=1(119904 minus 119888119899)

prod119873

119899=1(119904 minus 119901

119899)

(11)

being 119888119899the zeros and 119901

119899the poles of 119878

11(119904) 119872 the number

of zeros and 119873 the number of poles where it is satisfied that

119873 ge 119872 + 1 (11987811

(119904 = 119895120573) is a band limited function that tendsto zero when frequency goes to infinity) andR119890119901

119899 lt 0 (all

the polesmust be in the left-half 119904 plane to be a stable system)Finally 119903

0is a constant thatmust be adjusted to satisfy |119878

11(119904 =

119895120573)| lt 1 (passive system)Hence the 119878

21parameter of the device arises univocally

from the 11987811

parameter for our case of interest of reciprocaland lossless two-port networks Specifically the magnitudecan be calculated for each frequency (or equivalently 120573) asfollows [22]

100381610038161003816100381611987821

(119904 = 119895120573)1003816100381610038161003816

2

= 1 minus100381610038161003816100381611987811

(119904 = 119895120573)1003816100381610038161003816

2 (12)

4 International Journal of Antennas and Propagation

yielding to the following

11987821

(119904) =

prod119873

119899=1(119904 minus 119896

119899)

prod119873

119899=1(119904 minus 119901

119899)

(13)

being 119896119899the zeros and 119901

119899the poles of 119878

21(119904) whereR119890119896

119899 lt

0 (all the zeros are in the left-half 119904 plane because 11987821

(119904) isa minimum-phase function) and R119890119901

119899 lt 0 (all the poles

must be in the left-half 119904 plane to be a stable system)Appling the Laplace transform to (9) the coupling coef-

ficient can be calculated as follows [21]

119870 (119911) = minus2 sdot lim119904rarrminusinfin

(119890119904sdot119911

sdot 119904 sdot 1198862

(119911 119904)) (14)

By inspecting (14) it can be seen that the couplingcoefficient 119870(119911) necessary to implement a given frequencyresponse can be calculated analytically by obtaining first ananalytical solution for 119886

2(119911 119904) To do it we need to assume

that the 119873 poles of 11987811

(119904) and 11987821

(119904) 1199011 1199012 119901

119873 are

distinct that the 119873 zeros of 11987821

(119904) 1198961 1198962 119896

119873 are distinct

and that the119872 zeros of 11987811

(119904) 1198881 1198882 119888

119872 are different from

the conjugated poles with opposite sign minus119901lowast

1 minus119901lowast

2 minus119901

lowast

119873

Then 1198861(119911 119904) and 119886

2(119911 119904) can be expressed as a linear

combination of entire functions [21] and thus the soughtanalytical closed-form expression for the coupling coefficient119870(119911) of the microwave structure that satisfies the targetfrequency response is obtained [21]

119870 (119911) = 2 sdot

119873

sum

119899=1

1198892119899

(119911) sdot 119890119896119899sdot119911

minus 119889lowast

1119899(119911) sdot 119890

minus119896lowast

119899sdot119911

sdot 11987811

(minus119896lowast

119899)

(15)

where 1198891119899

(119911) and 1198892119899

(119911) are the solutions of the followinglinear system of 2 sdot 119873 equations [21]

119873

sum

119899=1

1

11987811

(119896119899)

sdot

119890minus119896119899sdot119911

119901119894minus 119896119899

sdot [

1198891119899

(119911)

1198892119899

(119911)] minus

119890119896lowast

119899sdot119911

119901119894+ 119896lowast

119899

sdot [

119889lowast

2119899(119911)

119889lowast

1119899(119911)

]

= [

0

1]

(16)

4 Applications of the Synthesis Techniques

Several devices have been designed following the above-mentioned synthesis methods in different technologiesTheyare classified by their intended application

41 Harmonic Control in Amplifier Applications To checkthe efficiency of an amplifier it is necessary to detect verytiny frequency spurious harmonics usually masked by thefundamental carrier power By using Section 31 a two-portspurious-free notch-filter can be designed [8] see Figures 1and 2

42 Directional Coupler with Enhanced Directivity and Cou-pling Manymicrowave systems demanddirectional couplerswith high directivity and coupling A fully planar device

Figure 1 Photograph of the fabricated prototype in microstriptechnology top view of the metallic strip and bottom view of theunaltered ground plane

0 2 4 6 8 10 12

0

Frequency (GHz)

minus5

minus10

minus15

minus20

minus25

minus30

|S11||S21|

(dB)

Figure 2 Measured |11987821

| (black line) and |11987811

| (grey line) parameterof the designed two-port EBG microstrip structure in Figure 1

1 2

43

Figure 3 Photograph of the fabricated EBG microstrip directionalcoupler with high directivity and coupling The ground plane isunaltered

where coupling level and frequency can be obtained followingthe method Section 31 for a four-port structure [23] seeFigures 3 and 4

43 Transmission-Type Dispersive Delay Lines for Phase-Engineering Application Phase engineering in microwaveshas drawn very much attention in the last years [24] Itis devoted to the development of analog signal processingsystems in the microwave frequency range with fundamentalbuilding blocks such as Dispersive Delay Lines of differentkinds Following the ideas of chirping and windowing inSection 32 a new transmission-type dispersive delay line canbe proposedwith closed formulas for the dispersion slope andbandwidth of operation [25] see Figures 5 6 7 and 8

International Journal of Antennas and Propagation 5

8 9 10 11 12

0

20

40

60

Frequency (GHz)

Dire

ctiv

ity an

d co

uplin

g (d

B)

minus20

Figure 4 Measured directivity (black line) and coupling (grey line)of the designed EBG microstrip directional coupler in Figure 3

Input

Output

1 2

43

Figure 5 Photograph of the fabricated prototype of transmission-type dispersive delay line indicating the input and output ports Azoom-in is included to show a detail of the deviceThe ground planeis unaltered

0 2 4 6 8 10 12Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

|S11||S31|

(dB)

Figure 6 Simulations (thin line) and measurements (thick line) of|11987811

| (grey line) and |11987831

| (black line) in the dispersive delay line ofFigure 5

44 Compact Design of High-Power Spurious-Free Low-Pass Waveguide Filters for Satellite Payloads High-powerspurious-free low-pass rectangular waveguide filters are keycomponents at the output of a satellite Output Multiplexer(OMUX) [26] As stated in Section 32 if the amplitudeof the sinusoidal coupling coefficient is high enough each

0 2 4 6 8 10 120

1

2

3

4

Frequency (GHz)

Gro

up d

elay

ofS

31

(ns)

Figure 7 Simulation (thin line) and measurement (thick line) ofthe group delay of the 119878

31parameter in the dispersive delay line of

Figure 5

0 2 4 6 8 10 12Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

|S21||S41|

(dB)

Figure 8 Simulations (thin line) and measurements (thick line) of|11987821

| (grey line) and |11987841

| (black line) in the dispersive delay line ofFigure 5

corrugation behaves like an individual bandstop elementwhose height is around 120582

1198924 being 120582

119892the guide wavelength

of the fundamental TE10mode at the frequency to be rejected

[11] see Figure 9The resulting device for a passband between 107GHz

and 127 GHz with return losses around 20 dB and a 60 dBrejection level for frequencies over 1375GHz and up to thethird harmonic (around 40GHz) has been manufactured incopper by electroforming The photograph of the fabricatedprototype is given in Figure 10(a) and in Figure 10(b) weshow the simulations using CSTMicrowave Studio (grey line)and the measurements (black line) that have been performedby means of an Agilent 8722 Vector Network Analyzerproper waveguide-to-coaxial transitions and Maury 7005Ecalibration kits

6 International Journal of Antennas and Propagation

l

h

L

zgmin0

A B C

(a)

Interpolatingfunction

hmin

hmax

z0

A B C

gmin 2

(b)

z0

A B C

(c)

Windowingfunction

Windowingfunction

z0

(d)

Figure 9 Schematics showing the design process of novel high-power spurious-free low-pass waveguide filters (a) sketch showing the finalfilter profile and its physical parameters (b) shaping of section 119861 (119892min ℎmin and ℎmax) (c) new bandstop elements added to define sections119860 and 119862 and (d) windowing applied to sections 119860 and 119862

45 Pulse Shapers for Advanced UWB Radar and Communi-cations and for Novel Breast Cancer Detection Systems Anewstrategy for generating customized pulse shapes intendedfor use in wideband applications has been proposed anddemonstrated [27] The strategy employs the exact analyticalseries solution proposed in Section 33 [19] Time-domainmeasurements are performed demonstrating the generationof two pulse shapes using microstrip technology The firstone satisfies the preestablished UWB mask requirements foradvanced radar and ultrafast communication systems [28]see Figures 11 12 and 13 The second one improves a time-domain microwave breast imaging system [29] see Figures14 and 15

46 Transmission-Type Nth-Order Differentiators for TunablePulse Generation 119873th-order differentiators are very promis-ing devices for temporal analog processing and for the designof advanced tunable pulse generators [30] Their generalmathematical expression is

119873(119891) = (2120587 sdot 119895 sdot 119891)

119873 where 119895 =

radicminus1 Here a 4th-order differentiator has been designed for

a frequency range from 31 to 74GHz which gives a goodtradeoff between energy efficiency andmaximum bandwidthfor UWB signals 119867

4(119891)

Following the synthesis procedure detailed in Section 33the required coupling coefficient 119870(119911) is calculated for thetarget frequency response 119867

4(119891) using (10) The device

will be implemented in coupled lines to work effectively intransmission and therefore the even and odd characteristicimpedance 119885

0119890(119911) and 119885

0119900(119911) need to be separated and

windowed to keep the ports matched Since microstriptechnology will be used to implement the resulting devicethe even and oddmodes will propagate at different velocitiesmaking the necessary to apply a compensation algorithm[30]

The resulting characteristic impedances together withthe photograph of the fabricated prototype are shown inFigure 16 Figure 17 shows a very good agreement betweenthe simulation using Agilent ADS Momentum (grey dottedline) and measurement results for the magnitude and phaseof the 119878

31(119891) parameter (grey solid line) compared with

International Journal of Antennas and Propagation 7

(a)

10 15 20 25 30 35 40

0

Frequency (GHz)

minus20

minus40

minus60

minus80

minus100

|S11||S21|

(dB)

(b)

Figure 10 (a) Photograph of the fabricated prototype and (b)simulations (grey line) and measurements (black line) of the novelcompact highpower spurious-free low-pass waveguide filter |119878

11| in

dashed line and |11987821

| in solid line Frequency specifications for |11987811

|

and |11987821

| are also given in dotted line

Figure 11 Photograph of a microstrip pulse shaper for UWB radarand communication systems

0 02 04 06 08

0

05

1

Pulse

1

(au

)

minus05

minus1

Time t (ns)

Figure 12 Performance of the pulse shaper for UWB radar andcommunications Sinusoidal waveform windowed by a squaredcosine the target pulse (thin line) and themeasurement (thick line)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

|Pul

se1|

(dB)

(a)

0 2 4 6 8 10 12

0

200

Frequency (GHz)

minus200

minus400

minus600

Phas

e of p

ulse

1(∘)

(b)

Figure 13 Spectrum (a)magnitude and (b) phase of the target signal(thin line) and Fourier-transformed measurement (thick line) ofthe pulse generated in the pulse shaper intended for UWB radarcommunications The FCC UWBmask is also shown in grey

the target specifications for the 4th-order differentiator (blackdashed line) Moreover the |119878

11| parameter (not shown)

is below minus20 dB in the entire frequency range of interestensuring a good matching at the input port

47 Robust Filter Design Tool A Cauer Filter Example Thesynthesis technique presented in Section 34 is incorporatedin an exact robust filter design tool The method is validatedwith an example in rectangular waveguide technology withWR-90 standard portsThe specifications are passbands from8GHz to 114GHz and from 189GHz up to 225GHz withreturn losses better than 20 dB and a rejected band from13GHz to 163 GHz with a rejection level higher than 60 dBA bandpass frequency response following a Cauer (Elliptic)approximation [21 31] will be used for the 119878

11parameter (a

bandstop frequency response will result for the 11987821

parame-ter)The order necessary for the approximationwill be 14 and

8 International Journal of Antennas and Propagation

(a) (b)

Figure 14 Two photographs of the heterogeneous breast phantoms (a) exterior view of the realistically shaped breast phantom and (b)coronal view of the 2mm skin layer and the conical gland structures embedded inside the phantom

minus80

minus60

minus40

minus20

0

20

40

60

80

minus50 0 50y (mm)

z(m

m)

Figure 15 A coronal slice of the reconstructed 3D image of therealistically shaped adipose breast phantomusing the designed pulseshaperThe dark red indicates higher intensity values correspondingto stronger EM scatterersThe ldquolowastrdquo denotes the global maximum andthe ldquoordquo represents the approximate tumour location based on theinsertion of the tumour into the breast phantom

the passband will extend from 131 GHz up to 162GHz witha passband ripple of 10

minus9 dB and a rejected band rippleof 25 dB From the magnitude of the 119878

11parameter the

magnitude of the 11987821

can be immediately obtained by using(12) and a bandstop frequency response results for the 119878

21

parameter with a rejected band attenuation of 67 dBFollowing the expressions in Section 34 a prototype is

designed and fabricated see Figure 18 As it can be seenin Figure 19 the target simulated using CST MicrowaveStudio and measured frequency responses are in a very goodagreement satisfying the frequency requirements mentionedabove and confirming the accuracy and flexibility of thesynthesis method proposed

0 2 4 6 8 10 12 14 1630

40

50

60

70

80

Z0eZ

0o(Ω

)

Propagation direction z (cm)

(a)

1 2

43

(b)

Figure 16 (a) Even (black line) and odd (grey line) characteristicimpedance of the 4th-order differentiator after the compensationprocess and (b) the corresponding photograph of the prototype inmicrostrip technology for the given characteristic impedance

5 Conclusion

Newdevices inmicrostrip technology rectangular waveguidetechnology and microstrip coupled line technology havebeen successfully designed easily fabricated and accuratelytested for very different applications A palate of InverseScattering microwave synthesis methods have been surveyedalong the paper highlighting their advantages and disad-vantages and confirming that all the techniques togetherrepresent a powerful tool for the design of passive microwavecomponents for the new emerging applications in the wire-less radar biomedical engineering and satellite worlds

International Journal of Antennas and Propagation 9

0 2 4 6 8 10 12

0

Frequency (GHz)

|H4|

and|S31|

(dB)

minus10

minus20

minus30

minus40

minus50

(a)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus1000

minus2000

minus3000

minus4000

minus5000

Phas

e ofH

4an

dS 3

1(∘)

(b)

Figure 17 Target (black dashed line) simulated (dark grey dotted line) and measured (light grey solid line) magnitude (a) and phase (b) ofthe frequency response of the 4th-order differentiator

Figure 18 Photograph of the fabricated filter prototype in rectan-gular waveguide technology Standard WR-90 ports are used

82 10 12 14 16 18 20 22

0

Frequency (GHz)

|S11||S21|

(dB)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Figure 19Magnitude of the 11987811-parameter (grey line) and of the 119878

21-

parameter (black line) for the final synthesized filter in waveguidetechnology in Figure 18 The target (thin solid line) simulated(dotted line) and measured (thick solid line) frequency responsesare given

Acknowledgments

This work has been supported by the Spanish Ministerio deCiencia e Innovacion through the Project TEC2011-28664-C02-01 Magdalena Chudzik would like also to acknowledgeSpanish Ministerio de Educacion for its FPU Grant

References

[1] D C Youla ldquoAnalysis and synthesis of arbitrarily terminatedlossless nonuniform linesrdquo IEEE Transactions on CircuitTheoryvol CT-11 pp 363ndash372 1964

[2] R W Klopfenstein ldquoA transmission-line taper of improveddesignrdquo Proceedings of the IRE vol 44 pp 31ndash35 1956

[3] M D Abouzahra and L Lewin ldquoRadiation from microstripdiscontinuitiesrdquo IEEE Transactions on Microwave Theory andTechniques vol MTT-27 no 8 pp 722ndash723 1979

[4] I Arregui I Arnedo T Lopetegi M A G Laso and AMarcotegui ldquoLow-pass filter for electromagnetic signalsrdquo U SPatent 20100308938 European Patent 2 244 330 January 212008

[5] C Elachi ldquoWaves in active and passive periodic structures areviewrdquo Proceedings of the IEEE vol 64 no 12 pp 1666ndash16981976

[6] Y Qian V Radisic and T Itoh ldquoSimulation and experiment ofphotonic band-gap structures for microstrip circuitsrdquo in Pro-ceedings of the 1997 Asia-Pacific Microwave Conference (APMCrsquo97) pp 585ndash588 Hong Kong December 1997

[7] F Yang R Coccioll Y Qian and T Itoh ldquoPlanar peg structuresbasic properties and applicationsrdquo IEICE Transactions on Elec-tronics vol E83-C no 5 pp 687ndash696 2000

[8] I ArnedoM Chudzik J D Schwartz et al ldquoAnalytical solutionfor the design of planar electromagnetic bandgap structureswith spurious-free frequency responserdquoMicrowave and OpticalTechnology Letters vol 54 no 4 pp 956ndash960 2012

[9] T Lopetegi M A G Laso R Gonzalo et al ldquoElectromagneticcrystals in microstrip technologyrdquo Optical and Quantum Elec-tronics vol 34 no 1ndash3 pp 279ndash295 2002

[10] M A G Laso T Lopetegi M J Erro et al ldquoReal-time spec-trum analysis in microstrip technologyrdquo IEEE Transactions onMicrowave Theory and Techniques vol 51 no 3 pp 705ndash7172003

[11] I Arregui I Arnedo A Lujambio et al ldquoA compact designof high-power spurious-free low-pass waveguide filterrdquo IEEE

10 International Journal of Antennas and Propagation

Microwave and Wireless Components Letters vol 20 no 11 pp595ndash597 2010

[12] E F Bolinder ldquoThe relationship of physical applications offourier transforms in various fields of wave theory and cir-cuitryrdquo IEEE Transactions onMicrowaveTheory and Techniquespp 153ndash158 1957

[13] B Z Katsenelenbaum L Mercader M Pereyaslavets MSorolla and M Thumm Theory of Nonuniform WaveguidesThe Cross-Section Method vol 44 of IEE Electromagnetic WavesSeries IET London UK 1998

[14] F Sporleder andHGUngerWaveguide Tapers Transitions andCouplers Peter Peregrinus London UK 1979

[15] I Arnedo J Gil N Ortiz et al ldquoKu-band high-power lowpassfilter with spurious rejectionrdquo Electronics Letters vol 42 no 25pp 1460ndash1461 2006

[16] I Arregui I Arnedo A Lujambio et al ldquoDesign method forsatellite output multiplexer low-pass filters exhibiting spurious-free frequency behavior and high-power operationrdquoMicrowaveand Optical Technology Letters vol 52 no 8 pp 1724ndash17282010

[17] J D Schwartz I Arnedo M A G Laso T Lopetegi J Azanaand D Plant ldquoAn electronic UWB continuously tunable time-delay system with nanosecond delaysrdquo IEEE Microwave andWireless Components Letters vol 18 no 2 pp 103ndash105 2008

[18] I Arregui F Teberio I Arnedo et al ldquoHigh-power low-passharmonic waveguide filter with TEn0-mode suppressionrdquo IEEEMicrowave and Wireless Components Letters vol 22 no 7 pp339ndash341 2012

[19] I Arnedo M A G Laso F Falcone D Benito and T LopetegildquoA series solution for the single-mode synthesis problem basedon the coupled-mode theoryrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 56 no 2 pp 457ndash466 2008

[20] M Chudzik I Arnedo I Arregui et al ldquoNovel synthesis tech-nique for microwave circuits based on inverse scattering effi-cient algorithm implementation and applicationrdquo InternationalJournal of RF and Microwave Computer-Aided Engineering vol21 no 2 pp 164ndash173 2011

[21] I Arnedo I Arregui A Lujambio M Chudzik M A GLaso and T Lopetegi ldquoSynthesis of microwave filters by inversescattering using a closed-form expression valid for rationalfrequency responsesrdquo IEEE Transactions on Microwave Theoryand Techniques vol 60 no 5 pp 1244ndash1257 2012

[22] M J Erro I Arnedo M A G Laso T Lopetegi and MA Muriel ldquoPhase-reconstruction in photonic crystals from S-parameter magnitude in microstrip technologyrdquo Optical andQuantum Electronics vol 39 no 4ndash6 pp 321ndash331 2007

[23] M Chudzik I Arnedo A Lujambio et al ldquoMicrostrip coupled-line directional coupler with enhanced coupling based on EBGconceptrdquo Electronics Letters vol 47 no 23 pp 1284ndash1286 2011

[24] C Caloz ldquoMetamaterial dispersion engineering concepts andapplicationsrdquo Proceedings of the IEEE vol 99 no 10 pp 1711ndash1719 2011

[25] A Lujambio I Arnedo M Chudzik I Arregui T Lopetegiand M A G Laso ldquoDispersive delay line with effectivetransmission-type operation in coupled-line technologyrdquo IEEEMicrowave and Wireless Components Letters vol 21 no 9 pp459ndash461 2011

[26] P Fortescue and J Stark Spacecraft Systems Engineering WileyChichester UK 1995

[27] Part 15 Rules for Unlicensed RF Devices Federal Communica-tions Commission (FCC) September 2007 httpwwwfccgovoetinforules

[28] I Amedo J D Schwartz M A G Laso T Lopetegi D V Plantand J Azana ldquoPassive microwave planar circuits for arbitraryUWBpulse shapingrdquo IEEEMicrowave andWireless ComponentsLetters vol 18 no 7 pp 452ndash454 2008

[29] A Santorelli M Chudzik E Kirshin et al ldquoExperimentaldemonstration of pulse shaping for time-domain microwavebrest imagingrdquo Progress in Electromagnetics Research vol 133pp 309ndash329 2013

[30] M Chudzik I Arnedo A Lujambio et al ldquoDesign of trans-mission-type Nth-order differentiators in planar microwavetechnologyrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 60 no 11 pp 3384ndash3394 2012

[31] I Arnedo A Lujambio T Lopetegi andM A G Laso ldquoDesignof microwave filters with arbitrary frequency response basedon digital methodsrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 634ndash636 2007

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International Journal of

Page 3: Review Article Passive Microwave Component Design Using ...downloads.hindawi.com/journals/ijap/2013/761278.pdf · InternationalJournal of Antennas and Propagation a generic frequency

International Journal of Antennas and Propagation 3

(5) the 119899th coefficient of the Fourier series 119870119899 is univocally

associated with the 119899th stopband and therefore to obtainan spurious-free EBG structure that features only the fun-damental stopband all the coefficients must be equal to zeroexcept for119870

plusmn1This results in a sinusoidal coupling coefficient

following the generic expression

119870 (119911) = 119860 sdot cos(

2 sdot 120587

Λ

sdot 119911 + 120579) (6)

where 119860 is the amplitude of the coupling coefficient and 120579 thephase that fixes its value at the origin

32 Synthesis of Quasi-Periodic Structures WindowedChirped and Oversized Structures In order to enrich thepanel of frequency responses that can be satisfied by the syn-thesized structures the purely periodic structure of sinus-oidal coupling coefficient (6) can be windowed (by makingthe amplitude a smooth function of 119911 [9 15 16]) or chirped(by making the period variable with 119911 [10 17]) Finally if theamplitude is high enough a transversal resonance can beachieved providing new degrees of freedom to the designer[11 18]

33 General Microwave Synthesis Technique for an ArbitraryFrequency Response as a Solution of the Gelrsquofand-Levitan-Marchenko 1D Inverse Scattering Problem In order to synthe-size a physical device with an arbitrary frequency response(just limited by causality stability and passivity) we startfrom the simplified system of coupled mode equations givenin (1a) and (1b) This system can be rewritten as a Zakharov-Shabat system of quantum mechanics [19] for which an

analytical solution can be found using the so-called Gelrsquofand-Levitan-Marchenko coupled integral equations valid for |119911| gt

120591 [19]

1198601

(119911 120591) + int

119911

minus120591

119860lowast

2(119911 119910) sdot 119865 (119910 + 120591) sdot 119889119910 = 0 (7a)

1198602

(119911 120591) + 119865 (119911 + 120591) + int

119911

minus120591

119860lowast

1(119911 119910) sdot 119865 (119910 + 120591) sdot 119889119910 = 0

(7b)

where 1198601(119911 120591) and 119860

2(119911 120591) are auxiliary functions to be

found and 119865(120591) is the inverse Fourier transform of the 11987811

(120573)

parameter (starting specifications)

119865 (120591) =

1

2120587

int

+infin

minusinfin

11987811

(120573) sdot 119890119895sdot120573sdot120591

sdot 119889120573 (8)

Thus applying the Fourier Transform to (1a) and (1b) andusing causality considerations the coupling coefficient can becalculated as follows [19]

119870 (119911) = 2 sdot 1198602

(119911 119911minus

) (9)

Now a series solution for 1198602(119911 120591) can be found by

alternating approximations of 1198601(119911 120591) and 119860

2(119911 120591) in (7a)

and (7b) in the following way We start by neglecting theintegral term in (7b) and the first approximation for 119860

2(119911 120591)

is achieved Introducing this result in (7a)1198601(119911 120591) is updated

and a new approximation of 1198602(119911 120591) is obtained Iterating

and taking finally into account that 119865(120591) will be real fora physical device we arrive at the exact analytical seriessolution for the coupling coefficient given in (10) shown atthe end of this subsection where 119909

1015840

119894= 119909119894+ 119909119894minus1

minus 2119911 for 119894 gt 1that can be efficiently implemented with a computer see [20]

119870 (119911) = minus2119865 (2119911) minus 2 int

2119911

0

1198891199091119865 (1199091) int

1199091

0

1198891199091015840

2119865 (1199091015840

2) 119865 (119909

1015840

2minus 1199091

+ 2119911) minus 2 int

2119911

0

1198891199091119865 (1199091) int

1199091

0

1198891199091015840

2119865 (1199091015840

2)

times int

1199092

0

1198891199091015840

3119865 (1199091015840

3) int

1199093

0

1198891199091015840

4119865 (1199091015840

4) 119865 (119909

1015840

4minus 1199093

+ 2119911) minus sdot sdot sdot minus 2 int

2119911

0

1198891199091119865 (1199091) int

1199091

0

1198891199091015840

2119865 (1199091015840

2)

times int

1199092

0

sdot sdot sdot int

1199092119873minus1

0

1198891199091015840

2119873119865 (1199091015840

2119873) 119865 (119909

1015840

2119873minus 1199092119873minus1

+ 2119911) minus sdot sdot sdot

(10)

34 General Microwave Synthesis Technique for RationalFrequency Responses by Means of the 1D Inverse ScatteringProblem in the Laplace Domain In the case that the targetfrequency response can be expressed as a rational function afast synthesismethod can be derived [21]Wewill assume that11987811

(119904) is a rational function that can be written as a quotientof polynomials as follows

11987811

(119904) =

119899 (119904)

119889 (119904)

=

1199030

sdot prod119872

119899=1(119904 minus 119888119899)

prod119873

119899=1(119904 minus 119901

119899)

(11)

being 119888119899the zeros and 119901

119899the poles of 119878

11(119904) 119872 the number

of zeros and 119873 the number of poles where it is satisfied that

119873 ge 119872 + 1 (11987811

(119904 = 119895120573) is a band limited function that tendsto zero when frequency goes to infinity) andR119890119901

119899 lt 0 (all

the polesmust be in the left-half 119904 plane to be a stable system)Finally 119903

0is a constant thatmust be adjusted to satisfy |119878

11(119904 =

119895120573)| lt 1 (passive system)Hence the 119878

21parameter of the device arises univocally

from the 11987811

parameter for our case of interest of reciprocaland lossless two-port networks Specifically the magnitudecan be calculated for each frequency (or equivalently 120573) asfollows [22]

100381610038161003816100381611987821

(119904 = 119895120573)1003816100381610038161003816

2

= 1 minus100381610038161003816100381611987811

(119904 = 119895120573)1003816100381610038161003816

2 (12)

4 International Journal of Antennas and Propagation

yielding to the following

11987821

(119904) =

prod119873

119899=1(119904 minus 119896

119899)

prod119873

119899=1(119904 minus 119901

119899)

(13)

being 119896119899the zeros and 119901

119899the poles of 119878

21(119904) whereR119890119896

119899 lt

0 (all the zeros are in the left-half 119904 plane because 11987821

(119904) isa minimum-phase function) and R119890119901

119899 lt 0 (all the poles

must be in the left-half 119904 plane to be a stable system)Appling the Laplace transform to (9) the coupling coef-

ficient can be calculated as follows [21]

119870 (119911) = minus2 sdot lim119904rarrminusinfin

(119890119904sdot119911

sdot 119904 sdot 1198862

(119911 119904)) (14)

By inspecting (14) it can be seen that the couplingcoefficient 119870(119911) necessary to implement a given frequencyresponse can be calculated analytically by obtaining first ananalytical solution for 119886

2(119911 119904) To do it we need to assume

that the 119873 poles of 11987811

(119904) and 11987821

(119904) 1199011 1199012 119901

119873 are

distinct that the 119873 zeros of 11987821

(119904) 1198961 1198962 119896

119873 are distinct

and that the119872 zeros of 11987811

(119904) 1198881 1198882 119888

119872 are different from

the conjugated poles with opposite sign minus119901lowast

1 minus119901lowast

2 minus119901

lowast

119873

Then 1198861(119911 119904) and 119886

2(119911 119904) can be expressed as a linear

combination of entire functions [21] and thus the soughtanalytical closed-form expression for the coupling coefficient119870(119911) of the microwave structure that satisfies the targetfrequency response is obtained [21]

119870 (119911) = 2 sdot

119873

sum

119899=1

1198892119899

(119911) sdot 119890119896119899sdot119911

minus 119889lowast

1119899(119911) sdot 119890

minus119896lowast

119899sdot119911

sdot 11987811

(minus119896lowast

119899)

(15)

where 1198891119899

(119911) and 1198892119899

(119911) are the solutions of the followinglinear system of 2 sdot 119873 equations [21]

119873

sum

119899=1

1

11987811

(119896119899)

sdot

119890minus119896119899sdot119911

119901119894minus 119896119899

sdot [

1198891119899

(119911)

1198892119899

(119911)] minus

119890119896lowast

119899sdot119911

119901119894+ 119896lowast

119899

sdot [

119889lowast

2119899(119911)

119889lowast

1119899(119911)

]

= [

0

1]

(16)

4 Applications of the Synthesis Techniques

Several devices have been designed following the above-mentioned synthesis methods in different technologiesTheyare classified by their intended application

41 Harmonic Control in Amplifier Applications To checkthe efficiency of an amplifier it is necessary to detect verytiny frequency spurious harmonics usually masked by thefundamental carrier power By using Section 31 a two-portspurious-free notch-filter can be designed [8] see Figures 1and 2

42 Directional Coupler with Enhanced Directivity and Cou-pling Manymicrowave systems demanddirectional couplerswith high directivity and coupling A fully planar device

Figure 1 Photograph of the fabricated prototype in microstriptechnology top view of the metallic strip and bottom view of theunaltered ground plane

0 2 4 6 8 10 12

0

Frequency (GHz)

minus5

minus10

minus15

minus20

minus25

minus30

|S11||S21|

(dB)

Figure 2 Measured |11987821

| (black line) and |11987811

| (grey line) parameterof the designed two-port EBG microstrip structure in Figure 1

1 2

43

Figure 3 Photograph of the fabricated EBG microstrip directionalcoupler with high directivity and coupling The ground plane isunaltered

where coupling level and frequency can be obtained followingthe method Section 31 for a four-port structure [23] seeFigures 3 and 4

43 Transmission-Type Dispersive Delay Lines for Phase-Engineering Application Phase engineering in microwaveshas drawn very much attention in the last years [24] Itis devoted to the development of analog signal processingsystems in the microwave frequency range with fundamentalbuilding blocks such as Dispersive Delay Lines of differentkinds Following the ideas of chirping and windowing inSection 32 a new transmission-type dispersive delay line canbe proposedwith closed formulas for the dispersion slope andbandwidth of operation [25] see Figures 5 6 7 and 8

International Journal of Antennas and Propagation 5

8 9 10 11 12

0

20

40

60

Frequency (GHz)

Dire

ctiv

ity an

d co

uplin

g (d

B)

minus20

Figure 4 Measured directivity (black line) and coupling (grey line)of the designed EBG microstrip directional coupler in Figure 3

Input

Output

1 2

43

Figure 5 Photograph of the fabricated prototype of transmission-type dispersive delay line indicating the input and output ports Azoom-in is included to show a detail of the deviceThe ground planeis unaltered

0 2 4 6 8 10 12Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

|S11||S31|

(dB)

Figure 6 Simulations (thin line) and measurements (thick line) of|11987811

| (grey line) and |11987831

| (black line) in the dispersive delay line ofFigure 5

44 Compact Design of High-Power Spurious-Free Low-Pass Waveguide Filters for Satellite Payloads High-powerspurious-free low-pass rectangular waveguide filters are keycomponents at the output of a satellite Output Multiplexer(OMUX) [26] As stated in Section 32 if the amplitudeof the sinusoidal coupling coefficient is high enough each

0 2 4 6 8 10 120

1

2

3

4

Frequency (GHz)

Gro

up d

elay

ofS

31

(ns)

Figure 7 Simulation (thin line) and measurement (thick line) ofthe group delay of the 119878

31parameter in the dispersive delay line of

Figure 5

0 2 4 6 8 10 12Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

|S21||S41|

(dB)

Figure 8 Simulations (thin line) and measurements (thick line) of|11987821

| (grey line) and |11987841

| (black line) in the dispersive delay line ofFigure 5

corrugation behaves like an individual bandstop elementwhose height is around 120582

1198924 being 120582

119892the guide wavelength

of the fundamental TE10mode at the frequency to be rejected

[11] see Figure 9The resulting device for a passband between 107GHz

and 127 GHz with return losses around 20 dB and a 60 dBrejection level for frequencies over 1375GHz and up to thethird harmonic (around 40GHz) has been manufactured incopper by electroforming The photograph of the fabricatedprototype is given in Figure 10(a) and in Figure 10(b) weshow the simulations using CSTMicrowave Studio (grey line)and the measurements (black line) that have been performedby means of an Agilent 8722 Vector Network Analyzerproper waveguide-to-coaxial transitions and Maury 7005Ecalibration kits

6 International Journal of Antennas and Propagation

l

h

L

zgmin0

A B C

(a)

Interpolatingfunction

hmin

hmax

z0

A B C

gmin 2

(b)

z0

A B C

(c)

Windowingfunction

Windowingfunction

z0

(d)

Figure 9 Schematics showing the design process of novel high-power spurious-free low-pass waveguide filters (a) sketch showing the finalfilter profile and its physical parameters (b) shaping of section 119861 (119892min ℎmin and ℎmax) (c) new bandstop elements added to define sections119860 and 119862 and (d) windowing applied to sections 119860 and 119862

45 Pulse Shapers for Advanced UWB Radar and Communi-cations and for Novel Breast Cancer Detection Systems Anewstrategy for generating customized pulse shapes intendedfor use in wideband applications has been proposed anddemonstrated [27] The strategy employs the exact analyticalseries solution proposed in Section 33 [19] Time-domainmeasurements are performed demonstrating the generationof two pulse shapes using microstrip technology The firstone satisfies the preestablished UWB mask requirements foradvanced radar and ultrafast communication systems [28]see Figures 11 12 and 13 The second one improves a time-domain microwave breast imaging system [29] see Figures14 and 15

46 Transmission-Type Nth-Order Differentiators for TunablePulse Generation 119873th-order differentiators are very promis-ing devices for temporal analog processing and for the designof advanced tunable pulse generators [30] Their generalmathematical expression is

119873(119891) = (2120587 sdot 119895 sdot 119891)

119873 where 119895 =

radicminus1 Here a 4th-order differentiator has been designed for

a frequency range from 31 to 74GHz which gives a goodtradeoff between energy efficiency andmaximum bandwidthfor UWB signals 119867

4(119891)

Following the synthesis procedure detailed in Section 33the required coupling coefficient 119870(119911) is calculated for thetarget frequency response 119867

4(119891) using (10) The device

will be implemented in coupled lines to work effectively intransmission and therefore the even and odd characteristicimpedance 119885

0119890(119911) and 119885

0119900(119911) need to be separated and

windowed to keep the ports matched Since microstriptechnology will be used to implement the resulting devicethe even and oddmodes will propagate at different velocitiesmaking the necessary to apply a compensation algorithm[30]

The resulting characteristic impedances together withthe photograph of the fabricated prototype are shown inFigure 16 Figure 17 shows a very good agreement betweenthe simulation using Agilent ADS Momentum (grey dottedline) and measurement results for the magnitude and phaseof the 119878

31(119891) parameter (grey solid line) compared with

International Journal of Antennas and Propagation 7

(a)

10 15 20 25 30 35 40

0

Frequency (GHz)

minus20

minus40

minus60

minus80

minus100

|S11||S21|

(dB)

(b)

Figure 10 (a) Photograph of the fabricated prototype and (b)simulations (grey line) and measurements (black line) of the novelcompact highpower spurious-free low-pass waveguide filter |119878

11| in

dashed line and |11987821

| in solid line Frequency specifications for |11987811

|

and |11987821

| are also given in dotted line

Figure 11 Photograph of a microstrip pulse shaper for UWB radarand communication systems

0 02 04 06 08

0

05

1

Pulse

1

(au

)

minus05

minus1

Time t (ns)

Figure 12 Performance of the pulse shaper for UWB radar andcommunications Sinusoidal waveform windowed by a squaredcosine the target pulse (thin line) and themeasurement (thick line)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

|Pul

se1|

(dB)

(a)

0 2 4 6 8 10 12

0

200

Frequency (GHz)

minus200

minus400

minus600

Phas

e of p

ulse

1(∘)

(b)

Figure 13 Spectrum (a)magnitude and (b) phase of the target signal(thin line) and Fourier-transformed measurement (thick line) ofthe pulse generated in the pulse shaper intended for UWB radarcommunications The FCC UWBmask is also shown in grey

the target specifications for the 4th-order differentiator (blackdashed line) Moreover the |119878

11| parameter (not shown)

is below minus20 dB in the entire frequency range of interestensuring a good matching at the input port

47 Robust Filter Design Tool A Cauer Filter Example Thesynthesis technique presented in Section 34 is incorporatedin an exact robust filter design tool The method is validatedwith an example in rectangular waveguide technology withWR-90 standard portsThe specifications are passbands from8GHz to 114GHz and from 189GHz up to 225GHz withreturn losses better than 20 dB and a rejected band from13GHz to 163 GHz with a rejection level higher than 60 dBA bandpass frequency response following a Cauer (Elliptic)approximation [21 31] will be used for the 119878

11parameter (a

bandstop frequency response will result for the 11987821

parame-ter)The order necessary for the approximationwill be 14 and

8 International Journal of Antennas and Propagation

(a) (b)

Figure 14 Two photographs of the heterogeneous breast phantoms (a) exterior view of the realistically shaped breast phantom and (b)coronal view of the 2mm skin layer and the conical gland structures embedded inside the phantom

minus80

minus60

minus40

minus20

0

20

40

60

80

minus50 0 50y (mm)

z(m

m)

Figure 15 A coronal slice of the reconstructed 3D image of therealistically shaped adipose breast phantomusing the designed pulseshaperThe dark red indicates higher intensity values correspondingto stronger EM scatterersThe ldquolowastrdquo denotes the global maximum andthe ldquoordquo represents the approximate tumour location based on theinsertion of the tumour into the breast phantom

the passband will extend from 131 GHz up to 162GHz witha passband ripple of 10

minus9 dB and a rejected band rippleof 25 dB From the magnitude of the 119878

11parameter the

magnitude of the 11987821

can be immediately obtained by using(12) and a bandstop frequency response results for the 119878

21

parameter with a rejected band attenuation of 67 dBFollowing the expressions in Section 34 a prototype is

designed and fabricated see Figure 18 As it can be seenin Figure 19 the target simulated using CST MicrowaveStudio and measured frequency responses are in a very goodagreement satisfying the frequency requirements mentionedabove and confirming the accuracy and flexibility of thesynthesis method proposed

0 2 4 6 8 10 12 14 1630

40

50

60

70

80

Z0eZ

0o(Ω

)

Propagation direction z (cm)

(a)

1 2

43

(b)

Figure 16 (a) Even (black line) and odd (grey line) characteristicimpedance of the 4th-order differentiator after the compensationprocess and (b) the corresponding photograph of the prototype inmicrostrip technology for the given characteristic impedance

5 Conclusion

Newdevices inmicrostrip technology rectangular waveguidetechnology and microstrip coupled line technology havebeen successfully designed easily fabricated and accuratelytested for very different applications A palate of InverseScattering microwave synthesis methods have been surveyedalong the paper highlighting their advantages and disad-vantages and confirming that all the techniques togetherrepresent a powerful tool for the design of passive microwavecomponents for the new emerging applications in the wire-less radar biomedical engineering and satellite worlds

International Journal of Antennas and Propagation 9

0 2 4 6 8 10 12

0

Frequency (GHz)

|H4|

and|S31|

(dB)

minus10

minus20

minus30

minus40

minus50

(a)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus1000

minus2000

minus3000

minus4000

minus5000

Phas

e ofH

4an

dS 3

1(∘)

(b)

Figure 17 Target (black dashed line) simulated (dark grey dotted line) and measured (light grey solid line) magnitude (a) and phase (b) ofthe frequency response of the 4th-order differentiator

Figure 18 Photograph of the fabricated filter prototype in rectan-gular waveguide technology Standard WR-90 ports are used

82 10 12 14 16 18 20 22

0

Frequency (GHz)

|S11||S21|

(dB)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Figure 19Magnitude of the 11987811-parameter (grey line) and of the 119878

21-

parameter (black line) for the final synthesized filter in waveguidetechnology in Figure 18 The target (thin solid line) simulated(dotted line) and measured (thick solid line) frequency responsesare given

Acknowledgments

This work has been supported by the Spanish Ministerio deCiencia e Innovacion through the Project TEC2011-28664-C02-01 Magdalena Chudzik would like also to acknowledgeSpanish Ministerio de Educacion for its FPU Grant

References

[1] D C Youla ldquoAnalysis and synthesis of arbitrarily terminatedlossless nonuniform linesrdquo IEEE Transactions on CircuitTheoryvol CT-11 pp 363ndash372 1964

[2] R W Klopfenstein ldquoA transmission-line taper of improveddesignrdquo Proceedings of the IRE vol 44 pp 31ndash35 1956

[3] M D Abouzahra and L Lewin ldquoRadiation from microstripdiscontinuitiesrdquo IEEE Transactions on Microwave Theory andTechniques vol MTT-27 no 8 pp 722ndash723 1979

[4] I Arregui I Arnedo T Lopetegi M A G Laso and AMarcotegui ldquoLow-pass filter for electromagnetic signalsrdquo U SPatent 20100308938 European Patent 2 244 330 January 212008

[5] C Elachi ldquoWaves in active and passive periodic structures areviewrdquo Proceedings of the IEEE vol 64 no 12 pp 1666ndash16981976

[6] Y Qian V Radisic and T Itoh ldquoSimulation and experiment ofphotonic band-gap structures for microstrip circuitsrdquo in Pro-ceedings of the 1997 Asia-Pacific Microwave Conference (APMCrsquo97) pp 585ndash588 Hong Kong December 1997

[7] F Yang R Coccioll Y Qian and T Itoh ldquoPlanar peg structuresbasic properties and applicationsrdquo IEICE Transactions on Elec-tronics vol E83-C no 5 pp 687ndash696 2000

[8] I ArnedoM Chudzik J D Schwartz et al ldquoAnalytical solutionfor the design of planar electromagnetic bandgap structureswith spurious-free frequency responserdquoMicrowave and OpticalTechnology Letters vol 54 no 4 pp 956ndash960 2012

[9] T Lopetegi M A G Laso R Gonzalo et al ldquoElectromagneticcrystals in microstrip technologyrdquo Optical and Quantum Elec-tronics vol 34 no 1ndash3 pp 279ndash295 2002

[10] M A G Laso T Lopetegi M J Erro et al ldquoReal-time spec-trum analysis in microstrip technologyrdquo IEEE Transactions onMicrowave Theory and Techniques vol 51 no 3 pp 705ndash7172003

[11] I Arregui I Arnedo A Lujambio et al ldquoA compact designof high-power spurious-free low-pass waveguide filterrdquo IEEE

10 International Journal of Antennas and Propagation

Microwave and Wireless Components Letters vol 20 no 11 pp595ndash597 2010

[12] E F Bolinder ldquoThe relationship of physical applications offourier transforms in various fields of wave theory and cir-cuitryrdquo IEEE Transactions onMicrowaveTheory and Techniquespp 153ndash158 1957

[13] B Z Katsenelenbaum L Mercader M Pereyaslavets MSorolla and M Thumm Theory of Nonuniform WaveguidesThe Cross-Section Method vol 44 of IEE Electromagnetic WavesSeries IET London UK 1998

[14] F Sporleder andHGUngerWaveguide Tapers Transitions andCouplers Peter Peregrinus London UK 1979

[15] I Arnedo J Gil N Ortiz et al ldquoKu-band high-power lowpassfilter with spurious rejectionrdquo Electronics Letters vol 42 no 25pp 1460ndash1461 2006

[16] I Arregui I Arnedo A Lujambio et al ldquoDesign method forsatellite output multiplexer low-pass filters exhibiting spurious-free frequency behavior and high-power operationrdquoMicrowaveand Optical Technology Letters vol 52 no 8 pp 1724ndash17282010

[17] J D Schwartz I Arnedo M A G Laso T Lopetegi J Azanaand D Plant ldquoAn electronic UWB continuously tunable time-delay system with nanosecond delaysrdquo IEEE Microwave andWireless Components Letters vol 18 no 2 pp 103ndash105 2008

[18] I Arregui F Teberio I Arnedo et al ldquoHigh-power low-passharmonic waveguide filter with TEn0-mode suppressionrdquo IEEEMicrowave and Wireless Components Letters vol 22 no 7 pp339ndash341 2012

[19] I Arnedo M A G Laso F Falcone D Benito and T LopetegildquoA series solution for the single-mode synthesis problem basedon the coupled-mode theoryrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 56 no 2 pp 457ndash466 2008

[20] M Chudzik I Arnedo I Arregui et al ldquoNovel synthesis tech-nique for microwave circuits based on inverse scattering effi-cient algorithm implementation and applicationrdquo InternationalJournal of RF and Microwave Computer-Aided Engineering vol21 no 2 pp 164ndash173 2011

[21] I Arnedo I Arregui A Lujambio M Chudzik M A GLaso and T Lopetegi ldquoSynthesis of microwave filters by inversescattering using a closed-form expression valid for rationalfrequency responsesrdquo IEEE Transactions on Microwave Theoryand Techniques vol 60 no 5 pp 1244ndash1257 2012

[22] M J Erro I Arnedo M A G Laso T Lopetegi and MA Muriel ldquoPhase-reconstruction in photonic crystals from S-parameter magnitude in microstrip technologyrdquo Optical andQuantum Electronics vol 39 no 4ndash6 pp 321ndash331 2007

[23] M Chudzik I Arnedo A Lujambio et al ldquoMicrostrip coupled-line directional coupler with enhanced coupling based on EBGconceptrdquo Electronics Letters vol 47 no 23 pp 1284ndash1286 2011

[24] C Caloz ldquoMetamaterial dispersion engineering concepts andapplicationsrdquo Proceedings of the IEEE vol 99 no 10 pp 1711ndash1719 2011

[25] A Lujambio I Arnedo M Chudzik I Arregui T Lopetegiand M A G Laso ldquoDispersive delay line with effectivetransmission-type operation in coupled-line technologyrdquo IEEEMicrowave and Wireless Components Letters vol 21 no 9 pp459ndash461 2011

[26] P Fortescue and J Stark Spacecraft Systems Engineering WileyChichester UK 1995

[27] Part 15 Rules for Unlicensed RF Devices Federal Communica-tions Commission (FCC) September 2007 httpwwwfccgovoetinforules

[28] I Amedo J D Schwartz M A G Laso T Lopetegi D V Plantand J Azana ldquoPassive microwave planar circuits for arbitraryUWBpulse shapingrdquo IEEEMicrowave andWireless ComponentsLetters vol 18 no 7 pp 452ndash454 2008

[29] A Santorelli M Chudzik E Kirshin et al ldquoExperimentaldemonstration of pulse shaping for time-domain microwavebrest imagingrdquo Progress in Electromagnetics Research vol 133pp 309ndash329 2013

[30] M Chudzik I Arnedo A Lujambio et al ldquoDesign of trans-mission-type Nth-order differentiators in planar microwavetechnologyrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 60 no 11 pp 3384ndash3394 2012

[31] I Arnedo A Lujambio T Lopetegi andM A G Laso ldquoDesignof microwave filters with arbitrary frequency response basedon digital methodsrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 634ndash636 2007

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Chemical EngineeringInternational Journal of Antennas and

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International Journal of

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DistributedSensor Networks

International Journal of

Page 4: Review Article Passive Microwave Component Design Using ...downloads.hindawi.com/journals/ijap/2013/761278.pdf · InternationalJournal of Antennas and Propagation a generic frequency

4 International Journal of Antennas and Propagation

yielding to the following

11987821

(119904) =

prod119873

119899=1(119904 minus 119896

119899)

prod119873

119899=1(119904 minus 119901

119899)

(13)

being 119896119899the zeros and 119901

119899the poles of 119878

21(119904) whereR119890119896

119899 lt

0 (all the zeros are in the left-half 119904 plane because 11987821

(119904) isa minimum-phase function) and R119890119901

119899 lt 0 (all the poles

must be in the left-half 119904 plane to be a stable system)Appling the Laplace transform to (9) the coupling coef-

ficient can be calculated as follows [21]

119870 (119911) = minus2 sdot lim119904rarrminusinfin

(119890119904sdot119911

sdot 119904 sdot 1198862

(119911 119904)) (14)

By inspecting (14) it can be seen that the couplingcoefficient 119870(119911) necessary to implement a given frequencyresponse can be calculated analytically by obtaining first ananalytical solution for 119886

2(119911 119904) To do it we need to assume

that the 119873 poles of 11987811

(119904) and 11987821

(119904) 1199011 1199012 119901

119873 are

distinct that the 119873 zeros of 11987821

(119904) 1198961 1198962 119896

119873 are distinct

and that the119872 zeros of 11987811

(119904) 1198881 1198882 119888

119872 are different from

the conjugated poles with opposite sign minus119901lowast

1 minus119901lowast

2 minus119901

lowast

119873

Then 1198861(119911 119904) and 119886

2(119911 119904) can be expressed as a linear

combination of entire functions [21] and thus the soughtanalytical closed-form expression for the coupling coefficient119870(119911) of the microwave structure that satisfies the targetfrequency response is obtained [21]

119870 (119911) = 2 sdot

119873

sum

119899=1

1198892119899

(119911) sdot 119890119896119899sdot119911

minus 119889lowast

1119899(119911) sdot 119890

minus119896lowast

119899sdot119911

sdot 11987811

(minus119896lowast

119899)

(15)

where 1198891119899

(119911) and 1198892119899

(119911) are the solutions of the followinglinear system of 2 sdot 119873 equations [21]

119873

sum

119899=1

1

11987811

(119896119899)

sdot

119890minus119896119899sdot119911

119901119894minus 119896119899

sdot [

1198891119899

(119911)

1198892119899

(119911)] minus

119890119896lowast

119899sdot119911

119901119894+ 119896lowast

119899

sdot [

119889lowast

2119899(119911)

119889lowast

1119899(119911)

]

= [

0

1]

(16)

4 Applications of the Synthesis Techniques

Several devices have been designed following the above-mentioned synthesis methods in different technologiesTheyare classified by their intended application

41 Harmonic Control in Amplifier Applications To checkthe efficiency of an amplifier it is necessary to detect verytiny frequency spurious harmonics usually masked by thefundamental carrier power By using Section 31 a two-portspurious-free notch-filter can be designed [8] see Figures 1and 2

42 Directional Coupler with Enhanced Directivity and Cou-pling Manymicrowave systems demanddirectional couplerswith high directivity and coupling A fully planar device

Figure 1 Photograph of the fabricated prototype in microstriptechnology top view of the metallic strip and bottom view of theunaltered ground plane

0 2 4 6 8 10 12

0

Frequency (GHz)

minus5

minus10

minus15

minus20

minus25

minus30

|S11||S21|

(dB)

Figure 2 Measured |11987821

| (black line) and |11987811

| (grey line) parameterof the designed two-port EBG microstrip structure in Figure 1

1 2

43

Figure 3 Photograph of the fabricated EBG microstrip directionalcoupler with high directivity and coupling The ground plane isunaltered

where coupling level and frequency can be obtained followingthe method Section 31 for a four-port structure [23] seeFigures 3 and 4

43 Transmission-Type Dispersive Delay Lines for Phase-Engineering Application Phase engineering in microwaveshas drawn very much attention in the last years [24] Itis devoted to the development of analog signal processingsystems in the microwave frequency range with fundamentalbuilding blocks such as Dispersive Delay Lines of differentkinds Following the ideas of chirping and windowing inSection 32 a new transmission-type dispersive delay line canbe proposedwith closed formulas for the dispersion slope andbandwidth of operation [25] see Figures 5 6 7 and 8

International Journal of Antennas and Propagation 5

8 9 10 11 12

0

20

40

60

Frequency (GHz)

Dire

ctiv

ity an

d co

uplin

g (d

B)

minus20

Figure 4 Measured directivity (black line) and coupling (grey line)of the designed EBG microstrip directional coupler in Figure 3

Input

Output

1 2

43

Figure 5 Photograph of the fabricated prototype of transmission-type dispersive delay line indicating the input and output ports Azoom-in is included to show a detail of the deviceThe ground planeis unaltered

0 2 4 6 8 10 12Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

|S11||S31|

(dB)

Figure 6 Simulations (thin line) and measurements (thick line) of|11987811

| (grey line) and |11987831

| (black line) in the dispersive delay line ofFigure 5

44 Compact Design of High-Power Spurious-Free Low-Pass Waveguide Filters for Satellite Payloads High-powerspurious-free low-pass rectangular waveguide filters are keycomponents at the output of a satellite Output Multiplexer(OMUX) [26] As stated in Section 32 if the amplitudeof the sinusoidal coupling coefficient is high enough each

0 2 4 6 8 10 120

1

2

3

4

Frequency (GHz)

Gro

up d

elay

ofS

31

(ns)

Figure 7 Simulation (thin line) and measurement (thick line) ofthe group delay of the 119878

31parameter in the dispersive delay line of

Figure 5

0 2 4 6 8 10 12Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

|S21||S41|

(dB)

Figure 8 Simulations (thin line) and measurements (thick line) of|11987821

| (grey line) and |11987841

| (black line) in the dispersive delay line ofFigure 5

corrugation behaves like an individual bandstop elementwhose height is around 120582

1198924 being 120582

119892the guide wavelength

of the fundamental TE10mode at the frequency to be rejected

[11] see Figure 9The resulting device for a passband between 107GHz

and 127 GHz with return losses around 20 dB and a 60 dBrejection level for frequencies over 1375GHz and up to thethird harmonic (around 40GHz) has been manufactured incopper by electroforming The photograph of the fabricatedprototype is given in Figure 10(a) and in Figure 10(b) weshow the simulations using CSTMicrowave Studio (grey line)and the measurements (black line) that have been performedby means of an Agilent 8722 Vector Network Analyzerproper waveguide-to-coaxial transitions and Maury 7005Ecalibration kits

6 International Journal of Antennas and Propagation

l

h

L

zgmin0

A B C

(a)

Interpolatingfunction

hmin

hmax

z0

A B C

gmin 2

(b)

z0

A B C

(c)

Windowingfunction

Windowingfunction

z0

(d)

Figure 9 Schematics showing the design process of novel high-power spurious-free low-pass waveguide filters (a) sketch showing the finalfilter profile and its physical parameters (b) shaping of section 119861 (119892min ℎmin and ℎmax) (c) new bandstop elements added to define sections119860 and 119862 and (d) windowing applied to sections 119860 and 119862

45 Pulse Shapers for Advanced UWB Radar and Communi-cations and for Novel Breast Cancer Detection Systems Anewstrategy for generating customized pulse shapes intendedfor use in wideband applications has been proposed anddemonstrated [27] The strategy employs the exact analyticalseries solution proposed in Section 33 [19] Time-domainmeasurements are performed demonstrating the generationof two pulse shapes using microstrip technology The firstone satisfies the preestablished UWB mask requirements foradvanced radar and ultrafast communication systems [28]see Figures 11 12 and 13 The second one improves a time-domain microwave breast imaging system [29] see Figures14 and 15

46 Transmission-Type Nth-Order Differentiators for TunablePulse Generation 119873th-order differentiators are very promis-ing devices for temporal analog processing and for the designof advanced tunable pulse generators [30] Their generalmathematical expression is

119873(119891) = (2120587 sdot 119895 sdot 119891)

119873 where 119895 =

radicminus1 Here a 4th-order differentiator has been designed for

a frequency range from 31 to 74GHz which gives a goodtradeoff between energy efficiency andmaximum bandwidthfor UWB signals 119867

4(119891)

Following the synthesis procedure detailed in Section 33the required coupling coefficient 119870(119911) is calculated for thetarget frequency response 119867

4(119891) using (10) The device

will be implemented in coupled lines to work effectively intransmission and therefore the even and odd characteristicimpedance 119885

0119890(119911) and 119885

0119900(119911) need to be separated and

windowed to keep the ports matched Since microstriptechnology will be used to implement the resulting devicethe even and oddmodes will propagate at different velocitiesmaking the necessary to apply a compensation algorithm[30]

The resulting characteristic impedances together withthe photograph of the fabricated prototype are shown inFigure 16 Figure 17 shows a very good agreement betweenthe simulation using Agilent ADS Momentum (grey dottedline) and measurement results for the magnitude and phaseof the 119878

31(119891) parameter (grey solid line) compared with

International Journal of Antennas and Propagation 7

(a)

10 15 20 25 30 35 40

0

Frequency (GHz)

minus20

minus40

minus60

minus80

minus100

|S11||S21|

(dB)

(b)

Figure 10 (a) Photograph of the fabricated prototype and (b)simulations (grey line) and measurements (black line) of the novelcompact highpower spurious-free low-pass waveguide filter |119878

11| in

dashed line and |11987821

| in solid line Frequency specifications for |11987811

|

and |11987821

| are also given in dotted line

Figure 11 Photograph of a microstrip pulse shaper for UWB radarand communication systems

0 02 04 06 08

0

05

1

Pulse

1

(au

)

minus05

minus1

Time t (ns)

Figure 12 Performance of the pulse shaper for UWB radar andcommunications Sinusoidal waveform windowed by a squaredcosine the target pulse (thin line) and themeasurement (thick line)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

|Pul

se1|

(dB)

(a)

0 2 4 6 8 10 12

0

200

Frequency (GHz)

minus200

minus400

minus600

Phas

e of p

ulse

1(∘)

(b)

Figure 13 Spectrum (a)magnitude and (b) phase of the target signal(thin line) and Fourier-transformed measurement (thick line) ofthe pulse generated in the pulse shaper intended for UWB radarcommunications The FCC UWBmask is also shown in grey

the target specifications for the 4th-order differentiator (blackdashed line) Moreover the |119878

11| parameter (not shown)

is below minus20 dB in the entire frequency range of interestensuring a good matching at the input port

47 Robust Filter Design Tool A Cauer Filter Example Thesynthesis technique presented in Section 34 is incorporatedin an exact robust filter design tool The method is validatedwith an example in rectangular waveguide technology withWR-90 standard portsThe specifications are passbands from8GHz to 114GHz and from 189GHz up to 225GHz withreturn losses better than 20 dB and a rejected band from13GHz to 163 GHz with a rejection level higher than 60 dBA bandpass frequency response following a Cauer (Elliptic)approximation [21 31] will be used for the 119878

11parameter (a

bandstop frequency response will result for the 11987821

parame-ter)The order necessary for the approximationwill be 14 and

8 International Journal of Antennas and Propagation

(a) (b)

Figure 14 Two photographs of the heterogeneous breast phantoms (a) exterior view of the realistically shaped breast phantom and (b)coronal view of the 2mm skin layer and the conical gland structures embedded inside the phantom

minus80

minus60

minus40

minus20

0

20

40

60

80

minus50 0 50y (mm)

z(m

m)

Figure 15 A coronal slice of the reconstructed 3D image of therealistically shaped adipose breast phantomusing the designed pulseshaperThe dark red indicates higher intensity values correspondingto stronger EM scatterersThe ldquolowastrdquo denotes the global maximum andthe ldquoordquo represents the approximate tumour location based on theinsertion of the tumour into the breast phantom

the passband will extend from 131 GHz up to 162GHz witha passband ripple of 10

minus9 dB and a rejected band rippleof 25 dB From the magnitude of the 119878

11parameter the

magnitude of the 11987821

can be immediately obtained by using(12) and a bandstop frequency response results for the 119878

21

parameter with a rejected band attenuation of 67 dBFollowing the expressions in Section 34 a prototype is

designed and fabricated see Figure 18 As it can be seenin Figure 19 the target simulated using CST MicrowaveStudio and measured frequency responses are in a very goodagreement satisfying the frequency requirements mentionedabove and confirming the accuracy and flexibility of thesynthesis method proposed

0 2 4 6 8 10 12 14 1630

40

50

60

70

80

Z0eZ

0o(Ω

)

Propagation direction z (cm)

(a)

1 2

43

(b)

Figure 16 (a) Even (black line) and odd (grey line) characteristicimpedance of the 4th-order differentiator after the compensationprocess and (b) the corresponding photograph of the prototype inmicrostrip technology for the given characteristic impedance

5 Conclusion

Newdevices inmicrostrip technology rectangular waveguidetechnology and microstrip coupled line technology havebeen successfully designed easily fabricated and accuratelytested for very different applications A palate of InverseScattering microwave synthesis methods have been surveyedalong the paper highlighting their advantages and disad-vantages and confirming that all the techniques togetherrepresent a powerful tool for the design of passive microwavecomponents for the new emerging applications in the wire-less radar biomedical engineering and satellite worlds

International Journal of Antennas and Propagation 9

0 2 4 6 8 10 12

0

Frequency (GHz)

|H4|

and|S31|

(dB)

minus10

minus20

minus30

minus40

minus50

(a)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus1000

minus2000

minus3000

minus4000

minus5000

Phas

e ofH

4an

dS 3

1(∘)

(b)

Figure 17 Target (black dashed line) simulated (dark grey dotted line) and measured (light grey solid line) magnitude (a) and phase (b) ofthe frequency response of the 4th-order differentiator

Figure 18 Photograph of the fabricated filter prototype in rectan-gular waveguide technology Standard WR-90 ports are used

82 10 12 14 16 18 20 22

0

Frequency (GHz)

|S11||S21|

(dB)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Figure 19Magnitude of the 11987811-parameter (grey line) and of the 119878

21-

parameter (black line) for the final synthesized filter in waveguidetechnology in Figure 18 The target (thin solid line) simulated(dotted line) and measured (thick solid line) frequency responsesare given

Acknowledgments

This work has been supported by the Spanish Ministerio deCiencia e Innovacion through the Project TEC2011-28664-C02-01 Magdalena Chudzik would like also to acknowledgeSpanish Ministerio de Educacion for its FPU Grant

References

[1] D C Youla ldquoAnalysis and synthesis of arbitrarily terminatedlossless nonuniform linesrdquo IEEE Transactions on CircuitTheoryvol CT-11 pp 363ndash372 1964

[2] R W Klopfenstein ldquoA transmission-line taper of improveddesignrdquo Proceedings of the IRE vol 44 pp 31ndash35 1956

[3] M D Abouzahra and L Lewin ldquoRadiation from microstripdiscontinuitiesrdquo IEEE Transactions on Microwave Theory andTechniques vol MTT-27 no 8 pp 722ndash723 1979

[4] I Arregui I Arnedo T Lopetegi M A G Laso and AMarcotegui ldquoLow-pass filter for electromagnetic signalsrdquo U SPatent 20100308938 European Patent 2 244 330 January 212008

[5] C Elachi ldquoWaves in active and passive periodic structures areviewrdquo Proceedings of the IEEE vol 64 no 12 pp 1666ndash16981976

[6] Y Qian V Radisic and T Itoh ldquoSimulation and experiment ofphotonic band-gap structures for microstrip circuitsrdquo in Pro-ceedings of the 1997 Asia-Pacific Microwave Conference (APMCrsquo97) pp 585ndash588 Hong Kong December 1997

[7] F Yang R Coccioll Y Qian and T Itoh ldquoPlanar peg structuresbasic properties and applicationsrdquo IEICE Transactions on Elec-tronics vol E83-C no 5 pp 687ndash696 2000

[8] I ArnedoM Chudzik J D Schwartz et al ldquoAnalytical solutionfor the design of planar electromagnetic bandgap structureswith spurious-free frequency responserdquoMicrowave and OpticalTechnology Letters vol 54 no 4 pp 956ndash960 2012

[9] T Lopetegi M A G Laso R Gonzalo et al ldquoElectromagneticcrystals in microstrip technologyrdquo Optical and Quantum Elec-tronics vol 34 no 1ndash3 pp 279ndash295 2002

[10] M A G Laso T Lopetegi M J Erro et al ldquoReal-time spec-trum analysis in microstrip technologyrdquo IEEE Transactions onMicrowave Theory and Techniques vol 51 no 3 pp 705ndash7172003

[11] I Arregui I Arnedo A Lujambio et al ldquoA compact designof high-power spurious-free low-pass waveguide filterrdquo IEEE

10 International Journal of Antennas and Propagation

Microwave and Wireless Components Letters vol 20 no 11 pp595ndash597 2010

[12] E F Bolinder ldquoThe relationship of physical applications offourier transforms in various fields of wave theory and cir-cuitryrdquo IEEE Transactions onMicrowaveTheory and Techniquespp 153ndash158 1957

[13] B Z Katsenelenbaum L Mercader M Pereyaslavets MSorolla and M Thumm Theory of Nonuniform WaveguidesThe Cross-Section Method vol 44 of IEE Electromagnetic WavesSeries IET London UK 1998

[14] F Sporleder andHGUngerWaveguide Tapers Transitions andCouplers Peter Peregrinus London UK 1979

[15] I Arnedo J Gil N Ortiz et al ldquoKu-band high-power lowpassfilter with spurious rejectionrdquo Electronics Letters vol 42 no 25pp 1460ndash1461 2006

[16] I Arregui I Arnedo A Lujambio et al ldquoDesign method forsatellite output multiplexer low-pass filters exhibiting spurious-free frequency behavior and high-power operationrdquoMicrowaveand Optical Technology Letters vol 52 no 8 pp 1724ndash17282010

[17] J D Schwartz I Arnedo M A G Laso T Lopetegi J Azanaand D Plant ldquoAn electronic UWB continuously tunable time-delay system with nanosecond delaysrdquo IEEE Microwave andWireless Components Letters vol 18 no 2 pp 103ndash105 2008

[18] I Arregui F Teberio I Arnedo et al ldquoHigh-power low-passharmonic waveguide filter with TEn0-mode suppressionrdquo IEEEMicrowave and Wireless Components Letters vol 22 no 7 pp339ndash341 2012

[19] I Arnedo M A G Laso F Falcone D Benito and T LopetegildquoA series solution for the single-mode synthesis problem basedon the coupled-mode theoryrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 56 no 2 pp 457ndash466 2008

[20] M Chudzik I Arnedo I Arregui et al ldquoNovel synthesis tech-nique for microwave circuits based on inverse scattering effi-cient algorithm implementation and applicationrdquo InternationalJournal of RF and Microwave Computer-Aided Engineering vol21 no 2 pp 164ndash173 2011

[21] I Arnedo I Arregui A Lujambio M Chudzik M A GLaso and T Lopetegi ldquoSynthesis of microwave filters by inversescattering using a closed-form expression valid for rationalfrequency responsesrdquo IEEE Transactions on Microwave Theoryand Techniques vol 60 no 5 pp 1244ndash1257 2012

[22] M J Erro I Arnedo M A G Laso T Lopetegi and MA Muriel ldquoPhase-reconstruction in photonic crystals from S-parameter magnitude in microstrip technologyrdquo Optical andQuantum Electronics vol 39 no 4ndash6 pp 321ndash331 2007

[23] M Chudzik I Arnedo A Lujambio et al ldquoMicrostrip coupled-line directional coupler with enhanced coupling based on EBGconceptrdquo Electronics Letters vol 47 no 23 pp 1284ndash1286 2011

[24] C Caloz ldquoMetamaterial dispersion engineering concepts andapplicationsrdquo Proceedings of the IEEE vol 99 no 10 pp 1711ndash1719 2011

[25] A Lujambio I Arnedo M Chudzik I Arregui T Lopetegiand M A G Laso ldquoDispersive delay line with effectivetransmission-type operation in coupled-line technologyrdquo IEEEMicrowave and Wireless Components Letters vol 21 no 9 pp459ndash461 2011

[26] P Fortescue and J Stark Spacecraft Systems Engineering WileyChichester UK 1995

[27] Part 15 Rules for Unlicensed RF Devices Federal Communica-tions Commission (FCC) September 2007 httpwwwfccgovoetinforules

[28] I Amedo J D Schwartz M A G Laso T Lopetegi D V Plantand J Azana ldquoPassive microwave planar circuits for arbitraryUWBpulse shapingrdquo IEEEMicrowave andWireless ComponentsLetters vol 18 no 7 pp 452ndash454 2008

[29] A Santorelli M Chudzik E Kirshin et al ldquoExperimentaldemonstration of pulse shaping for time-domain microwavebrest imagingrdquo Progress in Electromagnetics Research vol 133pp 309ndash329 2013

[30] M Chudzik I Arnedo A Lujambio et al ldquoDesign of trans-mission-type Nth-order differentiators in planar microwavetechnologyrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 60 no 11 pp 3384ndash3394 2012

[31] I Arnedo A Lujambio T Lopetegi andM A G Laso ldquoDesignof microwave filters with arbitrary frequency response basedon digital methodsrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 634ndash636 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 5: Review Article Passive Microwave Component Design Using ...downloads.hindawi.com/journals/ijap/2013/761278.pdf · InternationalJournal of Antennas and Propagation a generic frequency

International Journal of Antennas and Propagation 5

8 9 10 11 12

0

20

40

60

Frequency (GHz)

Dire

ctiv

ity an

d co

uplin

g (d

B)

minus20

Figure 4 Measured directivity (black line) and coupling (grey line)of the designed EBG microstrip directional coupler in Figure 3

Input

Output

1 2

43

Figure 5 Photograph of the fabricated prototype of transmission-type dispersive delay line indicating the input and output ports Azoom-in is included to show a detail of the deviceThe ground planeis unaltered

0 2 4 6 8 10 12Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

|S11||S31|

(dB)

Figure 6 Simulations (thin line) and measurements (thick line) of|11987811

| (grey line) and |11987831

| (black line) in the dispersive delay line ofFigure 5

44 Compact Design of High-Power Spurious-Free Low-Pass Waveguide Filters for Satellite Payloads High-powerspurious-free low-pass rectangular waveguide filters are keycomponents at the output of a satellite Output Multiplexer(OMUX) [26] As stated in Section 32 if the amplitudeof the sinusoidal coupling coefficient is high enough each

0 2 4 6 8 10 120

1

2

3

4

Frequency (GHz)

Gro

up d

elay

ofS

31

(ns)

Figure 7 Simulation (thin line) and measurement (thick line) ofthe group delay of the 119878

31parameter in the dispersive delay line of

Figure 5

0 2 4 6 8 10 12Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

|S21||S41|

(dB)

Figure 8 Simulations (thin line) and measurements (thick line) of|11987821

| (grey line) and |11987841

| (black line) in the dispersive delay line ofFigure 5

corrugation behaves like an individual bandstop elementwhose height is around 120582

1198924 being 120582

119892the guide wavelength

of the fundamental TE10mode at the frequency to be rejected

[11] see Figure 9The resulting device for a passband between 107GHz

and 127 GHz with return losses around 20 dB and a 60 dBrejection level for frequencies over 1375GHz and up to thethird harmonic (around 40GHz) has been manufactured incopper by electroforming The photograph of the fabricatedprototype is given in Figure 10(a) and in Figure 10(b) weshow the simulations using CSTMicrowave Studio (grey line)and the measurements (black line) that have been performedby means of an Agilent 8722 Vector Network Analyzerproper waveguide-to-coaxial transitions and Maury 7005Ecalibration kits

6 International Journal of Antennas and Propagation

l

h

L

zgmin0

A B C

(a)

Interpolatingfunction

hmin

hmax

z0

A B C

gmin 2

(b)

z0

A B C

(c)

Windowingfunction

Windowingfunction

z0

(d)

Figure 9 Schematics showing the design process of novel high-power spurious-free low-pass waveguide filters (a) sketch showing the finalfilter profile and its physical parameters (b) shaping of section 119861 (119892min ℎmin and ℎmax) (c) new bandstop elements added to define sections119860 and 119862 and (d) windowing applied to sections 119860 and 119862

45 Pulse Shapers for Advanced UWB Radar and Communi-cations and for Novel Breast Cancer Detection Systems Anewstrategy for generating customized pulse shapes intendedfor use in wideband applications has been proposed anddemonstrated [27] The strategy employs the exact analyticalseries solution proposed in Section 33 [19] Time-domainmeasurements are performed demonstrating the generationof two pulse shapes using microstrip technology The firstone satisfies the preestablished UWB mask requirements foradvanced radar and ultrafast communication systems [28]see Figures 11 12 and 13 The second one improves a time-domain microwave breast imaging system [29] see Figures14 and 15

46 Transmission-Type Nth-Order Differentiators for TunablePulse Generation 119873th-order differentiators are very promis-ing devices for temporal analog processing and for the designof advanced tunable pulse generators [30] Their generalmathematical expression is

119873(119891) = (2120587 sdot 119895 sdot 119891)

119873 where 119895 =

radicminus1 Here a 4th-order differentiator has been designed for

a frequency range from 31 to 74GHz which gives a goodtradeoff between energy efficiency andmaximum bandwidthfor UWB signals 119867

4(119891)

Following the synthesis procedure detailed in Section 33the required coupling coefficient 119870(119911) is calculated for thetarget frequency response 119867

4(119891) using (10) The device

will be implemented in coupled lines to work effectively intransmission and therefore the even and odd characteristicimpedance 119885

0119890(119911) and 119885

0119900(119911) need to be separated and

windowed to keep the ports matched Since microstriptechnology will be used to implement the resulting devicethe even and oddmodes will propagate at different velocitiesmaking the necessary to apply a compensation algorithm[30]

The resulting characteristic impedances together withthe photograph of the fabricated prototype are shown inFigure 16 Figure 17 shows a very good agreement betweenthe simulation using Agilent ADS Momentum (grey dottedline) and measurement results for the magnitude and phaseof the 119878

31(119891) parameter (grey solid line) compared with

International Journal of Antennas and Propagation 7

(a)

10 15 20 25 30 35 40

0

Frequency (GHz)

minus20

minus40

minus60

minus80

minus100

|S11||S21|

(dB)

(b)

Figure 10 (a) Photograph of the fabricated prototype and (b)simulations (grey line) and measurements (black line) of the novelcompact highpower spurious-free low-pass waveguide filter |119878

11| in

dashed line and |11987821

| in solid line Frequency specifications for |11987811

|

and |11987821

| are also given in dotted line

Figure 11 Photograph of a microstrip pulse shaper for UWB radarand communication systems

0 02 04 06 08

0

05

1

Pulse

1

(au

)

minus05

minus1

Time t (ns)

Figure 12 Performance of the pulse shaper for UWB radar andcommunications Sinusoidal waveform windowed by a squaredcosine the target pulse (thin line) and themeasurement (thick line)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

|Pul

se1|

(dB)

(a)

0 2 4 6 8 10 12

0

200

Frequency (GHz)

minus200

minus400

minus600

Phas

e of p

ulse

1(∘)

(b)

Figure 13 Spectrum (a)magnitude and (b) phase of the target signal(thin line) and Fourier-transformed measurement (thick line) ofthe pulse generated in the pulse shaper intended for UWB radarcommunications The FCC UWBmask is also shown in grey

the target specifications for the 4th-order differentiator (blackdashed line) Moreover the |119878

11| parameter (not shown)

is below minus20 dB in the entire frequency range of interestensuring a good matching at the input port

47 Robust Filter Design Tool A Cauer Filter Example Thesynthesis technique presented in Section 34 is incorporatedin an exact robust filter design tool The method is validatedwith an example in rectangular waveguide technology withWR-90 standard portsThe specifications are passbands from8GHz to 114GHz and from 189GHz up to 225GHz withreturn losses better than 20 dB and a rejected band from13GHz to 163 GHz with a rejection level higher than 60 dBA bandpass frequency response following a Cauer (Elliptic)approximation [21 31] will be used for the 119878

11parameter (a

bandstop frequency response will result for the 11987821

parame-ter)The order necessary for the approximationwill be 14 and

8 International Journal of Antennas and Propagation

(a) (b)

Figure 14 Two photographs of the heterogeneous breast phantoms (a) exterior view of the realistically shaped breast phantom and (b)coronal view of the 2mm skin layer and the conical gland structures embedded inside the phantom

minus80

minus60

minus40

minus20

0

20

40

60

80

minus50 0 50y (mm)

z(m

m)

Figure 15 A coronal slice of the reconstructed 3D image of therealistically shaped adipose breast phantomusing the designed pulseshaperThe dark red indicates higher intensity values correspondingto stronger EM scatterersThe ldquolowastrdquo denotes the global maximum andthe ldquoordquo represents the approximate tumour location based on theinsertion of the tumour into the breast phantom

the passband will extend from 131 GHz up to 162GHz witha passband ripple of 10

minus9 dB and a rejected band rippleof 25 dB From the magnitude of the 119878

11parameter the

magnitude of the 11987821

can be immediately obtained by using(12) and a bandstop frequency response results for the 119878

21

parameter with a rejected band attenuation of 67 dBFollowing the expressions in Section 34 a prototype is

designed and fabricated see Figure 18 As it can be seenin Figure 19 the target simulated using CST MicrowaveStudio and measured frequency responses are in a very goodagreement satisfying the frequency requirements mentionedabove and confirming the accuracy and flexibility of thesynthesis method proposed

0 2 4 6 8 10 12 14 1630

40

50

60

70

80

Z0eZ

0o(Ω

)

Propagation direction z (cm)

(a)

1 2

43

(b)

Figure 16 (a) Even (black line) and odd (grey line) characteristicimpedance of the 4th-order differentiator after the compensationprocess and (b) the corresponding photograph of the prototype inmicrostrip technology for the given characteristic impedance

5 Conclusion

Newdevices inmicrostrip technology rectangular waveguidetechnology and microstrip coupled line technology havebeen successfully designed easily fabricated and accuratelytested for very different applications A palate of InverseScattering microwave synthesis methods have been surveyedalong the paper highlighting their advantages and disad-vantages and confirming that all the techniques togetherrepresent a powerful tool for the design of passive microwavecomponents for the new emerging applications in the wire-less radar biomedical engineering and satellite worlds

International Journal of Antennas and Propagation 9

0 2 4 6 8 10 12

0

Frequency (GHz)

|H4|

and|S31|

(dB)

minus10

minus20

minus30

minus40

minus50

(a)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus1000

minus2000

minus3000

minus4000

minus5000

Phas

e ofH

4an

dS 3

1(∘)

(b)

Figure 17 Target (black dashed line) simulated (dark grey dotted line) and measured (light grey solid line) magnitude (a) and phase (b) ofthe frequency response of the 4th-order differentiator

Figure 18 Photograph of the fabricated filter prototype in rectan-gular waveguide technology Standard WR-90 ports are used

82 10 12 14 16 18 20 22

0

Frequency (GHz)

|S11||S21|

(dB)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Figure 19Magnitude of the 11987811-parameter (grey line) and of the 119878

21-

parameter (black line) for the final synthesized filter in waveguidetechnology in Figure 18 The target (thin solid line) simulated(dotted line) and measured (thick solid line) frequency responsesare given

Acknowledgments

This work has been supported by the Spanish Ministerio deCiencia e Innovacion through the Project TEC2011-28664-C02-01 Magdalena Chudzik would like also to acknowledgeSpanish Ministerio de Educacion for its FPU Grant

References

[1] D C Youla ldquoAnalysis and synthesis of arbitrarily terminatedlossless nonuniform linesrdquo IEEE Transactions on CircuitTheoryvol CT-11 pp 363ndash372 1964

[2] R W Klopfenstein ldquoA transmission-line taper of improveddesignrdquo Proceedings of the IRE vol 44 pp 31ndash35 1956

[3] M D Abouzahra and L Lewin ldquoRadiation from microstripdiscontinuitiesrdquo IEEE Transactions on Microwave Theory andTechniques vol MTT-27 no 8 pp 722ndash723 1979

[4] I Arregui I Arnedo T Lopetegi M A G Laso and AMarcotegui ldquoLow-pass filter for electromagnetic signalsrdquo U SPatent 20100308938 European Patent 2 244 330 January 212008

[5] C Elachi ldquoWaves in active and passive periodic structures areviewrdquo Proceedings of the IEEE vol 64 no 12 pp 1666ndash16981976

[6] Y Qian V Radisic and T Itoh ldquoSimulation and experiment ofphotonic band-gap structures for microstrip circuitsrdquo in Pro-ceedings of the 1997 Asia-Pacific Microwave Conference (APMCrsquo97) pp 585ndash588 Hong Kong December 1997

[7] F Yang R Coccioll Y Qian and T Itoh ldquoPlanar peg structuresbasic properties and applicationsrdquo IEICE Transactions on Elec-tronics vol E83-C no 5 pp 687ndash696 2000

[8] I ArnedoM Chudzik J D Schwartz et al ldquoAnalytical solutionfor the design of planar electromagnetic bandgap structureswith spurious-free frequency responserdquoMicrowave and OpticalTechnology Letters vol 54 no 4 pp 956ndash960 2012

[9] T Lopetegi M A G Laso R Gonzalo et al ldquoElectromagneticcrystals in microstrip technologyrdquo Optical and Quantum Elec-tronics vol 34 no 1ndash3 pp 279ndash295 2002

[10] M A G Laso T Lopetegi M J Erro et al ldquoReal-time spec-trum analysis in microstrip technologyrdquo IEEE Transactions onMicrowave Theory and Techniques vol 51 no 3 pp 705ndash7172003

[11] I Arregui I Arnedo A Lujambio et al ldquoA compact designof high-power spurious-free low-pass waveguide filterrdquo IEEE

10 International Journal of Antennas and Propagation

Microwave and Wireless Components Letters vol 20 no 11 pp595ndash597 2010

[12] E F Bolinder ldquoThe relationship of physical applications offourier transforms in various fields of wave theory and cir-cuitryrdquo IEEE Transactions onMicrowaveTheory and Techniquespp 153ndash158 1957

[13] B Z Katsenelenbaum L Mercader M Pereyaslavets MSorolla and M Thumm Theory of Nonuniform WaveguidesThe Cross-Section Method vol 44 of IEE Electromagnetic WavesSeries IET London UK 1998

[14] F Sporleder andHGUngerWaveguide Tapers Transitions andCouplers Peter Peregrinus London UK 1979

[15] I Arnedo J Gil N Ortiz et al ldquoKu-band high-power lowpassfilter with spurious rejectionrdquo Electronics Letters vol 42 no 25pp 1460ndash1461 2006

[16] I Arregui I Arnedo A Lujambio et al ldquoDesign method forsatellite output multiplexer low-pass filters exhibiting spurious-free frequency behavior and high-power operationrdquoMicrowaveand Optical Technology Letters vol 52 no 8 pp 1724ndash17282010

[17] J D Schwartz I Arnedo M A G Laso T Lopetegi J Azanaand D Plant ldquoAn electronic UWB continuously tunable time-delay system with nanosecond delaysrdquo IEEE Microwave andWireless Components Letters vol 18 no 2 pp 103ndash105 2008

[18] I Arregui F Teberio I Arnedo et al ldquoHigh-power low-passharmonic waveguide filter with TEn0-mode suppressionrdquo IEEEMicrowave and Wireless Components Letters vol 22 no 7 pp339ndash341 2012

[19] I Arnedo M A G Laso F Falcone D Benito and T LopetegildquoA series solution for the single-mode synthesis problem basedon the coupled-mode theoryrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 56 no 2 pp 457ndash466 2008

[20] M Chudzik I Arnedo I Arregui et al ldquoNovel synthesis tech-nique for microwave circuits based on inverse scattering effi-cient algorithm implementation and applicationrdquo InternationalJournal of RF and Microwave Computer-Aided Engineering vol21 no 2 pp 164ndash173 2011

[21] I Arnedo I Arregui A Lujambio M Chudzik M A GLaso and T Lopetegi ldquoSynthesis of microwave filters by inversescattering using a closed-form expression valid for rationalfrequency responsesrdquo IEEE Transactions on Microwave Theoryand Techniques vol 60 no 5 pp 1244ndash1257 2012

[22] M J Erro I Arnedo M A G Laso T Lopetegi and MA Muriel ldquoPhase-reconstruction in photonic crystals from S-parameter magnitude in microstrip technologyrdquo Optical andQuantum Electronics vol 39 no 4ndash6 pp 321ndash331 2007

[23] M Chudzik I Arnedo A Lujambio et al ldquoMicrostrip coupled-line directional coupler with enhanced coupling based on EBGconceptrdquo Electronics Letters vol 47 no 23 pp 1284ndash1286 2011

[24] C Caloz ldquoMetamaterial dispersion engineering concepts andapplicationsrdquo Proceedings of the IEEE vol 99 no 10 pp 1711ndash1719 2011

[25] A Lujambio I Arnedo M Chudzik I Arregui T Lopetegiand M A G Laso ldquoDispersive delay line with effectivetransmission-type operation in coupled-line technologyrdquo IEEEMicrowave and Wireless Components Letters vol 21 no 9 pp459ndash461 2011

[26] P Fortescue and J Stark Spacecraft Systems Engineering WileyChichester UK 1995

[27] Part 15 Rules for Unlicensed RF Devices Federal Communica-tions Commission (FCC) September 2007 httpwwwfccgovoetinforules

[28] I Amedo J D Schwartz M A G Laso T Lopetegi D V Plantand J Azana ldquoPassive microwave planar circuits for arbitraryUWBpulse shapingrdquo IEEEMicrowave andWireless ComponentsLetters vol 18 no 7 pp 452ndash454 2008

[29] A Santorelli M Chudzik E Kirshin et al ldquoExperimentaldemonstration of pulse shaping for time-domain microwavebrest imagingrdquo Progress in Electromagnetics Research vol 133pp 309ndash329 2013

[30] M Chudzik I Arnedo A Lujambio et al ldquoDesign of trans-mission-type Nth-order differentiators in planar microwavetechnologyrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 60 no 11 pp 3384ndash3394 2012

[31] I Arnedo A Lujambio T Lopetegi andM A G Laso ldquoDesignof microwave filters with arbitrary frequency response basedon digital methodsrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 634ndash636 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 6: Review Article Passive Microwave Component Design Using ...downloads.hindawi.com/journals/ijap/2013/761278.pdf · InternationalJournal of Antennas and Propagation a generic frequency

6 International Journal of Antennas and Propagation

l

h

L

zgmin0

A B C

(a)

Interpolatingfunction

hmin

hmax

z0

A B C

gmin 2

(b)

z0

A B C

(c)

Windowingfunction

Windowingfunction

z0

(d)

Figure 9 Schematics showing the design process of novel high-power spurious-free low-pass waveguide filters (a) sketch showing the finalfilter profile and its physical parameters (b) shaping of section 119861 (119892min ℎmin and ℎmax) (c) new bandstop elements added to define sections119860 and 119862 and (d) windowing applied to sections 119860 and 119862

45 Pulse Shapers for Advanced UWB Radar and Communi-cations and for Novel Breast Cancer Detection Systems Anewstrategy for generating customized pulse shapes intendedfor use in wideband applications has been proposed anddemonstrated [27] The strategy employs the exact analyticalseries solution proposed in Section 33 [19] Time-domainmeasurements are performed demonstrating the generationof two pulse shapes using microstrip technology The firstone satisfies the preestablished UWB mask requirements foradvanced radar and ultrafast communication systems [28]see Figures 11 12 and 13 The second one improves a time-domain microwave breast imaging system [29] see Figures14 and 15

46 Transmission-Type Nth-Order Differentiators for TunablePulse Generation 119873th-order differentiators are very promis-ing devices for temporal analog processing and for the designof advanced tunable pulse generators [30] Their generalmathematical expression is

119873(119891) = (2120587 sdot 119895 sdot 119891)

119873 where 119895 =

radicminus1 Here a 4th-order differentiator has been designed for

a frequency range from 31 to 74GHz which gives a goodtradeoff between energy efficiency andmaximum bandwidthfor UWB signals 119867

4(119891)

Following the synthesis procedure detailed in Section 33the required coupling coefficient 119870(119911) is calculated for thetarget frequency response 119867

4(119891) using (10) The device

will be implemented in coupled lines to work effectively intransmission and therefore the even and odd characteristicimpedance 119885

0119890(119911) and 119885

0119900(119911) need to be separated and

windowed to keep the ports matched Since microstriptechnology will be used to implement the resulting devicethe even and oddmodes will propagate at different velocitiesmaking the necessary to apply a compensation algorithm[30]

The resulting characteristic impedances together withthe photograph of the fabricated prototype are shown inFigure 16 Figure 17 shows a very good agreement betweenthe simulation using Agilent ADS Momentum (grey dottedline) and measurement results for the magnitude and phaseof the 119878

31(119891) parameter (grey solid line) compared with

International Journal of Antennas and Propagation 7

(a)

10 15 20 25 30 35 40

0

Frequency (GHz)

minus20

minus40

minus60

minus80

minus100

|S11||S21|

(dB)

(b)

Figure 10 (a) Photograph of the fabricated prototype and (b)simulations (grey line) and measurements (black line) of the novelcompact highpower spurious-free low-pass waveguide filter |119878

11| in

dashed line and |11987821

| in solid line Frequency specifications for |11987811

|

and |11987821

| are also given in dotted line

Figure 11 Photograph of a microstrip pulse shaper for UWB radarand communication systems

0 02 04 06 08

0

05

1

Pulse

1

(au

)

minus05

minus1

Time t (ns)

Figure 12 Performance of the pulse shaper for UWB radar andcommunications Sinusoidal waveform windowed by a squaredcosine the target pulse (thin line) and themeasurement (thick line)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

|Pul

se1|

(dB)

(a)

0 2 4 6 8 10 12

0

200

Frequency (GHz)

minus200

minus400

minus600

Phas

e of p

ulse

1(∘)

(b)

Figure 13 Spectrum (a)magnitude and (b) phase of the target signal(thin line) and Fourier-transformed measurement (thick line) ofthe pulse generated in the pulse shaper intended for UWB radarcommunications The FCC UWBmask is also shown in grey

the target specifications for the 4th-order differentiator (blackdashed line) Moreover the |119878

11| parameter (not shown)

is below minus20 dB in the entire frequency range of interestensuring a good matching at the input port

47 Robust Filter Design Tool A Cauer Filter Example Thesynthesis technique presented in Section 34 is incorporatedin an exact robust filter design tool The method is validatedwith an example in rectangular waveguide technology withWR-90 standard portsThe specifications are passbands from8GHz to 114GHz and from 189GHz up to 225GHz withreturn losses better than 20 dB and a rejected band from13GHz to 163 GHz with a rejection level higher than 60 dBA bandpass frequency response following a Cauer (Elliptic)approximation [21 31] will be used for the 119878

11parameter (a

bandstop frequency response will result for the 11987821

parame-ter)The order necessary for the approximationwill be 14 and

8 International Journal of Antennas and Propagation

(a) (b)

Figure 14 Two photographs of the heterogeneous breast phantoms (a) exterior view of the realistically shaped breast phantom and (b)coronal view of the 2mm skin layer and the conical gland structures embedded inside the phantom

minus80

minus60

minus40

minus20

0

20

40

60

80

minus50 0 50y (mm)

z(m

m)

Figure 15 A coronal slice of the reconstructed 3D image of therealistically shaped adipose breast phantomusing the designed pulseshaperThe dark red indicates higher intensity values correspondingto stronger EM scatterersThe ldquolowastrdquo denotes the global maximum andthe ldquoordquo represents the approximate tumour location based on theinsertion of the tumour into the breast phantom

the passband will extend from 131 GHz up to 162GHz witha passband ripple of 10

minus9 dB and a rejected band rippleof 25 dB From the magnitude of the 119878

11parameter the

magnitude of the 11987821

can be immediately obtained by using(12) and a bandstop frequency response results for the 119878

21

parameter with a rejected band attenuation of 67 dBFollowing the expressions in Section 34 a prototype is

designed and fabricated see Figure 18 As it can be seenin Figure 19 the target simulated using CST MicrowaveStudio and measured frequency responses are in a very goodagreement satisfying the frequency requirements mentionedabove and confirming the accuracy and flexibility of thesynthesis method proposed

0 2 4 6 8 10 12 14 1630

40

50

60

70

80

Z0eZ

0o(Ω

)

Propagation direction z (cm)

(a)

1 2

43

(b)

Figure 16 (a) Even (black line) and odd (grey line) characteristicimpedance of the 4th-order differentiator after the compensationprocess and (b) the corresponding photograph of the prototype inmicrostrip technology for the given characteristic impedance

5 Conclusion

Newdevices inmicrostrip technology rectangular waveguidetechnology and microstrip coupled line technology havebeen successfully designed easily fabricated and accuratelytested for very different applications A palate of InverseScattering microwave synthesis methods have been surveyedalong the paper highlighting their advantages and disad-vantages and confirming that all the techniques togetherrepresent a powerful tool for the design of passive microwavecomponents for the new emerging applications in the wire-less radar biomedical engineering and satellite worlds

International Journal of Antennas and Propagation 9

0 2 4 6 8 10 12

0

Frequency (GHz)

|H4|

and|S31|

(dB)

minus10

minus20

minus30

minus40

minus50

(a)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus1000

minus2000

minus3000

minus4000

minus5000

Phas

e ofH

4an

dS 3

1(∘)

(b)

Figure 17 Target (black dashed line) simulated (dark grey dotted line) and measured (light grey solid line) magnitude (a) and phase (b) ofthe frequency response of the 4th-order differentiator

Figure 18 Photograph of the fabricated filter prototype in rectan-gular waveguide technology Standard WR-90 ports are used

82 10 12 14 16 18 20 22

0

Frequency (GHz)

|S11||S21|

(dB)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Figure 19Magnitude of the 11987811-parameter (grey line) and of the 119878

21-

parameter (black line) for the final synthesized filter in waveguidetechnology in Figure 18 The target (thin solid line) simulated(dotted line) and measured (thick solid line) frequency responsesare given

Acknowledgments

This work has been supported by the Spanish Ministerio deCiencia e Innovacion through the Project TEC2011-28664-C02-01 Magdalena Chudzik would like also to acknowledgeSpanish Ministerio de Educacion for its FPU Grant

References

[1] D C Youla ldquoAnalysis and synthesis of arbitrarily terminatedlossless nonuniform linesrdquo IEEE Transactions on CircuitTheoryvol CT-11 pp 363ndash372 1964

[2] R W Klopfenstein ldquoA transmission-line taper of improveddesignrdquo Proceedings of the IRE vol 44 pp 31ndash35 1956

[3] M D Abouzahra and L Lewin ldquoRadiation from microstripdiscontinuitiesrdquo IEEE Transactions on Microwave Theory andTechniques vol MTT-27 no 8 pp 722ndash723 1979

[4] I Arregui I Arnedo T Lopetegi M A G Laso and AMarcotegui ldquoLow-pass filter for electromagnetic signalsrdquo U SPatent 20100308938 European Patent 2 244 330 January 212008

[5] C Elachi ldquoWaves in active and passive periodic structures areviewrdquo Proceedings of the IEEE vol 64 no 12 pp 1666ndash16981976

[6] Y Qian V Radisic and T Itoh ldquoSimulation and experiment ofphotonic band-gap structures for microstrip circuitsrdquo in Pro-ceedings of the 1997 Asia-Pacific Microwave Conference (APMCrsquo97) pp 585ndash588 Hong Kong December 1997

[7] F Yang R Coccioll Y Qian and T Itoh ldquoPlanar peg structuresbasic properties and applicationsrdquo IEICE Transactions on Elec-tronics vol E83-C no 5 pp 687ndash696 2000

[8] I ArnedoM Chudzik J D Schwartz et al ldquoAnalytical solutionfor the design of planar electromagnetic bandgap structureswith spurious-free frequency responserdquoMicrowave and OpticalTechnology Letters vol 54 no 4 pp 956ndash960 2012

[9] T Lopetegi M A G Laso R Gonzalo et al ldquoElectromagneticcrystals in microstrip technologyrdquo Optical and Quantum Elec-tronics vol 34 no 1ndash3 pp 279ndash295 2002

[10] M A G Laso T Lopetegi M J Erro et al ldquoReal-time spec-trum analysis in microstrip technologyrdquo IEEE Transactions onMicrowave Theory and Techniques vol 51 no 3 pp 705ndash7172003

[11] I Arregui I Arnedo A Lujambio et al ldquoA compact designof high-power spurious-free low-pass waveguide filterrdquo IEEE

10 International Journal of Antennas and Propagation

Microwave and Wireless Components Letters vol 20 no 11 pp595ndash597 2010

[12] E F Bolinder ldquoThe relationship of physical applications offourier transforms in various fields of wave theory and cir-cuitryrdquo IEEE Transactions onMicrowaveTheory and Techniquespp 153ndash158 1957

[13] B Z Katsenelenbaum L Mercader M Pereyaslavets MSorolla and M Thumm Theory of Nonuniform WaveguidesThe Cross-Section Method vol 44 of IEE Electromagnetic WavesSeries IET London UK 1998

[14] F Sporleder andHGUngerWaveguide Tapers Transitions andCouplers Peter Peregrinus London UK 1979

[15] I Arnedo J Gil N Ortiz et al ldquoKu-band high-power lowpassfilter with spurious rejectionrdquo Electronics Letters vol 42 no 25pp 1460ndash1461 2006

[16] I Arregui I Arnedo A Lujambio et al ldquoDesign method forsatellite output multiplexer low-pass filters exhibiting spurious-free frequency behavior and high-power operationrdquoMicrowaveand Optical Technology Letters vol 52 no 8 pp 1724ndash17282010

[17] J D Schwartz I Arnedo M A G Laso T Lopetegi J Azanaand D Plant ldquoAn electronic UWB continuously tunable time-delay system with nanosecond delaysrdquo IEEE Microwave andWireless Components Letters vol 18 no 2 pp 103ndash105 2008

[18] I Arregui F Teberio I Arnedo et al ldquoHigh-power low-passharmonic waveguide filter with TEn0-mode suppressionrdquo IEEEMicrowave and Wireless Components Letters vol 22 no 7 pp339ndash341 2012

[19] I Arnedo M A G Laso F Falcone D Benito and T LopetegildquoA series solution for the single-mode synthesis problem basedon the coupled-mode theoryrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 56 no 2 pp 457ndash466 2008

[20] M Chudzik I Arnedo I Arregui et al ldquoNovel synthesis tech-nique for microwave circuits based on inverse scattering effi-cient algorithm implementation and applicationrdquo InternationalJournal of RF and Microwave Computer-Aided Engineering vol21 no 2 pp 164ndash173 2011

[21] I Arnedo I Arregui A Lujambio M Chudzik M A GLaso and T Lopetegi ldquoSynthesis of microwave filters by inversescattering using a closed-form expression valid for rationalfrequency responsesrdquo IEEE Transactions on Microwave Theoryand Techniques vol 60 no 5 pp 1244ndash1257 2012

[22] M J Erro I Arnedo M A G Laso T Lopetegi and MA Muriel ldquoPhase-reconstruction in photonic crystals from S-parameter magnitude in microstrip technologyrdquo Optical andQuantum Electronics vol 39 no 4ndash6 pp 321ndash331 2007

[23] M Chudzik I Arnedo A Lujambio et al ldquoMicrostrip coupled-line directional coupler with enhanced coupling based on EBGconceptrdquo Electronics Letters vol 47 no 23 pp 1284ndash1286 2011

[24] C Caloz ldquoMetamaterial dispersion engineering concepts andapplicationsrdquo Proceedings of the IEEE vol 99 no 10 pp 1711ndash1719 2011

[25] A Lujambio I Arnedo M Chudzik I Arregui T Lopetegiand M A G Laso ldquoDispersive delay line with effectivetransmission-type operation in coupled-line technologyrdquo IEEEMicrowave and Wireless Components Letters vol 21 no 9 pp459ndash461 2011

[26] P Fortescue and J Stark Spacecraft Systems Engineering WileyChichester UK 1995

[27] Part 15 Rules for Unlicensed RF Devices Federal Communica-tions Commission (FCC) September 2007 httpwwwfccgovoetinforules

[28] I Amedo J D Schwartz M A G Laso T Lopetegi D V Plantand J Azana ldquoPassive microwave planar circuits for arbitraryUWBpulse shapingrdquo IEEEMicrowave andWireless ComponentsLetters vol 18 no 7 pp 452ndash454 2008

[29] A Santorelli M Chudzik E Kirshin et al ldquoExperimentaldemonstration of pulse shaping for time-domain microwavebrest imagingrdquo Progress in Electromagnetics Research vol 133pp 309ndash329 2013

[30] M Chudzik I Arnedo A Lujambio et al ldquoDesign of trans-mission-type Nth-order differentiators in planar microwavetechnologyrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 60 no 11 pp 3384ndash3394 2012

[31] I Arnedo A Lujambio T Lopetegi andM A G Laso ldquoDesignof microwave filters with arbitrary frequency response basedon digital methodsrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 634ndash636 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 7: Review Article Passive Microwave Component Design Using ...downloads.hindawi.com/journals/ijap/2013/761278.pdf · InternationalJournal of Antennas and Propagation a generic frequency

International Journal of Antennas and Propagation 7

(a)

10 15 20 25 30 35 40

0

Frequency (GHz)

minus20

minus40

minus60

minus80

minus100

|S11||S21|

(dB)

(b)

Figure 10 (a) Photograph of the fabricated prototype and (b)simulations (grey line) and measurements (black line) of the novelcompact highpower spurious-free low-pass waveguide filter |119878

11| in

dashed line and |11987821

| in solid line Frequency specifications for |11987811

|

and |11987821

| are also given in dotted line

Figure 11 Photograph of a microstrip pulse shaper for UWB radarand communication systems

0 02 04 06 08

0

05

1

Pulse

1

(au

)

minus05

minus1

Time t (ns)

Figure 12 Performance of the pulse shaper for UWB radar andcommunications Sinusoidal waveform windowed by a squaredcosine the target pulse (thin line) and themeasurement (thick line)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus10

minus20

minus30

minus40

minus50

|Pul

se1|

(dB)

(a)

0 2 4 6 8 10 12

0

200

Frequency (GHz)

minus200

minus400

minus600

Phas

e of p

ulse

1(∘)

(b)

Figure 13 Spectrum (a)magnitude and (b) phase of the target signal(thin line) and Fourier-transformed measurement (thick line) ofthe pulse generated in the pulse shaper intended for UWB radarcommunications The FCC UWBmask is also shown in grey

the target specifications for the 4th-order differentiator (blackdashed line) Moreover the |119878

11| parameter (not shown)

is below minus20 dB in the entire frequency range of interestensuring a good matching at the input port

47 Robust Filter Design Tool A Cauer Filter Example Thesynthesis technique presented in Section 34 is incorporatedin an exact robust filter design tool The method is validatedwith an example in rectangular waveguide technology withWR-90 standard portsThe specifications are passbands from8GHz to 114GHz and from 189GHz up to 225GHz withreturn losses better than 20 dB and a rejected band from13GHz to 163 GHz with a rejection level higher than 60 dBA bandpass frequency response following a Cauer (Elliptic)approximation [21 31] will be used for the 119878

11parameter (a

bandstop frequency response will result for the 11987821

parame-ter)The order necessary for the approximationwill be 14 and

8 International Journal of Antennas and Propagation

(a) (b)

Figure 14 Two photographs of the heterogeneous breast phantoms (a) exterior view of the realistically shaped breast phantom and (b)coronal view of the 2mm skin layer and the conical gland structures embedded inside the phantom

minus80

minus60

minus40

minus20

0

20

40

60

80

minus50 0 50y (mm)

z(m

m)

Figure 15 A coronal slice of the reconstructed 3D image of therealistically shaped adipose breast phantomusing the designed pulseshaperThe dark red indicates higher intensity values correspondingto stronger EM scatterersThe ldquolowastrdquo denotes the global maximum andthe ldquoordquo represents the approximate tumour location based on theinsertion of the tumour into the breast phantom

the passband will extend from 131 GHz up to 162GHz witha passband ripple of 10

minus9 dB and a rejected band rippleof 25 dB From the magnitude of the 119878

11parameter the

magnitude of the 11987821

can be immediately obtained by using(12) and a bandstop frequency response results for the 119878

21

parameter with a rejected band attenuation of 67 dBFollowing the expressions in Section 34 a prototype is

designed and fabricated see Figure 18 As it can be seenin Figure 19 the target simulated using CST MicrowaveStudio and measured frequency responses are in a very goodagreement satisfying the frequency requirements mentionedabove and confirming the accuracy and flexibility of thesynthesis method proposed

0 2 4 6 8 10 12 14 1630

40

50

60

70

80

Z0eZ

0o(Ω

)

Propagation direction z (cm)

(a)

1 2

43

(b)

Figure 16 (a) Even (black line) and odd (grey line) characteristicimpedance of the 4th-order differentiator after the compensationprocess and (b) the corresponding photograph of the prototype inmicrostrip technology for the given characteristic impedance

5 Conclusion

Newdevices inmicrostrip technology rectangular waveguidetechnology and microstrip coupled line technology havebeen successfully designed easily fabricated and accuratelytested for very different applications A palate of InverseScattering microwave synthesis methods have been surveyedalong the paper highlighting their advantages and disad-vantages and confirming that all the techniques togetherrepresent a powerful tool for the design of passive microwavecomponents for the new emerging applications in the wire-less radar biomedical engineering and satellite worlds

International Journal of Antennas and Propagation 9

0 2 4 6 8 10 12

0

Frequency (GHz)

|H4|

and|S31|

(dB)

minus10

minus20

minus30

minus40

minus50

(a)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus1000

minus2000

minus3000

minus4000

minus5000

Phas

e ofH

4an

dS 3

1(∘)

(b)

Figure 17 Target (black dashed line) simulated (dark grey dotted line) and measured (light grey solid line) magnitude (a) and phase (b) ofthe frequency response of the 4th-order differentiator

Figure 18 Photograph of the fabricated filter prototype in rectan-gular waveguide technology Standard WR-90 ports are used

82 10 12 14 16 18 20 22

0

Frequency (GHz)

|S11||S21|

(dB)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Figure 19Magnitude of the 11987811-parameter (grey line) and of the 119878

21-

parameter (black line) for the final synthesized filter in waveguidetechnology in Figure 18 The target (thin solid line) simulated(dotted line) and measured (thick solid line) frequency responsesare given

Acknowledgments

This work has been supported by the Spanish Ministerio deCiencia e Innovacion through the Project TEC2011-28664-C02-01 Magdalena Chudzik would like also to acknowledgeSpanish Ministerio de Educacion for its FPU Grant

References

[1] D C Youla ldquoAnalysis and synthesis of arbitrarily terminatedlossless nonuniform linesrdquo IEEE Transactions on CircuitTheoryvol CT-11 pp 363ndash372 1964

[2] R W Klopfenstein ldquoA transmission-line taper of improveddesignrdquo Proceedings of the IRE vol 44 pp 31ndash35 1956

[3] M D Abouzahra and L Lewin ldquoRadiation from microstripdiscontinuitiesrdquo IEEE Transactions on Microwave Theory andTechniques vol MTT-27 no 8 pp 722ndash723 1979

[4] I Arregui I Arnedo T Lopetegi M A G Laso and AMarcotegui ldquoLow-pass filter for electromagnetic signalsrdquo U SPatent 20100308938 European Patent 2 244 330 January 212008

[5] C Elachi ldquoWaves in active and passive periodic structures areviewrdquo Proceedings of the IEEE vol 64 no 12 pp 1666ndash16981976

[6] Y Qian V Radisic and T Itoh ldquoSimulation and experiment ofphotonic band-gap structures for microstrip circuitsrdquo in Pro-ceedings of the 1997 Asia-Pacific Microwave Conference (APMCrsquo97) pp 585ndash588 Hong Kong December 1997

[7] F Yang R Coccioll Y Qian and T Itoh ldquoPlanar peg structuresbasic properties and applicationsrdquo IEICE Transactions on Elec-tronics vol E83-C no 5 pp 687ndash696 2000

[8] I ArnedoM Chudzik J D Schwartz et al ldquoAnalytical solutionfor the design of planar electromagnetic bandgap structureswith spurious-free frequency responserdquoMicrowave and OpticalTechnology Letters vol 54 no 4 pp 956ndash960 2012

[9] T Lopetegi M A G Laso R Gonzalo et al ldquoElectromagneticcrystals in microstrip technologyrdquo Optical and Quantum Elec-tronics vol 34 no 1ndash3 pp 279ndash295 2002

[10] M A G Laso T Lopetegi M J Erro et al ldquoReal-time spec-trum analysis in microstrip technologyrdquo IEEE Transactions onMicrowave Theory and Techniques vol 51 no 3 pp 705ndash7172003

[11] I Arregui I Arnedo A Lujambio et al ldquoA compact designof high-power spurious-free low-pass waveguide filterrdquo IEEE

10 International Journal of Antennas and Propagation

Microwave and Wireless Components Letters vol 20 no 11 pp595ndash597 2010

[12] E F Bolinder ldquoThe relationship of physical applications offourier transforms in various fields of wave theory and cir-cuitryrdquo IEEE Transactions onMicrowaveTheory and Techniquespp 153ndash158 1957

[13] B Z Katsenelenbaum L Mercader M Pereyaslavets MSorolla and M Thumm Theory of Nonuniform WaveguidesThe Cross-Section Method vol 44 of IEE Electromagnetic WavesSeries IET London UK 1998

[14] F Sporleder andHGUngerWaveguide Tapers Transitions andCouplers Peter Peregrinus London UK 1979

[15] I Arnedo J Gil N Ortiz et al ldquoKu-band high-power lowpassfilter with spurious rejectionrdquo Electronics Letters vol 42 no 25pp 1460ndash1461 2006

[16] I Arregui I Arnedo A Lujambio et al ldquoDesign method forsatellite output multiplexer low-pass filters exhibiting spurious-free frequency behavior and high-power operationrdquoMicrowaveand Optical Technology Letters vol 52 no 8 pp 1724ndash17282010

[17] J D Schwartz I Arnedo M A G Laso T Lopetegi J Azanaand D Plant ldquoAn electronic UWB continuously tunable time-delay system with nanosecond delaysrdquo IEEE Microwave andWireless Components Letters vol 18 no 2 pp 103ndash105 2008

[18] I Arregui F Teberio I Arnedo et al ldquoHigh-power low-passharmonic waveguide filter with TEn0-mode suppressionrdquo IEEEMicrowave and Wireless Components Letters vol 22 no 7 pp339ndash341 2012

[19] I Arnedo M A G Laso F Falcone D Benito and T LopetegildquoA series solution for the single-mode synthesis problem basedon the coupled-mode theoryrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 56 no 2 pp 457ndash466 2008

[20] M Chudzik I Arnedo I Arregui et al ldquoNovel synthesis tech-nique for microwave circuits based on inverse scattering effi-cient algorithm implementation and applicationrdquo InternationalJournal of RF and Microwave Computer-Aided Engineering vol21 no 2 pp 164ndash173 2011

[21] I Arnedo I Arregui A Lujambio M Chudzik M A GLaso and T Lopetegi ldquoSynthesis of microwave filters by inversescattering using a closed-form expression valid for rationalfrequency responsesrdquo IEEE Transactions on Microwave Theoryand Techniques vol 60 no 5 pp 1244ndash1257 2012

[22] M J Erro I Arnedo M A G Laso T Lopetegi and MA Muriel ldquoPhase-reconstruction in photonic crystals from S-parameter magnitude in microstrip technologyrdquo Optical andQuantum Electronics vol 39 no 4ndash6 pp 321ndash331 2007

[23] M Chudzik I Arnedo A Lujambio et al ldquoMicrostrip coupled-line directional coupler with enhanced coupling based on EBGconceptrdquo Electronics Letters vol 47 no 23 pp 1284ndash1286 2011

[24] C Caloz ldquoMetamaterial dispersion engineering concepts andapplicationsrdquo Proceedings of the IEEE vol 99 no 10 pp 1711ndash1719 2011

[25] A Lujambio I Arnedo M Chudzik I Arregui T Lopetegiand M A G Laso ldquoDispersive delay line with effectivetransmission-type operation in coupled-line technologyrdquo IEEEMicrowave and Wireless Components Letters vol 21 no 9 pp459ndash461 2011

[26] P Fortescue and J Stark Spacecraft Systems Engineering WileyChichester UK 1995

[27] Part 15 Rules for Unlicensed RF Devices Federal Communica-tions Commission (FCC) September 2007 httpwwwfccgovoetinforules

[28] I Amedo J D Schwartz M A G Laso T Lopetegi D V Plantand J Azana ldquoPassive microwave planar circuits for arbitraryUWBpulse shapingrdquo IEEEMicrowave andWireless ComponentsLetters vol 18 no 7 pp 452ndash454 2008

[29] A Santorelli M Chudzik E Kirshin et al ldquoExperimentaldemonstration of pulse shaping for time-domain microwavebrest imagingrdquo Progress in Electromagnetics Research vol 133pp 309ndash329 2013

[30] M Chudzik I Arnedo A Lujambio et al ldquoDesign of trans-mission-type Nth-order differentiators in planar microwavetechnologyrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 60 no 11 pp 3384ndash3394 2012

[31] I Arnedo A Lujambio T Lopetegi andM A G Laso ldquoDesignof microwave filters with arbitrary frequency response basedon digital methodsrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 634ndash636 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 8: Review Article Passive Microwave Component Design Using ...downloads.hindawi.com/journals/ijap/2013/761278.pdf · InternationalJournal of Antennas and Propagation a generic frequency

8 International Journal of Antennas and Propagation

(a) (b)

Figure 14 Two photographs of the heterogeneous breast phantoms (a) exterior view of the realistically shaped breast phantom and (b)coronal view of the 2mm skin layer and the conical gland structures embedded inside the phantom

minus80

minus60

minus40

minus20

0

20

40

60

80

minus50 0 50y (mm)

z(m

m)

Figure 15 A coronal slice of the reconstructed 3D image of therealistically shaped adipose breast phantomusing the designed pulseshaperThe dark red indicates higher intensity values correspondingto stronger EM scatterersThe ldquolowastrdquo denotes the global maximum andthe ldquoordquo represents the approximate tumour location based on theinsertion of the tumour into the breast phantom

the passband will extend from 131 GHz up to 162GHz witha passband ripple of 10

minus9 dB and a rejected band rippleof 25 dB From the magnitude of the 119878

11parameter the

magnitude of the 11987821

can be immediately obtained by using(12) and a bandstop frequency response results for the 119878

21

parameter with a rejected band attenuation of 67 dBFollowing the expressions in Section 34 a prototype is

designed and fabricated see Figure 18 As it can be seenin Figure 19 the target simulated using CST MicrowaveStudio and measured frequency responses are in a very goodagreement satisfying the frequency requirements mentionedabove and confirming the accuracy and flexibility of thesynthesis method proposed

0 2 4 6 8 10 12 14 1630

40

50

60

70

80

Z0eZ

0o(Ω

)

Propagation direction z (cm)

(a)

1 2

43

(b)

Figure 16 (a) Even (black line) and odd (grey line) characteristicimpedance of the 4th-order differentiator after the compensationprocess and (b) the corresponding photograph of the prototype inmicrostrip technology for the given characteristic impedance

5 Conclusion

Newdevices inmicrostrip technology rectangular waveguidetechnology and microstrip coupled line technology havebeen successfully designed easily fabricated and accuratelytested for very different applications A palate of InverseScattering microwave synthesis methods have been surveyedalong the paper highlighting their advantages and disad-vantages and confirming that all the techniques togetherrepresent a powerful tool for the design of passive microwavecomponents for the new emerging applications in the wire-less radar biomedical engineering and satellite worlds

International Journal of Antennas and Propagation 9

0 2 4 6 8 10 12

0

Frequency (GHz)

|H4|

and|S31|

(dB)

minus10

minus20

minus30

minus40

minus50

(a)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus1000

minus2000

minus3000

minus4000

minus5000

Phas

e ofH

4an

dS 3

1(∘)

(b)

Figure 17 Target (black dashed line) simulated (dark grey dotted line) and measured (light grey solid line) magnitude (a) and phase (b) ofthe frequency response of the 4th-order differentiator

Figure 18 Photograph of the fabricated filter prototype in rectan-gular waveguide technology Standard WR-90 ports are used

82 10 12 14 16 18 20 22

0

Frequency (GHz)

|S11||S21|

(dB)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Figure 19Magnitude of the 11987811-parameter (grey line) and of the 119878

21-

parameter (black line) for the final synthesized filter in waveguidetechnology in Figure 18 The target (thin solid line) simulated(dotted line) and measured (thick solid line) frequency responsesare given

Acknowledgments

This work has been supported by the Spanish Ministerio deCiencia e Innovacion through the Project TEC2011-28664-C02-01 Magdalena Chudzik would like also to acknowledgeSpanish Ministerio de Educacion for its FPU Grant

References

[1] D C Youla ldquoAnalysis and synthesis of arbitrarily terminatedlossless nonuniform linesrdquo IEEE Transactions on CircuitTheoryvol CT-11 pp 363ndash372 1964

[2] R W Klopfenstein ldquoA transmission-line taper of improveddesignrdquo Proceedings of the IRE vol 44 pp 31ndash35 1956

[3] M D Abouzahra and L Lewin ldquoRadiation from microstripdiscontinuitiesrdquo IEEE Transactions on Microwave Theory andTechniques vol MTT-27 no 8 pp 722ndash723 1979

[4] I Arregui I Arnedo T Lopetegi M A G Laso and AMarcotegui ldquoLow-pass filter for electromagnetic signalsrdquo U SPatent 20100308938 European Patent 2 244 330 January 212008

[5] C Elachi ldquoWaves in active and passive periodic structures areviewrdquo Proceedings of the IEEE vol 64 no 12 pp 1666ndash16981976

[6] Y Qian V Radisic and T Itoh ldquoSimulation and experiment ofphotonic band-gap structures for microstrip circuitsrdquo in Pro-ceedings of the 1997 Asia-Pacific Microwave Conference (APMCrsquo97) pp 585ndash588 Hong Kong December 1997

[7] F Yang R Coccioll Y Qian and T Itoh ldquoPlanar peg structuresbasic properties and applicationsrdquo IEICE Transactions on Elec-tronics vol E83-C no 5 pp 687ndash696 2000

[8] I ArnedoM Chudzik J D Schwartz et al ldquoAnalytical solutionfor the design of planar electromagnetic bandgap structureswith spurious-free frequency responserdquoMicrowave and OpticalTechnology Letters vol 54 no 4 pp 956ndash960 2012

[9] T Lopetegi M A G Laso R Gonzalo et al ldquoElectromagneticcrystals in microstrip technologyrdquo Optical and Quantum Elec-tronics vol 34 no 1ndash3 pp 279ndash295 2002

[10] M A G Laso T Lopetegi M J Erro et al ldquoReal-time spec-trum analysis in microstrip technologyrdquo IEEE Transactions onMicrowave Theory and Techniques vol 51 no 3 pp 705ndash7172003

[11] I Arregui I Arnedo A Lujambio et al ldquoA compact designof high-power spurious-free low-pass waveguide filterrdquo IEEE

10 International Journal of Antennas and Propagation

Microwave and Wireless Components Letters vol 20 no 11 pp595ndash597 2010

[12] E F Bolinder ldquoThe relationship of physical applications offourier transforms in various fields of wave theory and cir-cuitryrdquo IEEE Transactions onMicrowaveTheory and Techniquespp 153ndash158 1957

[13] B Z Katsenelenbaum L Mercader M Pereyaslavets MSorolla and M Thumm Theory of Nonuniform WaveguidesThe Cross-Section Method vol 44 of IEE Electromagnetic WavesSeries IET London UK 1998

[14] F Sporleder andHGUngerWaveguide Tapers Transitions andCouplers Peter Peregrinus London UK 1979

[15] I Arnedo J Gil N Ortiz et al ldquoKu-band high-power lowpassfilter with spurious rejectionrdquo Electronics Letters vol 42 no 25pp 1460ndash1461 2006

[16] I Arregui I Arnedo A Lujambio et al ldquoDesign method forsatellite output multiplexer low-pass filters exhibiting spurious-free frequency behavior and high-power operationrdquoMicrowaveand Optical Technology Letters vol 52 no 8 pp 1724ndash17282010

[17] J D Schwartz I Arnedo M A G Laso T Lopetegi J Azanaand D Plant ldquoAn electronic UWB continuously tunable time-delay system with nanosecond delaysrdquo IEEE Microwave andWireless Components Letters vol 18 no 2 pp 103ndash105 2008

[18] I Arregui F Teberio I Arnedo et al ldquoHigh-power low-passharmonic waveguide filter with TEn0-mode suppressionrdquo IEEEMicrowave and Wireless Components Letters vol 22 no 7 pp339ndash341 2012

[19] I Arnedo M A G Laso F Falcone D Benito and T LopetegildquoA series solution for the single-mode synthesis problem basedon the coupled-mode theoryrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 56 no 2 pp 457ndash466 2008

[20] M Chudzik I Arnedo I Arregui et al ldquoNovel synthesis tech-nique for microwave circuits based on inverse scattering effi-cient algorithm implementation and applicationrdquo InternationalJournal of RF and Microwave Computer-Aided Engineering vol21 no 2 pp 164ndash173 2011

[21] I Arnedo I Arregui A Lujambio M Chudzik M A GLaso and T Lopetegi ldquoSynthesis of microwave filters by inversescattering using a closed-form expression valid for rationalfrequency responsesrdquo IEEE Transactions on Microwave Theoryand Techniques vol 60 no 5 pp 1244ndash1257 2012

[22] M J Erro I Arnedo M A G Laso T Lopetegi and MA Muriel ldquoPhase-reconstruction in photonic crystals from S-parameter magnitude in microstrip technologyrdquo Optical andQuantum Electronics vol 39 no 4ndash6 pp 321ndash331 2007

[23] M Chudzik I Arnedo A Lujambio et al ldquoMicrostrip coupled-line directional coupler with enhanced coupling based on EBGconceptrdquo Electronics Letters vol 47 no 23 pp 1284ndash1286 2011

[24] C Caloz ldquoMetamaterial dispersion engineering concepts andapplicationsrdquo Proceedings of the IEEE vol 99 no 10 pp 1711ndash1719 2011

[25] A Lujambio I Arnedo M Chudzik I Arregui T Lopetegiand M A G Laso ldquoDispersive delay line with effectivetransmission-type operation in coupled-line technologyrdquo IEEEMicrowave and Wireless Components Letters vol 21 no 9 pp459ndash461 2011

[26] P Fortescue and J Stark Spacecraft Systems Engineering WileyChichester UK 1995

[27] Part 15 Rules for Unlicensed RF Devices Federal Communica-tions Commission (FCC) September 2007 httpwwwfccgovoetinforules

[28] I Amedo J D Schwartz M A G Laso T Lopetegi D V Plantand J Azana ldquoPassive microwave planar circuits for arbitraryUWBpulse shapingrdquo IEEEMicrowave andWireless ComponentsLetters vol 18 no 7 pp 452ndash454 2008

[29] A Santorelli M Chudzik E Kirshin et al ldquoExperimentaldemonstration of pulse shaping for time-domain microwavebrest imagingrdquo Progress in Electromagnetics Research vol 133pp 309ndash329 2013

[30] M Chudzik I Arnedo A Lujambio et al ldquoDesign of trans-mission-type Nth-order differentiators in planar microwavetechnologyrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 60 no 11 pp 3384ndash3394 2012

[31] I Arnedo A Lujambio T Lopetegi andM A G Laso ldquoDesignof microwave filters with arbitrary frequency response basedon digital methodsrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 634ndash636 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 9: Review Article Passive Microwave Component Design Using ...downloads.hindawi.com/journals/ijap/2013/761278.pdf · InternationalJournal of Antennas and Propagation a generic frequency

International Journal of Antennas and Propagation 9

0 2 4 6 8 10 12

0

Frequency (GHz)

|H4|

and|S31|

(dB)

minus10

minus20

minus30

minus40

minus50

(a)

0 2 4 6 8 10 12

0

Frequency (GHz)

minus1000

minus2000

minus3000

minus4000

minus5000

Phas

e ofH

4an

dS 3

1(∘)

(b)

Figure 17 Target (black dashed line) simulated (dark grey dotted line) and measured (light grey solid line) magnitude (a) and phase (b) ofthe frequency response of the 4th-order differentiator

Figure 18 Photograph of the fabricated filter prototype in rectan-gular waveguide technology Standard WR-90 ports are used

82 10 12 14 16 18 20 22

0

Frequency (GHz)

|S11||S21|

(dB)

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Figure 19Magnitude of the 11987811-parameter (grey line) and of the 119878

21-

parameter (black line) for the final synthesized filter in waveguidetechnology in Figure 18 The target (thin solid line) simulated(dotted line) and measured (thick solid line) frequency responsesare given

Acknowledgments

This work has been supported by the Spanish Ministerio deCiencia e Innovacion through the Project TEC2011-28664-C02-01 Magdalena Chudzik would like also to acknowledgeSpanish Ministerio de Educacion for its FPU Grant

References

[1] D C Youla ldquoAnalysis and synthesis of arbitrarily terminatedlossless nonuniform linesrdquo IEEE Transactions on CircuitTheoryvol CT-11 pp 363ndash372 1964

[2] R W Klopfenstein ldquoA transmission-line taper of improveddesignrdquo Proceedings of the IRE vol 44 pp 31ndash35 1956

[3] M D Abouzahra and L Lewin ldquoRadiation from microstripdiscontinuitiesrdquo IEEE Transactions on Microwave Theory andTechniques vol MTT-27 no 8 pp 722ndash723 1979

[4] I Arregui I Arnedo T Lopetegi M A G Laso and AMarcotegui ldquoLow-pass filter for electromagnetic signalsrdquo U SPatent 20100308938 European Patent 2 244 330 January 212008

[5] C Elachi ldquoWaves in active and passive periodic structures areviewrdquo Proceedings of the IEEE vol 64 no 12 pp 1666ndash16981976

[6] Y Qian V Radisic and T Itoh ldquoSimulation and experiment ofphotonic band-gap structures for microstrip circuitsrdquo in Pro-ceedings of the 1997 Asia-Pacific Microwave Conference (APMCrsquo97) pp 585ndash588 Hong Kong December 1997

[7] F Yang R Coccioll Y Qian and T Itoh ldquoPlanar peg structuresbasic properties and applicationsrdquo IEICE Transactions on Elec-tronics vol E83-C no 5 pp 687ndash696 2000

[8] I ArnedoM Chudzik J D Schwartz et al ldquoAnalytical solutionfor the design of planar electromagnetic bandgap structureswith spurious-free frequency responserdquoMicrowave and OpticalTechnology Letters vol 54 no 4 pp 956ndash960 2012

[9] T Lopetegi M A G Laso R Gonzalo et al ldquoElectromagneticcrystals in microstrip technologyrdquo Optical and Quantum Elec-tronics vol 34 no 1ndash3 pp 279ndash295 2002

[10] M A G Laso T Lopetegi M J Erro et al ldquoReal-time spec-trum analysis in microstrip technologyrdquo IEEE Transactions onMicrowave Theory and Techniques vol 51 no 3 pp 705ndash7172003

[11] I Arregui I Arnedo A Lujambio et al ldquoA compact designof high-power spurious-free low-pass waveguide filterrdquo IEEE

10 International Journal of Antennas and Propagation

Microwave and Wireless Components Letters vol 20 no 11 pp595ndash597 2010

[12] E F Bolinder ldquoThe relationship of physical applications offourier transforms in various fields of wave theory and cir-cuitryrdquo IEEE Transactions onMicrowaveTheory and Techniquespp 153ndash158 1957

[13] B Z Katsenelenbaum L Mercader M Pereyaslavets MSorolla and M Thumm Theory of Nonuniform WaveguidesThe Cross-Section Method vol 44 of IEE Electromagnetic WavesSeries IET London UK 1998

[14] F Sporleder andHGUngerWaveguide Tapers Transitions andCouplers Peter Peregrinus London UK 1979

[15] I Arnedo J Gil N Ortiz et al ldquoKu-band high-power lowpassfilter with spurious rejectionrdquo Electronics Letters vol 42 no 25pp 1460ndash1461 2006

[16] I Arregui I Arnedo A Lujambio et al ldquoDesign method forsatellite output multiplexer low-pass filters exhibiting spurious-free frequency behavior and high-power operationrdquoMicrowaveand Optical Technology Letters vol 52 no 8 pp 1724ndash17282010

[17] J D Schwartz I Arnedo M A G Laso T Lopetegi J Azanaand D Plant ldquoAn electronic UWB continuously tunable time-delay system with nanosecond delaysrdquo IEEE Microwave andWireless Components Letters vol 18 no 2 pp 103ndash105 2008

[18] I Arregui F Teberio I Arnedo et al ldquoHigh-power low-passharmonic waveguide filter with TEn0-mode suppressionrdquo IEEEMicrowave and Wireless Components Letters vol 22 no 7 pp339ndash341 2012

[19] I Arnedo M A G Laso F Falcone D Benito and T LopetegildquoA series solution for the single-mode synthesis problem basedon the coupled-mode theoryrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 56 no 2 pp 457ndash466 2008

[20] M Chudzik I Arnedo I Arregui et al ldquoNovel synthesis tech-nique for microwave circuits based on inverse scattering effi-cient algorithm implementation and applicationrdquo InternationalJournal of RF and Microwave Computer-Aided Engineering vol21 no 2 pp 164ndash173 2011

[21] I Arnedo I Arregui A Lujambio M Chudzik M A GLaso and T Lopetegi ldquoSynthesis of microwave filters by inversescattering using a closed-form expression valid for rationalfrequency responsesrdquo IEEE Transactions on Microwave Theoryand Techniques vol 60 no 5 pp 1244ndash1257 2012

[22] M J Erro I Arnedo M A G Laso T Lopetegi and MA Muriel ldquoPhase-reconstruction in photonic crystals from S-parameter magnitude in microstrip technologyrdquo Optical andQuantum Electronics vol 39 no 4ndash6 pp 321ndash331 2007

[23] M Chudzik I Arnedo A Lujambio et al ldquoMicrostrip coupled-line directional coupler with enhanced coupling based on EBGconceptrdquo Electronics Letters vol 47 no 23 pp 1284ndash1286 2011

[24] C Caloz ldquoMetamaterial dispersion engineering concepts andapplicationsrdquo Proceedings of the IEEE vol 99 no 10 pp 1711ndash1719 2011

[25] A Lujambio I Arnedo M Chudzik I Arregui T Lopetegiand M A G Laso ldquoDispersive delay line with effectivetransmission-type operation in coupled-line technologyrdquo IEEEMicrowave and Wireless Components Letters vol 21 no 9 pp459ndash461 2011

[26] P Fortescue and J Stark Spacecraft Systems Engineering WileyChichester UK 1995

[27] Part 15 Rules for Unlicensed RF Devices Federal Communica-tions Commission (FCC) September 2007 httpwwwfccgovoetinforules

[28] I Amedo J D Schwartz M A G Laso T Lopetegi D V Plantand J Azana ldquoPassive microwave planar circuits for arbitraryUWBpulse shapingrdquo IEEEMicrowave andWireless ComponentsLetters vol 18 no 7 pp 452ndash454 2008

[29] A Santorelli M Chudzik E Kirshin et al ldquoExperimentaldemonstration of pulse shaping for time-domain microwavebrest imagingrdquo Progress in Electromagnetics Research vol 133pp 309ndash329 2013

[30] M Chudzik I Arnedo A Lujambio et al ldquoDesign of trans-mission-type Nth-order differentiators in planar microwavetechnologyrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 60 no 11 pp 3384ndash3394 2012

[31] I Arnedo A Lujambio T Lopetegi andM A G Laso ldquoDesignof microwave filters with arbitrary frequency response basedon digital methodsrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 634ndash636 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 10: Review Article Passive Microwave Component Design Using ...downloads.hindawi.com/journals/ijap/2013/761278.pdf · InternationalJournal of Antennas and Propagation a generic frequency

10 International Journal of Antennas and Propagation

Microwave and Wireless Components Letters vol 20 no 11 pp595ndash597 2010

[12] E F Bolinder ldquoThe relationship of physical applications offourier transforms in various fields of wave theory and cir-cuitryrdquo IEEE Transactions onMicrowaveTheory and Techniquespp 153ndash158 1957

[13] B Z Katsenelenbaum L Mercader M Pereyaslavets MSorolla and M Thumm Theory of Nonuniform WaveguidesThe Cross-Section Method vol 44 of IEE Electromagnetic WavesSeries IET London UK 1998

[14] F Sporleder andHGUngerWaveguide Tapers Transitions andCouplers Peter Peregrinus London UK 1979

[15] I Arnedo J Gil N Ortiz et al ldquoKu-band high-power lowpassfilter with spurious rejectionrdquo Electronics Letters vol 42 no 25pp 1460ndash1461 2006

[16] I Arregui I Arnedo A Lujambio et al ldquoDesign method forsatellite output multiplexer low-pass filters exhibiting spurious-free frequency behavior and high-power operationrdquoMicrowaveand Optical Technology Letters vol 52 no 8 pp 1724ndash17282010

[17] J D Schwartz I Arnedo M A G Laso T Lopetegi J Azanaand D Plant ldquoAn electronic UWB continuously tunable time-delay system with nanosecond delaysrdquo IEEE Microwave andWireless Components Letters vol 18 no 2 pp 103ndash105 2008

[18] I Arregui F Teberio I Arnedo et al ldquoHigh-power low-passharmonic waveguide filter with TEn0-mode suppressionrdquo IEEEMicrowave and Wireless Components Letters vol 22 no 7 pp339ndash341 2012

[19] I Arnedo M A G Laso F Falcone D Benito and T LopetegildquoA series solution for the single-mode synthesis problem basedon the coupled-mode theoryrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 56 no 2 pp 457ndash466 2008

[20] M Chudzik I Arnedo I Arregui et al ldquoNovel synthesis tech-nique for microwave circuits based on inverse scattering effi-cient algorithm implementation and applicationrdquo InternationalJournal of RF and Microwave Computer-Aided Engineering vol21 no 2 pp 164ndash173 2011

[21] I Arnedo I Arregui A Lujambio M Chudzik M A GLaso and T Lopetegi ldquoSynthesis of microwave filters by inversescattering using a closed-form expression valid for rationalfrequency responsesrdquo IEEE Transactions on Microwave Theoryand Techniques vol 60 no 5 pp 1244ndash1257 2012

[22] M J Erro I Arnedo M A G Laso T Lopetegi and MA Muriel ldquoPhase-reconstruction in photonic crystals from S-parameter magnitude in microstrip technologyrdquo Optical andQuantum Electronics vol 39 no 4ndash6 pp 321ndash331 2007

[23] M Chudzik I Arnedo A Lujambio et al ldquoMicrostrip coupled-line directional coupler with enhanced coupling based on EBGconceptrdquo Electronics Letters vol 47 no 23 pp 1284ndash1286 2011

[24] C Caloz ldquoMetamaterial dispersion engineering concepts andapplicationsrdquo Proceedings of the IEEE vol 99 no 10 pp 1711ndash1719 2011

[25] A Lujambio I Arnedo M Chudzik I Arregui T Lopetegiand M A G Laso ldquoDispersive delay line with effectivetransmission-type operation in coupled-line technologyrdquo IEEEMicrowave and Wireless Components Letters vol 21 no 9 pp459ndash461 2011

[26] P Fortescue and J Stark Spacecraft Systems Engineering WileyChichester UK 1995

[27] Part 15 Rules for Unlicensed RF Devices Federal Communica-tions Commission (FCC) September 2007 httpwwwfccgovoetinforules

[28] I Amedo J D Schwartz M A G Laso T Lopetegi D V Plantand J Azana ldquoPassive microwave planar circuits for arbitraryUWBpulse shapingrdquo IEEEMicrowave andWireless ComponentsLetters vol 18 no 7 pp 452ndash454 2008

[29] A Santorelli M Chudzik E Kirshin et al ldquoExperimentaldemonstration of pulse shaping for time-domain microwavebrest imagingrdquo Progress in Electromagnetics Research vol 133pp 309ndash329 2013

[30] M Chudzik I Arnedo A Lujambio et al ldquoDesign of trans-mission-type Nth-order differentiators in planar microwavetechnologyrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 60 no 11 pp 3384ndash3394 2012

[31] I Arnedo A Lujambio T Lopetegi andM A G Laso ldquoDesignof microwave filters with arbitrary frequency response basedon digital methodsrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 634ndash636 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 11: Review Article Passive Microwave Component Design Using ...downloads.hindawi.com/journals/ijap/2013/761278.pdf · InternationalJournal of Antennas and Propagation a generic frequency

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of