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An Application of Singly-Inductive Compensated Parallel-Coupled Microstrip Lines Ravee Phromloungsri

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An Application of Singly-Inductive Compensated Parallel-Coupled Microstrip Lines Ravee Phromloungsri
An Application of Singly-Inductive Compensated Parallel-Coupled Microstrip Lines
123
An Application of Singly-Inductive
Compensated Parallel-Coupled Microstrip
Lines
Ravee Phromloungsri1 and Mitchai Chongcheawchamnan2 , Non-members
ABSTRACT
A method using lumped inductors to compensate
unequal even and odd mode phase velocities in microstrip parallel- coupled lines is presented. The optimum inductor value and the electrical length of the
compensated coupled lines are given in closed-form
expressions. Improvement of 7 dB on the directivity of microstrip coupled lines over the uncompensated coupled lines at operating frequency f0 is obtained. To demonstrate the technique’s applicability,
the compensated coupled lines are used to improve
the amplitude/phase balance in a Marchand balun as
well as to suppress the spurious response in parallelcoupled filter. The experimental results of a compensated microstrip Marchand balun operating at 900
MHz and parallel-coupled microstrip filter operating
at 1.8 GHz are presented.
Keywords: Parallel-coupled lines, microstrip, coupled line resonator, Marchand balun, parallel-coupled
filter
1. INTRODUCTION
Parallel-coupled lines are extensively used in
microwave and millimeter-wave circuits for filters,
impedance matching networks, directional couplers,
baluns and combiners [1],[2], since they are easily incorporated in hybrid and monolithic microwave integrated circuits [3] which are commonly designed
with microstrip technology. However poor directivity [4] resulting from the inequality of even- and oddmode wave phase velocities [5],[6] can be obtained
from parallel-coupled microstrip lines.
The unequal phase velocities in parallel-coupled
microstrip lines not only cause poor directivity in
couplers but also significantly deteriorate the performance of other component based circuits. For example, it is well known that parallel-coupled microstripline filters does have asymmetrical passband response
and spurious responses at harmonics of the filter passband [7]. Recently [8], it was reported that degra-
dation in amplitude/phase balance of the microstrip
Marchand balun partly stems from the unequal phase
velocities. In the past decades, the notorious problem of unequal phase velocities in parallel-coupled microstrip lines has been tackled by several previously
proposed techniques. The techniques can be classified into two main categories,which are distributed
and lumped compensation approaches. The methodology based on the distributed approach is to modify
either the parallel-coupled line structure [9], [10], dielectric layer or ground plane, such that the phase
velocities of both modes are equalized. The main
disadvantage of this approach is lack of closed-form
design equations, meaning the design task relies heavily on the electromagnetic simulation stage which
in turn consumes much effort and computing time.
The lumped compensation approach [1],[11] involves
connecting external reactive components between or
shunted with the parallel-coupled lines’ ports. Based
on the reactive types, this approach can be categorized into two techniques, which are capacitive [1],[9]
and inductive compensation techniques [9],[11]. The
size of the lumped-compensated parallel-coupled lines
is about the same as the uncompensated coupled
lines. Another distinct advantage of the lumped compensation technique is its simple design procedure
because the closed-form design equations can be derived. The disadvantages of the technique are the
lumped components’ parasitics and difficulty in layout [1],[9]. In this paper, we present a simple effective
inductive compensation technique to improve the directivity of the parallel-coupled microstrip lines by
connecting small inductors in series with the coupled
lines’ ports.
The paper is organized as follows: Section 2
presents the proposed singly-inductive compensated
parallelcoupled lines. Applications of the inductively
compensated coupled-line circuit to the microstrip
Marchand balun and parallel-coupled microstrip filter
will be illustrated in Section 3. The paper is finally
concluded in Section 4.
2. THEORY
Manuscript received on July 23, 2006 ; revised on November
1, 2006.
1 The author is with Department of Telecommunication Engineering, E-mail:[email protected]
1,2 The authors are with Research Center of ElectromagneticWave Applications (RCEWs), Mahanakorn University of Technology (MUT), Thailand, E-mail: [email protected]
Due to the different phase velocities associated
with the even- and odd-mode wave propagation, parallelcoupled microstrip lines cannot easily achieve directivity values better than 12 dB [3]. Here, we propose an inductive compensation technique to equal-
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ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.1 February 2007
ize phase velocities in coupled microstrip lines, which
in turn leads to a high-isolation and hence highdirectivity coupled microstrip lines.
2. 1 Singly-Inductive Compensated ParallelCoupled Lines
Fig. 1 shows the schematic of parallel-coupled
lines using a single inductor for compensation. These
coupled-lines has characteristic impedance of Z0 and
Fig.1: Schematic of the singly-compensated parallelcoupled lines.
coupling coefficient of k which are related to the evenand odd-mode characteristic impedances (Zoe and
Zoo ) [3]. After some mathematical manipulation, we
obtain the optimum value of Ls as shown [12],[13]:½
¾
1
Zoe sinh θe − Zoo sinh θo Zo ∂
Ls =
Im
(1)
4πf0
Zoe sinh θo − Zoo sinh θe Zo ∂
where ∂ = cosh θo − cosh θe , the validity of the
singly inductive compensation technique for parallelcoupled line design is proven by comparing their directivity and isolation performances of the compensated coupled lines with those of the uncompensated
one [11, 12, 13, 14].
Fig.2: Schematic of the singly-compensated coupled
line based Marchand balun.
driving-point impedance at unbalanced port (port 1)
at f0 , denoted by Zmb (f0 ), is calculated from the Zparameters of the singly-compensated coupled line.
For our analysis, the electrical length of each compensated coupled-line section (θf ) is obtained by applying the following condition:Re[Zmb (f0 )] ≈ Zu
Hence,
½
θf (Ls ) = cot−1
4πf0 Ls + Zoo cot(π/2)Θ
Zoe + Zoo
¾
(4)
Designing the proposed balun with Ls and θf calculated from (1) and (4), the real part of Zmb (f0 )
is nearly equal to Zu while the imaginary part of
Zmb (f0 ) is inductive. This inductive part must be
cancelled out to make the compensated Marchand
balun well matched at the unbalanced port by a series
capacitor :Cs (f0 ) = 1/ω0 IM{Zmb (f0 )}
2. 2 Marchand Balun
(3)
(5)
The planar Marchand balun is basically formed by
two parallel-coupled line sections connected in backto-back configuration. Each coupled-line section has
coupling coefficient of k, characteristic impedance
of Z0 , and electrical length of π/2. This conventional (uncompensated) Marchand balun can transform unbalanced port impedance (Zu ) to balanced
port impedance (Zb ) if k is selected as follows [8]:k=q
1
2Zb
Zu
(2)
+1
It has been reported that the Marchand balun exhibits poor amplitude/phase balance when the circuit is realized in inhomogeneous media such as microstrip. The imbalance partly comes from the poor
directivity of the parallel-coupled microstrip lines [8],
hence an approach to improve the directivity of the
coupled lines can enhance the amplitude/phase balance of the Marchand balun.
For simplicity’s sake, the singly-compensated technique is applied to the Marchand balun. Fig. 3
shows the efficiency of proposed technique based on
the singly-compensated technique compare with the
uncompensated technique. The optimum value of
Ls can be calculated from (1). From Fig. 2, the
(a)
(b)
Fig.3: Analysis results of (a) amplitude and (b)
phase imbalance of the 50-150 Ω compensated Marchand balun with various values of the compensating
inductors.
An Application of Singly-Inductive Compensated Parallel-Coupled Microstrip Lines
The design procedure of the balun based on the
singly-compensated coupled lines starts by determining k from (2). With the known substrate and uncompensated coupled-line parameters, all electrical
parameters (Zoo , Zoe , θo , θe , εef f e , εef f o ) can be calculated. Subsequently, Ls , θf and Cs are calculated
from (1), (4) and (5). With this design procedure, a
balun design with good amplitude/phase balance and
good return loss at unbalanced port across a large
bandwidth can be obtained. The sensitivity to Ls
of the amplitude/phase imbalance is investigated for
the 50 − 150Ω Marchand balun. Based on the analysis results, variations of amplitude and phase balance resulting from different compensated inductors
are shown in Fig. 3 (a) and (b), respectively. The amplitude and phase balance of the singly-compensated
Marchand balun is excellent across the operation
bandwidth. The proposed technique is rather practical for the balun since the balance performance is
not very sensitive to the optimum value of the compensating inductor.
125
parallel-coupled lines operating at 1.0 GHz on RF600600 microwave substrate from Taconic.
(a)
(b)
Fig.4: Schematics of (a) the uncompensated, and
(b) the singly-compensated coupled-line resonators.
2. 3 Parallel-Coupled Filter
In an inhomogeneous media such as microstrip,
each coupled-line resonator in the parallel-coupled filter cooperatively contributes a spurious response at
twice the center frequency (2f0 ) and beyond. Since
the poor directivity is an outcome of phase-velocity
inequality, so the inductively compensated coupledline resonator with high directivity can suppress
the spurious response of the filter effectively [1],[7].
The resonators based on uncompensated and singlycompensated coupled lines are depicted in Fig. 4(a),
and (b). The optimum values of compensating inductors Ls in Fig. 4(b) can be determined from (1). To
preserve the original filter response, the transmission
response (S21 ) of the compensated resonator would be
preserved or minimal change from that of the uncompensated resonator. Hence this condition will be applied for extracting the electrical lengths of each compensated coupler. For tight coupling (k > -13 dB),
the electrical length of singly inductive-compensated
coupled-line resonator (θs ) can be determined by:o
n
π
θf (Ls ) = cot−1 4πf0 Ls − Zoo cot( Θ)/2Zoe (6)
2
and for loose coupling (-23 dB > k < -13 dB)
n
o
π
θf (Ls ) = cot−1 4πf0 Ls − Zoe + Zoo cot( Θ)/2Zoo
2
(7)
To explicitly show the spurious-suppression performances of singly-compensated coupled-line resonators, a resonator based on the proposed technique was designed and its frequency response is compared with the result of the uncompensated parallelcoupled resonator. We start with the uncompensated
coupled-line resonator, which is designed from 8.6 dB
Fig.5: Frequency responses of the singly- (—) compensated coupled lines resonator and the uncompensated case (- - - - -
The required values of Zoe , Zoo are 78.84 Ω and
36.48 Ω. Then, the values of Ls and θs for singlycompensated coupled-line resonators were calculated
from (1) and (6) and found to be 2.13 nH and 0.46π
respectively. The magnitude of S21 of the uncompensated coupled-line resonator is around -7 dB at the
first harmonic of the desired passband response (2f0 )
as shown in Fig.5. Comparing the responses obtained
from the singly-compensated resonators with that obtained from the uncompensated resonator, the magnitudes of S21 around f0 are nearly equal while the
responses around 2f0 and beyond are distinctly different. The suppression performances obtained from
the compensated coupled-line resonators at odd and
even harmonics of f0 are considerably better than
the uncompensated coupled-line resonator. For the
singly-compensated case, the degree of suppression
at 2f0 , 3f0 , and 4f0 are approximately 14, 7, and 7
dB, respectively. To apply the compensated coupledline resonators to bandpass filter design, the uncompensated coupled-line resonators are initially synthesized. Then each coupled-line resonator is replaced
with the singly-compensated coupled-line resonator.
All electrical parameters of the compensated coupledline resonators are calculated from (1), (6) and (7).
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ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.1 February 2007
3. DESIGN AND EXPERIMENTAL RESULT S21 S
3. 1 Marchand Balun
To prove the validity of the technique for the Marchand balun, 900 MHz microstrip 50-150 Ω impedance
transformation Marchand baluns based on the uncompensated and the singly-compensated coupled
lines were designed on FR4 substrate (εr = 4.55, h
= 1.6 mm, tan δ = 0.02). The Zoo and Zoe of the
coupled lines are 33.59 Ω and 74.42 Ω. Calculated
from (1) and (4), Ls , and θf are 1.95 nH, 0.42π, and
Cs is 11.5 pF, respectively. With these parameters,
the physical dimensions of two baluns were synthesized and shown in Table I. Fig. 6 (a) shows the
measured results of the uncompensated and proposed
Marchand balun. The conventional Marchand balun
achieved 3.5 dB transmission coefficient and less than
13 dB return loss at unbalanced port. The amplitude
balance is good only at 900 MHz, while at other frequencies, especially in high- frequency band edge, it
is very poor. Fig. 6 (b) shows the measured results
of the singly-compensated Marchand balun transmission coefficient at 900 MHz is around 3.7 dB and the
return loss of the unbalanced port is better than 25
dB. The amplitude balance of the proposed technique
is excellent, with ±0.1dB tracking from 700 MHz to
1.1 GHz as shown in Fig. 7. Comparing the measured 10 dB return loss bandwidth, the bandwidth of
the proposed technique is 170 MHz larger than the
uncompensated balun. The comparison of the measured output ports phase balance Frequency (GHz)
Fig.7:
Measured amplitude and imbalance of
the uncompensated(- - - - -)and the phase singlycompensated (—) Marchand balun.
(a)
(b)
Fig.8: PCB photographs of the fabricated (a) uncompensated and (b) singly- compensated Marchand
balun.
obtained from the uncompensated balun and the
singly-compensated balun, the uncompensated Marchand balun’s phase balance (dotted line) is within
±10◦ over 10% operating bandwidth, while the
singly-compensated Marchand balun’s phase imbalance (solid line) is less than ±1o degrees over 40%
bandwidth from 720 MHz-1.08 GHz. PCB photographs of the uncompensated and the proposed
singly-compensated Marchand balun are shown in
Fig. 8.
(a)
Table 1: Parameters of The Baluns at 0.9 GHz
Balun
Uncompensated
Singly inductive
Zoe
(Ω)
74.42
74.42
Zoo
(Ω)
33.59
33.59
Cs
(pF)
11.5
Ls
(nH)
1.95
θf
(rad)
0.5π
0.42π
3. 2 Parallel-Coupled Filter
(b)
Fig.6:
Measured insertion and return losses of
the (a) uncompensated (- - - - -) and (b) singlycompensated (—) Marchand balun.
The effectiveness of the singly-inductive compensated parallel-coupled filter is proven with two filter
designs. These two filters are an uncompensated and
singly-compensated design as shown in Fig. 9. The
filter prototype is a third-order Chebyshev bandpass
filter designed at center frequency (f0 ) of 1.8 GHz,
fractional
An Application of Singly-Inductive Compensated Parallel-Coupled Microstrip Lines
127
(a)
Fig.9: Schematics of (a) the uncompensated and (b)
the singly- compensated parallel-coupled filters.
(b)
Fig.11: PCB Photographs of (a) the conventional,
(b) the singly-compensated parallel-coupled filters.
(a)
Matlabr were used for simulation, data processing,
and display. The EM simulated results of the microstrip filter designed with the uncompensated and
compensated coupled-line resonators are shown in
Fig. 10 (a), while the measured results are shown
in Fig. 10(b). The measured spurious response obtained from the uncompensated parallel-coupled filter
(dash line) is around -13 dB at 2f0 .
More than 39 and 42 dB suppression of spurious
response at 2f0 and 3f0 are obtained from the singlycompensated parallel-coupled filter. Over the operating bandwidth, insertion losses of singly-compensated
parallel-coupled filters are less than 2.0 dB, while input and output return losses are better than 12 dB.
Fig. 11(a), and (b) show the PCB photographs of
two filters designed with the uncompensated, and
singly-compensated coupled-line section. The total
size of the singly-compensated parallel-coupled filters
is 17 × 70 mm2, which is about 85.4% of the uncompensated parallel-coupled filter’s size.
(b)
Fig.10: Comparisons of (a) EM simulated and (b)
measured results of the singly- (—) compensated compared with the uncompensated case (- - - - -) parallel
coupled filters.
bandwidth (∆) of 10%, and passband ripple of 0.1
dB. The circuits were designed and fabricated on the
RF60-0600 substrate from Taconic. With the design
procedure mentioned in Section III, the parameters
of two filters were derived and are shown in Table
II. The physical dimensions of all two filters are synthesized from the parameters in Section 2. In our
design, the compensation inductor was implemented
by shorted stub. The measurement was performed
with an HP8720C Vector Network Analyzer test system calibrated from 0.1 to 10 GHz with an SOLT
technique.
HPVEE6.0T M software was used to collect the experimental data via GPIB card. Sonnet-LiteT M and
4. CONCLUSIONS
We have presented a new method to achieve high
directivity parallel-coupled lines in inhomogeneous
media and demonstrated the technique applicability
to microwave applications. The compensation inductor connected in series with coupled port of the
coupled-line structure to equalize phase velocity, leading to a high directivity coupled-line design. The inductive compensation technique is demonstrated in
two microwave coupled-line based circuits, which are
the planar Marchand balun and parallel-coupled filter. Design procedures for these circuits with the
proposed compensation technique have been provided. More important, the closed-form expressions
for determining the compensation inductor values
and coupled-line parameters are given to facilitate
the design task considerably. The authors believed
that the technique is highly applicable and suitable
for modern wireless communication systems.
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ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.1 February 2007
5. ACKNOWLEDGEMENT
The authors are grateful to TACONIC Inc. for
supplying Taconic RF60-0600 microwave substrate
for this research. The authors also thank to unanimous reviewers for their valuable comments and suggestions.
References
[1]
M. Dydyk, “Accurate design of microstrip directional couplers with capacitive compensation”,
in 1990 IEEE MTT-S Int. Microwave Symp.
Dig., May 1990, pp. 581-584.
[2] G. L. Matthaei, L. Yoling, and E.M.T. Jones,
Microwave Impedance-Matching Network and
Coupling Structures, New York: McGraw-Hill,
pp.583-593, 1964.
[3] T. Edward, Foundation for Microstrip Circuit
Design, West Sussex, England: John Wiley Son,
pp. 173-228, 1992.
[4] S. L. March, “Phase velocity compensation
in parallel-coupled microstrip”, in 1982 IEEE
MTT-S Int. Microwave Symp. Dig., June, 1982,
pp. 581-584.
[5] A. Riddle, “High performance parallel coupled
microstrip filter”, in 1988 IEEE MTT-S Int. Microwave Symp. Dig., May 1988, pp.427-430.
[6] A. Podell, “A high directivity microstrip coupled
lines technique”, in 1970 IEEE MTT-S Int. Microwave Symp. Dig., May 1970, pp. 33-56.
[7] I. J. Bahl, “Capacitively compensated performance parallel coupled microstrip filter”, in 1989
IEEE MTT-S Int. Microwave Symp. Dig., June
1989, pp.679-682.
[8] C. Y. Ng, M. Chongcheawchamnan, and I. D.
Robertson, “Analysis and design of a highperformanceplanar marchand balun”, in 2002 IEEE
MTT-S Int. Microwave Symp. Dig., June 2002,
pp.113-116.
[9] M. Dydyk, “Microstrip directional couplers with
ideal performance via single-element compensation”, IEEE Trans. Microwave Theory Tech.,
vol. 47, no.6,pp. 969-976, June 1989.
[10] S. Uysal and H. Aghvami, “Synthesis, design,
and construction of ultra- wide-band nonuniform quadrature directional couplers in inhomogeneous media ”, IEEE Trans. Microwave Theory Tech., vol. 37, no.6, pp. 969-976, June 1989.
[11] R. Phromloungsri, S. Patisang, K. Srisathit,
and M. Chongcheawchamnan, “A harmonicsuppression microwave bandpass filter based on
an inductively compensated microstrip coupler”,
in 2005 Asia Pacific Microwave Con., Dec. 2005,
pp. 2836-2839.
Phromloungsri,
K.
Srisathit,
M.
[12] R.
Chongchaewchamnan, and I. D. Robertson,
“Novel Technique for Performance Improvement
in Impedance Transforming Planar Marchand
Baluns”, in 2005 European Microwave Conf.,
the 35th EuMC2005, Paris, France, Oct. 2005.
[13] R. Phromloungsri, and M. Chongcheawchamnan, “A high directivity design using an inductive compensation technique”, in 2005 Asia Pacific Microwave Con., Dec. 2005, pp. 2840-2843.
[14] R. Phromloungsri, Chongcheawchamnan, and
I. D. Robertson, “Inductively compensated
parallel-coupled microstrip lines and their applications”, in 2006 IEEE Trans. Microwave Theory Tech., vol. 54, no.9, pp. 3571-3582, Sept.
2006.
Table 2:
GHz
Parameters of The Filter Design @ 1.8
BPF
Uncompensated
Singlycompensated
Section
(Ω)
1,4
2,3
1,4
2,3
Zoe
(Ω)
78.44
66.42
78.44
66.42
Zoo
(pF)
36.69
49.89
36.69
49.89
Ls
(nH)
1.7
2.5
θf
(rad)
0.5π
0.5π
0.47π
0.42π
Ravee Phromloungsri was born in
Khon Kaen, Thailand.
He received
the B.Sc (Applied Physics in Solid
State Electronics) from King Mongkut
Institute of Technology, Ladkrabang
(KMITL) in 1992, M.Eng. and D.Eng
in Electrical Engineering (Telecommunication) from Mahanakorn University of
Technology (MUT) in 2000 and 2006, respectively. Since 1992 he joined MUT
as a lecturer in department of telecommunication engineering. His research and teaching interests
include microwave passive/active and radio frequency circuits
design. He is a member of Research Center of Electromagnetic Waves Applications (RCEWs). and power distribution
systems.
Mitchai Chongcheawchamnan (M’96)
was born in Trang, Thailand. He received the B. Eng. (Telecommunication
Engineering) from KMITL in 1992, the
M.Sc degree in Communication and Signal Processing from Imperial College,
University of London, UK in 1995 and
the Ph.D. degree in Electrical Engineering from University of Surrey, Surrey,
UK in 2001. He is currently a Director
of Research Center of ElectromagneticWave Applications and Assistant Professor with the Department of Telecommunication Engineering, Mahankorn University of Technology. His research and teaching interests include
RF and microwave passive and active circuits. He is a member
of IEEE and IET.
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