This paper introduces a novel branch-line 90° hybrid coupler incorporating varactor diodes which allow tuning of the frequency response. A design covering the DCS, PCS and IMT2000 cellular frequency bands (1710-2170 MHz) is presented. Given a varactor tunability of 2.5:1, simulations suggest 20 dB return loss and 3±1 dB coupling is achievable across each transmit and receive sub-band by tuning the varactors. These results offer an improvement over a conventional single-section branch-line hybrid centred at 1950 MHz, and some miniaturisation is also achieved due to the capacitive loading. A prototype is constructed using commercially available varactor diodes, and reasonable agreement between the measured and simulated results is achieved

Fardin, E

Ghorbani, K

Holland, A

RMIT Research Repository

A Varactor Tuned Branch-Line Hybrid Coupler
Ernest A. Fardin, Kamran Ghorbani and Anthony S. Holland
School of Electrical and Computer Engineering
RMIT University
GPO Box 2476V, Melbourne, 3001, Australia
Email: efardin@ieee.org
Telephone: +61 3 9925 3250
Fax: +61 3 9925 2007
Abstract— This paper introduces a novel branch-line 90◦
hybrid coupler incorporating varactor diodes which allow tuning
of the frequency response. A design covering the DCS, PCS and
IMT2000 cellular frequency bands (1710-2170 MHz) is presented.
Given a varactor tunability of 2.5:1, simulations suggest 20
dB return loss and 3±1 dB coupling is achievable across
each transmit and receive sub-band by tuning the varactors.
These results offer an improvement over a conventional single-
section branch-line hybrid centred at 1950 MHz, and some
miniaturisation is also achieved due to the capacitive loading. A
prototype is constructed using commercially available varactor
diodes, and reasonable agreement between the measured and
simulated results is achieved.
I. INTRODUCTION
With the proliferation of wireless applications over the past
decade, there is a need to incorporate radios operating at differ-
ent frequency bands into a single hardware device. Separate
transceivers for each band lead to an increased component
count and hence cost [1]. This means there is an incentive
to employ frequency agile components in future RF front-end
designs which must cover several frequency bands. Possible
alternatives would be to use broad band components, or to
switch between multiple narrow band components. However,
these solutions often require more circuit real-estate and result
in higher cost.
Varactor diodes have been used for many years to elec-
tronically tune microwave circuits. They have previously been
integrated into a microstrip directional coupler for the 4 GHz
band [2]. The purpose of the varactors in [2] was to vary the
coupling level from 4 dB to 20 dB. More recently, a varactor
tuned LC resonator was used to extend the operating frequency
range of a microstrip directional coupler [3]. In the resonator-
based tunable coupler, the regions of flat coupling, high return
loss and high directivity are narrow-band, but the return loss
and directivity nulls can be tuned in frequency by the varactor.
This paper applies the varactor tuning technique to a 3 dB
hybrid coupler.
A schematic diagram of the proposed hybrid coupler is
shown in Fig. 1. The design is based on the branch-line 90◦
hybrid coupler, a standard component in many microwave
systems. The conventional design employs two 35 Ω series
arms and two 50 Ω shunt arms, 1/4-wavelength long at the
centre frequency, to provide 3 dB power split with 90◦ phase
offset between the coupled ports [4]. In this design, four
Y1 1θ, Y1 1θ,
Y1 1θ, Y1 1θ,
,2 θY 2
,2 θY 2
,2 θY 2
,2 θY 2
C
C
CC
b
1 2
b’
4 3
a a’
Fig. 1. Schematic diagram of the varactor tuned hybrid coupler.
varactors are employed to extend the operating frequency
range of the conventional hybrid, while maintaining a 3 dB
coupling level. Changing the varactor capacitance, C, modifies
the electrical length of the series and shunt transmission line
sections, and therefore the frequency at which 3 dB coupling
is achieved.
II. ANALYSIS OF VARACTOR TUNED HYBRID
The equations for the S-parameters of the varactor tuned
hybrid can be determined by the even-odd mode technique [5].
With aa′ and bb′ in Fig. 1 alternately open circuit and short
circuit, and by considering the fourfold symmetry of the
structure, the four subnetworks shown in Fig. 2 are obtained.
The capacitor only appears in (b) and (c), since it is open
circuit and short circuit in (a) and (d), respectively. Starting
with the circuit of Fig. 2(a),
Yin,1a = jY1 tan θ1 (1)
Yin,2a = jY2 tan θ2 (2)
where Yin,1a and Yin,2a are the input admittances of the
microstrip lines with characteristic admittance Y1 and Y2 and
electrical length θ1 and θ2, respectively. In this case, both
microstrip lines are terminated in an open circuit. Therefore,
0-7803-9433-X/05/$20.00 ©2005 IEEE. APMC2005 Proceedings 
 
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(a)
(c) (d)
(b)
a
b
1
a
b
1
a
b
1
a
b
1
O.C.
C/2
C/2
,
,Y2 2
O.C.
θ
Y 1
,Y1 1θ
,Y2 2θ ,Y2 2θ
,Y 1θ
θ
,Y2 2θ
,Y1 1θ
O.C.
O.C.
S.C. S.C.
S.C.
S.C.1
1
Fig. 2. Even-odd mode subnetworks (a) aa′ and bb′ open circuit (b) aa′
open circuit, bb′ short circuit (c) aa′ short circuit, bb′ open circuit (d) aa′
and bb′ short circuit.
the reflection coefficient at port 1 is
Γa =
Yo − (Yin,1a + Yin,2a)
Yo + Yin,1a + Yin,2a
(3)
where Yo is the characteristic admittance. Similarly,
Yin,1b =
Y1
j tan θ1
(4)
Yin,2b =
1
Y2
+ ( 2ωC ) tan θ2
( 1Y2 ) · ( 2jωC + j 1Y1 tan θ2)
(5)
Yin,1c =
1
Y1
+ ( 2ωC ) tan θ1
( 1Y1 ) · ( 2jωC + j 1Y1 tan θ1)
(6)
Yin,2c =
Y2
j tan θ2
(7)
Yin,1d = Yin,1b (8)
Yin,2d = Yin,2c (9)
Finally, by superposition, the S-parameters can be calculated
using
S11 =
1
4
(Γa + Γb + Γc + Γd) (10)
S21 =
1
4
(Γa − Γb + Γc − Γd) (11)
S31 =
1
4
(Γa − Γb − Γc + Γd) (12)
S41 =
1
4
(Γa + Γb − Γc − Γd) (13)
where Γa, Γb, Γc and Γd are the reflection coefficients at port
1 under the four different conditions illustrated in Fig. 2(a)-(d).
In order to simulate the circuit, the values of Yo and Y2 are set
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
−20
−18
−16
−14
−12
−10
−8
−6
−4
−2
0
Frequency (GHz)
M
ag
ni
tu
de
 (d
B)
S11
S21
S31 (a) 
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
50
100
150
200
250
Frequency (GHz)
Ph
as
e 
O
ffs
et
 (°
)
∠S21−∠S31 Meas.
∠S21−∠S31 Sim.
(b) 
Fig. 3. Coupler characteristics at DCS uplink band (a) measured and
simulated S-parameters (b) measured and simulated phase offset between
coupled ports. The measured and simulated results are presented as point
series and dashed lines, respectively.
to 1/50 Ω−1, and Y1 is set to 1/35 Ω−1, as in the conventional
design [4]. The electrical length of the microstrip lines can be
calculated using
θ =
ω
√
r,eff
c
(14)
where  is the physical length of the line, r,eff is the effective
dielectric constant of the substrate material, and c is the speed
of light.
III. SIMULATED AND MEASURED RESULTS
In order to validate the design prior to fabrication, the circuit
was simulated using both the analytical solutions (10) to (13)
and Agilent Advanced Design System 2004A (ADS) software.
The substrate material is 0.508 mm Rogers 4003C (r = 3.38).
A circuit model identical to that of Fig. 1 was simulated
using ADS, with series and shunt branch line lengths of 18
mm. The simulation results, shown as dashed lines in Figs. 3
and 4, were obtained using (10) to (13). In Figs. 3 and 4, the
varactor capacitance is set to 2.0 pF and 0.8 pF, respectively.
Adjusting the varactor capacitance over this range allows the
tunable hybrid to cover 1710 to 2170 MHz with better than 20
dB return loss. The required varactor tuning range of 2.5:1 is
well with in the capability of commercially available varactor
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TABLE I
SUMMARY OF MEASURED RESULTS
Frequency Band Band Edge (MHz) Coupling (S21, dB) Return Loss (dB) Coupled Port Phase Offset (◦) Vbias (V )
DCS uplink 1710 3.7 21.1 89.8 2.1
1785 3.8 22.4 92.8
DCS downlink 1805 3.5 26.8 90.7 2.7
1850 3.6 25.9 92.0
PCS uplink 1850 3.5 24.6 90.9 3.2
1910 3.5 25.0 92.2
PCS downlink 1930 3.4 24.7 91.0 4.1
1990 3.5 26.1 92.2
IMT2000 uplink 1920 3.5 24.7 90.9 4.0
1980 3.5 26.2 92.0
IMT2000 downlink 2110 3.3 27.4 91.6 8.0
2170 3.4 22.3 92.1
diodes. As expected, the results of the ADS simulation were
identical to the analytical values. Note that ideal varactors are
assumed for the simulated results.
A prototype circuit was constructed using Skyworks
SMV1231-079 varactors in place of the ideal components. DC
bias was applied to port 1 via a bias tee, and DC blocking
capacitors were placed at ports 2, 3 and 4. A 10 nH chip
inductor was placed between the common node of the varactor
diodes and ground, in order to establish a bias voltage across
the diodes.
The measured results are presented as marker series in
Figs. 3 and 4. Bias voltages of 2.1 and 8.0 V were ap-
plied to tune the hybrid to the DCS uplink (Fig. 3) and
IMT2000 downlink (Fig. 4), respectively. It is evident from
these results that the coupler bandwidth decreases as the
varactor capacitance increases. The bandwidth should still be
sufficient to cover a single cellular uplink or downlink channel
with acceptable coupling variation. There is good agreement
between measured and simulated results in Fig. 4. However,
the analytical model loses accuracy beyond 1.8 GHz in Fig. 3.
This could be attributed to the series resistance and lead
inductance of the varactor diodes. Also, a short length of high
impedance transmission line must be placed between the anode
of each diode and the common node, for layout purposes. The
effect of this transmission line was not modelled.
A summary of measured results for each uplink and down-
link channel in the DCS, PCS and IMT2000 frequency bands
is presented in Table I. The coupling level at ports 2 and 3
is within 3±1 dB and the return loss better than 20 dB in
each case. A coupled port phase offset of 90±3◦ is achieved.
In comparison, the S11 response of a conventional single-
section branch-line hybrid designed for 1950 MHz has a 20 dB
return loss bandwidth of ∼200 MHz. Each of the four branch
lines in the conventional design [4] is 23.3 mm long, while
the varactor tuned design uses 18 mm branches. Some useful
miniaturisation is therefore achieved by the use of varactors.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
−20
−18
−16
−14
−12
−10
−8
−6
−4
−2
0
Frequency (GHz)
M
ag
ni
tu
de
 (d
B)
S11
S21
S31(a) 
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
0
50
100
150
200
250
Frequency (GHz)
Ph
as
e 
O
ffs
et
 (°
)
∠S21−∠S31 Meas.
∠S21−∠S31 Sim.
(b) 
Fig. 4. Coupler characteristics at IMT2000 downlink band (a) measured
and simulated S-parameters (b) measured and simulated phase offset between
coupled ports. The measured and simulated results are presented as point
series and dashed lines, respectively.
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IV. CONCLUSIONS
This paper has presented a novel branch-line coupler con-
figuration which uses varactors to extend the bandwidth of
the conventional 3 dB branch-line hybrid design. Equations
for the S-parameters of the device have been derived by
the even-odd mode analysis technique. The suitability for
implementation was demonstrated by even-odd mode analysis
and ADS simulations. A single-section hybrid covering 1710
to 2170 MHz with 3±1 dB coupling and 20 dB minimum
return loss was fabricated. This design approach may provide
a lower cost alternative to implementing several conventional
90◦ hybrids in a multiband transceiver.
ACKNOWLEDGMENT
The authors would like to thank the CASS Foundation, for
their support of the project. Thanks also to RFMW, Ltd. for
supplying the varactor diode samples, and to Tri Components,
Pty. Ltd. for supplying chip inductor samples.
REFERENCES
[1] A. R. Rofougaran, M. Rofougaran, and A. Behzad, “Radios for the next-
generation wireless networks,” IEEE Microwave, vol. 6, pp. 38–43, 2005.
[2] S. Toyoda, “Variable coupling directional couplers using varactor diodes,”
in IEEE MTT-S Int. Microwave Symp. Dig., vol. 82, 1982, pp. 419–421.
[3] C.-S. Kim, C.-S. Yoon, J.-S. Park, D. Ahn, J.-B. Lim, and S.-I. Yang,
“Design of the novel varactor tuned directional coupler,” in IEEE MTT-S
Int. Microwave Symp. Dig., vol. 4, 1999, pp. 1725–1728.
[4] D. M. Pozar, Microwave Engineering, 2nd ed. New York: John Wiley,
1998.
[5] R. E. Collin, Foundations for Microwave Engineering. New York:
McGraw Hill, 1992.
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