IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 10, OCTOBER 2005 3221
Using the Branch-Line Directional Coupler in the
Design of Microwave Bandpass Filters
Roberto Gómez-García, Student Member, IEEE, José I. Alonso, Member, IEEE, and
Daniel Amor-Martín, Member, IEEE
Abstract—This paper addresses the application of the branch-
line directional coupler to the design of microwave bandpass fil-
ters. The basic idea consists of using the branch-line coupler as
a transversal filtering section by loading the coupled ports of the
the signal interference philosophy involved in classic transversal
filter schemes, bandpass transfer functions with perceptible stop-
bands and sharp cutoff slopes are derived. Furthermore, the main
characteristics of the synthesized filtering response, such as the
bandwidth or the position of the out-of-band power transmission
the transversal section. Hence, a large variety of bandpass filtering
profiles different from those offered by classical filter schemes can
be realized. Finally, the experimental usefulness of the transversal
bandpass filter prototypes at 5 GHz.
Index Terms—Branch-line directional coupler, microstrip,
microwave bandpass filter, transmission line, transmission zero,
transversal filtering section.
modern wireless and high-speed data communication appli-
cations . In the design of passive filters, the major issue
is the realization of low insertion-loss and high-selectivity
filtering responses to accomplish appropriate band selections
by efficiently rejecting spurious signals and out-of-band noise
. Regarding active filters, some other important factors, such
as linearity, noise performance, and power transmission gain,
must also be considered .
Over the last few years, one of the most followed choices in
research into novel microwave filter topologies is based on the
use of circuits providing more than one input-to-output signal
propagation path. Microwave transversal filters are a good ex-
ponent of this trend, appearing from the extrapolation to the
ERY sophisticated filter solutions are required in the
development of high-performance RF subsystems for
Manuscript received March 3, 2005; revised May 11, 2005. This work was
supported in part by the National Board of Scientific and Technology Research
under Project TIC2002-04569-C02-01 and Project TIC2002-02657, and in part
by the Spanish Ministry of Education and Culture under a doctoral scholarship.
R. Gómez-García and J. I. Alonso are with the Grupo de Microondas
y Radar, Departamento de Señales, Sistemas y Radiocomunicaciones,
D. Amor-Martín is with INDRA Sistemas S.A., 28850 Torrejón de Ardoz,
Madrid, Spain (e-mail: email@example.com).
Digital Object Identifier 10.1109/TMTT.2005.855140
28040 Madrid, Spain(e-mail:
that make up the overall filter. Thus, the filtering action comes
about through the combination of these signal subcomponents
oncetheyhavebeen processed.By forcinga passbandconstruc-
tive interference and out-of-band signal energy cancellations to
produce power transmission zeros, high-selective filtering re-
sponses with sharp cutoff slopes can be derived. Furthermore,
since only feedforward techniques and not feedback principles
are used in microwave transversal filters, instability problems
caused by the presence of active devices to carry out active fil-
tering functions are avoided .
Traditionally, the main drawback to overcoming in mi-
crowave transversal filter design has been the large number of
transversal branches needed to synthesize high-order transfer
functions, usually leading to circuits with excessive physical
dimensions. In the most basic transversal structures, which are
made up of constant amplitude-weight and time-delay blocks
and where interactions between signals is the only available
medium to define the bandpass filtering response, this imped-
iment has become unaffordable . Lately, the inclusion of
frequency-dependent processing blocks in the filter branches
or even the use of more advanced feedfordward architectures
emerging as generalizations of the transversal arrangement
have allowed the size constraint in high-selectivity situations to
be partially circumvented, but at the expense of increasing the
design complexity , . The introduction of monolithic-mi-
crowave integrated-circuit (MMIC) technology has also been
important to demonstrate transversal filtering concepts in small
circuits for low-pass, high-pass, bandpass, and stopband appli-
cations with the tunability as an added feature , .
A new alternative to designing microwave bandpass filters
using signal-interference sections based on the branch-line di-
rectional coupler is presented in this paper . The idea is to
use the branch-line coupler as a transversal filtering section by
connecting the coupled ports to opened load stubs. Thus, taking
the isolated port of the coupler as the output node, two input-to-
output signal paths are generated so that bandpass transfer func-
signal components derived from the input signal and traveling
through these propagation paths.
The main advantage of the proposed transversal filtering
topology with respect to the existing ones is its capability to
amplitude and phase relationships between the transversal sig-
nals to be combined. This is experimentally proven in this study
0018-9480/$20.00 © 2005 IEEE
3222IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 10, OCTOBER 2005
Detail of the transversal filtering section based on the branch-line
with the construction and characterization of two microstrip
filter prototypes at 5 GHz. Other relevant features to be re-
marked upon are the simplicity of the design process and the
flexibility to adjust the main characteristics of the transversal
section transfer function by acting on its design parameters.
II. TRANSVERSAL FILTERING SECTION BASED ON THE
BRANCH-LINE DIRECTIONAL COUPLER
The detail of the transversal filtering section based on the
branch-line directional coupler is given in Fig. 1. As shown, the
transversal section is made up of a typical branch-line coupler
ending in an open circuit. The output node of the transversal fil-
tering section is just the isolated port of the branch-line coupler.
The characteristic impedances of the transmission lines making
up the coupler are denoted as
and characteristic impedances of the load stubs are referred to
, , and, , respectively.
The operating principle involved in the proposed filtering
section consists of obtaining the overall frequency-selective
transfer function from the feedforward combination of the
signal components derived from the input signal, and propa-
gating through the different paths of the branch-line coupler
in the transversal configuration. The basic idea is to generate
power transmission zeros out of the intended filter passband
through destructive signal interactions, preserving a construc-
tive interference at the center frequency. Thus, sharp-rejection
bandpass filtering responses with perceptible stopbands can be
The theoretical analysis of the branch-line coupler in the
transversal configuration is described later. The aim is to es-
tablish some design rules to obtain sharp-rejection bandpass
filtering responses by means of a suitable selection of the values
for the design parameters of the transversal section.
and . The electrical lengths
A. Design of the Load Transmission-Line Segments
A branch-line directional coupler designed for a 3-dB cou-
pling factor is considered as an initial approach, i.e.,
and , where
The characteristic impedances
mission line segments are assumed to be equal to
generator and output load connected to the ports 1 and 4 of the
coupler are matched to the impedance
is the reference impedance.
and of the load trans-
. The input
Under the previous conditions, the following matrix system
erenced to the impedance
in the four ports of the coupler
and can be established:
3-dB branch-line coupler , and
nary unity. Note that only four different scattering parameters
for characterizing the branch-line coupler are needed as a result
of being a reciprocal lossless network with two planes of sym-
metry. Furthermore, the following relationships derived from
the termination conditions of the directional coupler operating
as a transversal filtering section have been used:
are the scattering parameters of the
is the imagi-
From solving (1), the following analytical expressions for
the reflection and transmission coefficients
transversal filtering section are obtained:
The bandpass filtering response of the transversal section
is strongly influenced by the action of the transmission-line
segments loading the directional coupler. The main task of
these load stubs is to generate appropriate amplitude and phase
relationships between the signal components to be combined.
Therefore, the suitable design of the electrical lengths
becomes a key issue to achieving high-selective filtering
The following considerations are established to synthesize a
symmetrical bandpass transfer function with a maximum power
transmission at a specified center frequency
1) The power transmission maximum condition is fulfilled
by forcing a constructive interference at
passband of the transversal section transfer function is
not destroyed by the signal interaction. As the result of
the passiveness and lossless property satisfied by the
. Thus, the
GÓMEZ-GARCÍA et al.: USING BRANCH-LINE DIRECTIONAL COUPLER IN DESIGN OF MICROWAVE BANDPASS FILTERS3223
transversal filtering section (i.e.,
), the aforementioned condition is achieved by
assuming that the 3-dB branch-line coupler is designed
for a perfect power division at
Equation (4) results in
is the scattering matrix of the 3-dB branch-line
is considered without a loss of generality.
2) The symmetry condition of the transversal filtering sec-
tion response in relation to the center frequency
obtained from imposing the appropriate relationship be-
tween the electrical lengths of the load transmission-line
segments. As is well known, the following properties are
satisfied by the scattering parameters of the 3-dB branch-
line coupler designed at
and the phase of a complex number.
From the definitions given in (3), it is deduced that the
properties (7) will also be assured for the reflection and
transmission coefficients of the transversal filtering sec-
tion only if the following relation is imposed on the elec-
trical lengths of the load stubs:
and denote, respectively, the absolute value
Taking into account the linear frequency dependence of
the electrical length of a transmission-line segment as
, the previous condition leads to
From (6) and (9), the following relations are obtained:
Thus, by using the above expressions to design the load stubs,
symmetrical bandpass frequency-selective responses are de-
rived from the transversal filtering section.
filtering section on the electrical lengths of the load stubs (?
? ? ?
? ? ). (a) ? ? ?. (b) ? ? ?.
Dependence of the power transmission response of the transversal
? ? ???,
The effect of the electrical lengths
transmission response of the transversal filtering section is
analyzed in Fig. 2. As shown, narrower bandwidths and
sharper passband-to-stopband transitions are obtained when
higher values for the index
by increasing the frequency variation velocity of the phase
difference generated between the feedforward signals to be
combined since a faster phase-difference rotation implies a
signal interaction going from a passband constructive interfer-
ence to a stopband suppression in a narrower frequency span.
Nevertheless, signal-amplitude relationships are also important
in the proposed transversal scheme to obtain filtering responses
exhibiting a good out-of-band rejection performance. Thus, the
best transfer function regarding close-to-passband selectivity
and stopband rejection is achieved for
out-of-band power transmission zeros through a mutual can-
cellation between signal components with optimum amplitude
and phase characteristics.
andon the power
are selected. This is caused
) as the result of generating
3224IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 10, OCTOBER 2005
B. Control of Bandwidth and Power Transmission Zeros
The passband behavior and the out-of-band performance of
the transversal filtering section are strongly dependent on the
characteristic impedance design parameters. Thereby, these pa-
resulting filtering response such as the bandwidth, the location
of the out-of-band power transmission zeros, or the attenuation
levels in the stopbands.
Here, the following considerations are taken into account.
1) The transversal filtering section behaves as a
sion-line segment at the center frequency
is forcedto accomplish thepowertrans-
mission maximum requisite at
2) The symmetry condition of the transversal filtering sec-
tion response in relation to
(10), not depending on the characteristic-impedance de-
Thus, the design parameters to be used for controlling the
transversal filtering section performance are
The dependence of the transversal section transfer function on
these parameters has been researched (case
The main results are described below.
). Therefore, the
is assured by satisfying
, , and.
• The characteristic impedances
stubs are useful to adjust the bandwidth of the transversal
section filtering response. This is proven in Fig. 3(a) for
the design parameter
. As shown, a narrower band-
width of the stopbands are slightly reduced with the de-
crease in the bandwidth, the general shape of the out-of-
band filtering response is preserved.
• The characteristic impedance
the branch-line coupler is appropriate to control the
out-of-band performance of the transversal filtering sec-
tion. This is demonstrated in Fig. 3(b). As observed, both
the spectral width and power rejection levels of the stop-
bands are varied considerably by actingon the
the result of modifying the position of power transmission
nulls. Moreover, stopband control is achieved without
distorting the filter passband.
tain filtering responses exhibiting a sharp filter-flank steepness
and high attenuation levels in the stopbands. Therefore, the se-
lection of the values for the transversal section design param-
eters must always be directed to the generation of the power
The generation of out-of-band power transmission zeros de-
pending on the characteristic impedance design parameters has
been researched. Specifically, the curves corresponding to the
3-dB relative bandwidth
dBand the relative spectral sep-
aration between the adjacent transmission zeros
and of the load
the 3-dB relative bandwidth. ?
between adjacent transmission zeros. (a) Influence of the characteristic
on the power transmission response of the transversal filtering
section (? ? ?, ? ? ?, ?
? ? ???, ?
control. (b) Influence of the characteristic impedance ?
transmission response of the transversal filtering section (? ? ?, ? ? ?,
? ? ? ? ). Out-of-band performance control.
refers to the relative spectral separation
? ? ). Bandwidth
on the power
transversal section transfer function as a function of the param-
in Fig. 4. These curves have been obtained numerically, being
drawn only for the
value range in which the power trans-
mission nulls are produced. As shown, the
be used is reduced when a lower
from Fig. 4 that there is an infinite number of solutions for the
and satisfying a fixed bandwidth specifica-
tion for the transversal filtering section. As a design guideline,
bandpass transfer functions with higher out-of-band attenuation
levels are obtained when lower
This is done at the expense of increasing the difference between
, i.e., decreasing the sharpness of the pass-
band-to-stopband filter transition.
) are detailed
value range to
value is chosen. Note also
andvalues are selected.
GÓMEZ-GARCÍA et al.: USING BRANCH-LINE DIRECTIONAL COUPLER IN DESIGN OF MICROWAVE BANDPASS FILTERS3225
and the relative spectral separation between the adjacent transmission zeros
(dashed line)of the transversal filtering section on the design parameters
? , ?
(? ? ?, ? ? ?, ? ? ?
Dependence of the 3-dB relative bandwidth ?dB(continuous line)
? ? ).
III. EXPERIMENTAL RESULTS
The usefulness of the transversal filtering section based on
the branch-line directional coupler in microwave bandpass filter
design is experimentally validated here.
Specifically, the design, construction in microstrip tech-
nology, and characterization of both a passive and an active
microwave filter prototype at 5 GHz using the proposed
transversal filtering section is described below.
A. Microwave Passive Filter With Sharp-Rejection Stopbands
The design of a microwave passive bandpass filter with
sharp-rejection stopbands has been approached. This kind of
filter is especially suitable for the input duplexer of transceiver
where hard isolation levels between the adjacent channels cor-
responding tothetransmitter and receiver modules are required.
The overall filter has been derived empirically, but using the
design rules provided in Section II, starting from the cascade
connection of two identical transversal filtering sections based
on the branch-line coupler. Thus, without coupling gaps be-
tween the transversal sections and the input/output lines, the
filter insertion losses are minimized by avoiding any radiation
and inter-stage mismatching losses. Consequently, the filter
noise performanceis alsoimproved.The initialspecificationsto
be met are a 5-GHz center frequency, a 3-dB relative bandwidth
equal to 10%, and a power transmission rejection level higher
than 40 dB in the bands allocated at 3.3–4.2 and 5.8–6.7 GHz.
Note that if the two transversal filtering sections are directly
cascaded, then the power transmission parameter of the overall
tering parameters of the transversal section. Obviously, the re-
and are the reflection and transmission scat-
Simulated power transmission response of the ideal designed passive
range since the condition
fore, the overall filter should be optimized as a unit using the
design parameters of the transversal filtering section, the trans-
mission-line segment cascading the sections, and the filter input
line as degrees of freedom.
The commercial simulator HP-EEsof Libra has been used in
the design and optimization process of the filter. For both the
transversal filtering sections, the obtained values for the char-
acteristic impedances of thetransmission-line segmentsmaking
is thereference impedance. Theloadstubs are designed as 50-
(, ) line segments with electrical lengths
andat 5 GHz. The filter input line and the line
cascading the transversal sections are implemented as quarter
acteristic impedance, respectively.
The simulated power transmission response of the ideal de-
signed overall filter is shown in Fig. 5. The attenuation mask
to be satisfied is also provided. As shown, a highly selective
filtering response with sharp-rejection stopbands is achieved
avoiding the use of cross-couplings.
The designed ideal filter has been constructed in microstrip
technology. The parameters of the selected Cu-clad microstrip
substrate are a relative dielectric constant
m, and metal thickness
making use of the line calculator LineCalc. A photograph of the
developed microstrip filter prototype is given in Fig. 6. When
the circuit size is a critical issue, further reductions in the filter
surface area can be achieved by using fractal-type geometrical
arrangements for the couplers and the load stubs  or other
miniaturization techniques –.
The measured and simulated power reflection and transmis-
sion responses of the constructed filter prototype are shown in
Fig. 7(a). The results corresponding to the single transversal fil-
tering section are given in Fig. 7(b). These measurements have
is not satisfied in all the specified frequency
is not always met. There-
3226IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 10, OCTOBER 2005
sharp-rejection stopbands at 5 GHz.
Constructed microstrip passive bandpass filter prototype with
of the constructed passive filter prototype and the single transversal filtering
section. (a) Overall passive filter. (b) Transversal filtering section.
Simulated and measured power reflection and transmission responses
Block diagram of the proposed high-selective microwave active
been obtained by making use of an HP-8510C network ana-
lyzer. The increase in selectivity obtained from adding a second
transversal stage must be highlighted.
The main characteristics of the overall filter measured re-
sponse are described below. The filter passband is exactly
centered at 5 GHz, having a 3-dB relative bandwidth equal to
10.71%. The power transmission losses at the center frequency
are 1.63 dB. The stopbands, situated at both sides of the filter
passband, exhibit a power rejection level higher than 40 dB
throughout 3.3–4.2 and 5.67–7.03 GHz.
Note also that larger stopband widths can be achieved by
bandstop planar filtering cell, as described in –. Thus,
by locating the rejected bands of the wide-band bandstop cell
in the frequency ranges to be suppressed, an overall filtering
response demonstrating an improved out-of-band power rejec-
tion performance and preserving both the in-band and close-to-
passband characteristics of the transversal section-based filter is
B. High-Selective Microwave Active Bandpass Filter
The branch-line directional coupler has been applied to the
design of a high-selective microwave active bandpass filter as a
second practical example.
The proposed active filter structure is shaped by the cas-
cade connection of a transversal filtering section based on the
branch-line coupler, an active isolation stage, and a passive
filter (Fig. 8). The passive filter is designed as a low-order ap-
proximation to the overall transfer function to be synthesized.
The transversal filtering section is used to increase the passive
filter selectivity through the generation of multiple out-of-band
power transmission zeros. Thus, the profile of the total filtering
response is obtained from the combination of the passive filter
and transversal section transfer functions. The active isolation
stage is included for providing both a good matching between
the passive blocks and power transmission gain in the filter
A microstrip active bandpass filter circuit has been designed
quency, a 3-dB relative bandwidth equal to 17.5%, and a power
transmission rejection level greater than 35 dB at frequencies
whose separation from 5 GHz is more than 1 GHz.
The ideal filter design has been carried out using a general-
ization of the design technique described in  for two-branch
channelized active bandpass filters, whose transfer function is
GÓMEZ-GARCÍA et al.: USING BRANCH-LINE DIRECTIONAL COUPLER IN DESIGN OF MICROWAVE BANDPASS FILTERS3227
designed active filter.
Simulated normalized power transmission response of the ideal
at 5 GHz.
Constructed high-selective microstrip active bandpass filterprototype
responding to the passive filters embodied in the filter branches
and an interference term caused by the action of the delay sec-
tion of the transversal filtering section designed in the previous
design parametersallowing amaximum flatnessperformancein
the overall filter response to be obtained are directly computed:
a second-order Chebyshev response with 20.3% relative band-
width at 1.26-dB ripple.
designed ideal filter is shown in Fig. 9. The attenuation mask to
Chebyshev-type filtering response is synthesized. Furthermore,
since the prefixed set of specifications would be satisfied by a
of six, the increase in selectivity obtained from cascading the
transversal section must be emphasized.
A photograph of the constructed microwave active filter pro-
totype in microstrip technology is shown in Fig. 10 (parameters
of the substrate were given in Section III-A). As observed, the
of the constructed active filter prototype and the active-isolation-stage
Simulated and measured power reflection and transmission responses
passivefilter has been implemented in a coupled-line configura-
amplifier sections with low input-to-output power transmission
boro, NC) and
-type resistive attenuators matched to 50
The simulated and measured power reflection and transmis-
sion responses of the constructed microstrip active filter proto-
type are compared in Fig. 11. The characterization of the set
made up of the active isolation stage and the passive filter is
also included. The main parameters of the overall filter mea-
sured power transmission response are a center frequency equal
to 4.91 GHz, a 17.8% 3-dB relative bandwidth, and a power re-
jection level higher than 40.4 dB within the specified rejected
bands. The power transmission gain at the center frequency is
The main features of the proposed active-filter topology must
be remarked. By only interacting two signal components in the
branch-line coupler stage, an overall selectivity performance
3228IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 10, OCTOBER 2005
comparable to that of more complex active-filter topologies has
been demonstrated , , . This is done with an obvious
reduction in the number of elements needed to achieve similar
results in other filtering architectures and, hence, with a cir-
cuit-size advantage. Moreover, the main drawback of past re-
search dealing with active-filter design techniques regarding the
lack of analytical procedures to synthesize the intended filtering
The design of microwave bandpass filters using novel
transversal filtering sections has been approached in this paper.
branch-line coupler with the coupled ports connected to appro-
priate opened load stubs just to generate two input-to-output
signal paths. Thus, using signal-interference techniques, band-
pass transfer functions with perceptible stopbands can be
obtained from the feedforward combination in the isolated
port of the coupler of the different signal components derived
from the input signal and traveling through these signal paths.
Furthermore, design guidelines to control the bandwidth and
the out-of-band performance of the transversal filtering section
response have been provided. Finally, to prove the experimental
viability of the proposed transversal filtering section in mi-
crowave bandpass filter design, two microwave filter prototypes
at 5 GHz have been manufactured in microstrip technology
and characterized. These are a microwave passive filter with
sharp-rejection stopbands, and a highly selective microwave ac-
tive filter. The resulting agreement between the measurements
and simulations has been fairly close. Hence, the suitability of
this kind of filters based on signal-interference techniques to
complexity advantages over more conventional filter solutions
has been demonstrated. Future research is the generalization of
theproposed filter topologyto lumped-elementhybridsfor their
use in other technologies such as MMICs, and the research on
novel high-performance transversal signal-interference filtering
sections with special emphasis on ultra-wide-band applications.
The authors thank J. Mellado and J. M. Montero, both of
the Grupo de Microondas y Radar, Departamento de Señales,
Sistemas y Radiocomunicaciones, Universidad Politécnica
de Madrid, Madrid, Spain, for helping in the manufacturing
process of the filter prototypes. The authors would also like to
thank the anonymous reviewers for their valuable suggestions
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Roberto Gómez-García (S’02) was born in Madrid,
Spain, in 1977. He received the Ingeniero de Teleco-
municación degree from the Universidad Politécnica
rently working toward the Ph.D. degree at UPM. His
Ingeniero de Telecomunicación thesis concerned the
design of microwave channelized active filters. His
of novel tunable and active microwave filter topolo-
Since October 2000, he has been with the Grupo
de Microondas y Radar, Departamento de Señales, Sistemas y Radiocomuni-
caciones (SSR), UPM. His research activities are in the area of high-frequency
circuit design for communication and radar systems.
GÓMEZ-GARCÍA et al.: USING BRANCH-LINE DIRECTIONAL COUPLER IN DESIGN OF MICROWAVE BANDPASS FILTERS3229 Download full-text
José I. Alonso (M’04) was born in Villacañas
(Toledo), Spain. He received the Ingeniero de
Telecomunicación and Ph.D. degrees from the
Universidad Politécnica de Madrid, Madrid, Spain,
in 1982 and 1989, respectively.
From 1982 to 1985, he was a Microwave Design
Engineer with Telettra España S.A. (now Alcatel
Standard S.A.). In 1985, he joined the Departamento
Escuela Técnica Superior de Ingenieros de Tele-
comunicación, Universidad Politécnica de Madrid,
where he is currently a Full Professor. He has taught courses in microwave
circuits design, electrical networks and filter theory, test and measurements of
microwave circuits, and laboratories related to analog and digital communica-
tion systems. He has developed his research with the Grupo de Microondas y
Radar in the areas of the analysis and simulation of high-speed/high-frequency
integrated circuits and their interconnections, the computer-aided design and
measurements of hybrid and GaAs monolithic microwave integrated circuits
(MMICs) and their applications in the development and implementation of
mobile, satellite, optical-fiber communication, and adaptive antenna systems.
He is also involved in the development of circuits and subsystems for the
local multipoint distribution system (LMDS) and wireless local-area networks
Daniel Amor-Martín (M’04) was born in Madrid,
Spain, in 1980. He received the Ingeniero de Teleco-
municación degree from the Universidad Politécnica
rently working toward the Ph.D. degree at UPM.
Since November 2003, he has been with INDRA
the fields of microstrip filter design and heterolithic-
research interests are in the area of high-frequency
circuit design for communication and radar systems