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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

couplerwithsuitabletransmission-linesegmentsendinginanopen

circuitandtakingtheisolatedportastheoutputnode.Thus,under

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

zeros,canbeeasilycontrolledbymeansofthedesignparametersof

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

filteringsectionbasedonthebranch-linecouplerisprovenwiththe

designandconstructioninmicrostriptechnologyoftwomicrowave

bandpass filter prototypes at 5 GHz.

Index Terms—Branch-line directional coupler, microstrip,

microwave bandpass filter, transmission line, transmission zero,

transversal filtering section.

I. INTRODUCTION

V

modern wireless and high-speed data communication appli-

cations [1]. 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

[2]. Regarding active filters, some other important factors, such

as linearity, noise performance, and power transmission gain,

must also be considered [3].

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

analogdomainofthetheoreticalconceptsinvolvedinclassicde-

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,

UniversidadPolitécnicade Madrid,

roberto.gomez.garcia@ieee.org; ignacio@gmr.ssr.upm.es).

D. Amor-Martín is with INDRA Sistemas S.A., 28850 Torrejón de Ardoz,

Madrid, Spain (e-mail: damor@indra.es).

Digital Object Identifier 10.1109/TMTT.2005.855140

28040Madrid,Spain(e-mail:

signtechniquesofdigitalfilters[4].Intransversalstructures,the

inputsignaltobefilteredissplitintoamultiplicityofsubcompo-

nentspropagatingthroughthedifferentfeedforwardsignalpaths

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 [5].

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 [6]. 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 [7], [8]. 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 [9], [10].

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 [11]. 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-

tionscanbeobtainedthroughthetransversalcombinationofthe

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

achievehigh-selectivityperformancesbyproducingappropriate

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

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3222IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 10, OCTOBER 2005

Fig. 1.

directional coupler.

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

whosecoupledportsareloadedwithtransmission-linesegments

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

as

, , 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

derived.

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

ofequationsrelatingtheincidentandreflected powerwavesref-

erenced to the impedance

in the four ports of the coupler

andcan be established:

(1)

where

3-dB branch-line coupler [12], 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-

(2)

From solving (1), the following analytical expressions for

the reflection and transmission coefficients

transversal filtering section are obtained:

andof the

(3)

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

responses.

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

and

.

. Thus, the

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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

imposing

,

(4)

assuming that the 3-dB branch-line coupler is designed

for a perfect power division at

, i.e.,

(5)

where

coupler.

Equation (4) results in

is the scattering matrix of the 3-dB branch-line

(6)

where

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

is

:

(7)

where

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

(8)

Taking into account the linear frequency dependence of

the electrical length of a transmission-line segment as

, the previous condition leads to

(9)

From (6) and (9), the following relations are obtained:

(10)

Thus, by using the above expressions to design the load stubs,

symmetrical bandpass frequency-selective responses are de-

rived from the transversal filtering section.

(a)

(b)

Fig. 2.

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

and

) as the result of generating

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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-

rameterscanbeusedforadjustingthemaincharacteristicsofthe

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

teristicimpedanceandquarter-wavelength-longtransmis-

sion-line segment at the center frequency

(,

relation

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-

sign parameters.

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.

charac-

for,

). Therefore, the

.

is assured by satisfying

,, and.

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-

widthisobtainedwhenahigher

thermore,althoughboththeattenuationlevelsandspectral

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.

Theout-of-bandpowertransmissionzerosareessentialtoob-

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

transmission nulls.

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

andof the load

valueisselected.Fur-

corresponding to

value as

of the

(a)

(b)

Fig.3.

the 3-dB relative bandwidth. ?

between adjacent transmission zeros. (a) Influence of the characteristic

impedance ?

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.

Controlofthetransversalfilteringsectionperformance.?dBdenotes

refers to the relative spectral separation

? ?

? ? ). Bandwidth

on the power

transversal section transfer function as a function of the param-

eters

,(,,

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

parameters

andsatisfying 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

dBand

, 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.

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GÓMEZ-GARCÍA et al.: USING BRANCH-LINE DIRECTIONAL COUPLER IN DESIGN OF MICROWAVE BANDPASS FILTERS3225

Fig. 4.

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

subsystemsdirectedatfull-duplexcommunicationapplications,

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

filter is

(11)

where

tering parameters of the transversal section. Obviously, the re-

andare the reflection and transmission scat-

Fig. 5.

filter.

Simulated power transmission response of the ideal designed passive

sult

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

upthecouplerare

and

is thereference impedance. Theloadstubs are designed as 50-

(,) line segments with electrical lengths

and at 5 GHz. The filter input line and the line

cascading the transversal sections are implemented as quarter

center-wavelength-longlinesegmentswith25-and 100-

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

thickness

m, and metal thickness

dimensionsofthelinesmakingupthefilterhavebeencomputed

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 [13] or other

miniaturization techniques [14]–[16].

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-

,where

char-

, dielectric

m. The