774
1
Design Method of Miniaturized HTS Coplanar
Waveguide Bandpass Filters using Cross Coupling
H. Kanaya, Member, IEEE , J. Fujiyama, R. Oba, and K. Yoshida

Abstract—A new design method of miniaturizing HTS coplanar
waveguide bandpass filters using cross coupling is presented.
When the size of the filter decreases, the cross coupling between
the resonators tends to appear, which causes attenuation poles. In
order to control the cross-coupling section, we reformed the
meanderline interval and shape, so that we can design the
frequency and number of the attenuation poles. The half-wave
length resonator bandpss filter (BPF) is designed by using the
2.5-dimensional electromagnetic field simulator. 7-pole
cross-coupled CPW BPF (center frequency of 2GHz, bandwidth of
15MHz, ripple of 0.1dB and two attenuation poles on both sides of
pass band) is packed within 6mm × 10mm square substrate.
Simulated performance is in good agreement with the designed one.
This BPF has the skirt steepness of 20dB/MHz (40dB attenuation),
which is the same skirt characteristic of 11-pole Chebyshev BPF.
Moreover, in order for further miniaturization, we designed and
tested quarter wavelength resonator BPF by using our present
design theory.
and interdigital gaps. In order to realize the cross-coupling
section, we varied the meanderline interval and shape. The
frequency responses of the cross-coupled CPW BPF with two
attenuation poles on both sides of pass band, is compared with
that of the standard Chebyshev BPF. Moreover, for further
miniaturization, we designed and tested quarter wavelength
(/4) resonator BPF by using our present design theory.
II. DESIGN OF CHEBYCHEV CPW BPF
Fig. 1(a) shows the equivalent circuit model of the BPF.
When fractional bandwidth (w) and ripple (LAr) of BPF are
requested, J inverters are given by,
Index Terms—Mobile telecommunication, HTS filter, Coplanar
waveguide, Cross coupling, Attenuation pole
J 01  w
Y0b1
,
g 0 g1
(1)
J i ,i 1  w
bi bi 1
, (i  1, 2,  , n  1)
g i g i 1
(2)
J n ,n 1  w
I. INTRODUCTION
H
IGH Tc superconducting (HTS) films have extremely low
surface resistance in the microwave and millimeter wave
regions. This indicates that HTS passive devices such as filters
and antennas have a high potential in the mobile and satellite
telecommunication systems. There are many reports on
micro-stripline bandpass filter (BPF) [1], [2] and HTS BPF
based cryogenic receiver front-ends [3], [4]. On the other hand,
the coplanar waveguide (CPW) structure is more advantageous
than the micro-stripline structure because of only one side HTS
coating and easy for size reductions [5]. Finally, we will
fabricate the single chip HTS integrated microwave receiver
that is connecting a HTS slot antenna [6] and a Si-CMOS low
noise amplifier (LNA) with a broadband matching circuit.
Moreover, elliptic and quasi-elliptic filter using
cross-coupled resonators have sharper skirt property than that of
Chebyshev filter in the same pole numbers [7]. In this paper, we
designed the miniaturized cross-coupled CPW BPF by using
highly packed meanderline half-wavelength (/2) resonators
bnY0
,
g n g n 1
where gi is the element vale of BPF, and bi is the susceptance
slope parameter of the resonator which has suseptance=Bi [8].
We can realize this circuit model as the equivalent CPW
configuration. In order to realize the J inverter using CPW
structure, interdigital gaps are adopted in the signal line as
shown as shown in Fig. 1(b). In order to realize the miniaturized
BPF, we coupled highly packed meanderline resonators with
interdigital gaps. The exact values such as J values and length of
the resonator of meanderline are calculated from the S-matrix
and F-matrix (cascade matrix) by the 2.5-dimensional
electromagnetic field simulator (Momentum: Agilent).
(a)
J01 jB1 J12 jB2 J23 jB3 J34 jB4 J45 jB5 J56
Ｊ－Inverter
Ｊ-Inverter
/2 Line
(b)
Interdigital Gap
Manuscript received August 5, 2002.
H. Kanaya, J. Fujiyama, R. Oba, and K. Yoshida are with Department of
Electronics, Graduate School of Information Science and Electrical
Engineering, Kyushu University, Fukuoka 812-8581, (phone: +81-92-6423917; fax: +81-92-642-3943; e-mail: kanaya@ ed.kyushu-u.ac.jp).
(3)
Interdigital Gap
Fig. 1. Equivalent circuit model of the BPF (a) and the equivalent CPW
configuration (b).
774
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III. CHARACTERISTIC OF CROSS-COUPLING
J’2,4 = 0
J’2,4 > 0
0
|S11| (dB)
0
|S11| (dB)
|S11| (dB)
-20
-20
-20
-40
-40
-40
-60
-60
1.96
2.04
2
Frequency(GHz)
-60
1.96
Ｃ（Electric）Coupling
2.04
2
Frequency(GHz)
1.96
Non Coupling
Ｍ（Magnetic）Coupling
Fig. 4. Frequency responses of the Fig.3 (a).
di
Meanderline
Interval (di )
Fig. 5. EM-simulation pattern for the coupling measurement.
1.5
J'2,4 (×10 S)
1
Ｍ（Magnetic）Coupling
0.5
0
-0.5
Ｃ（Electric）Coupling
di
-1
J01
jB1 J
12
jB2
J’35
J23 jB3 J34
-1.5
jB4 J45
J23
jB3
jB4
J34
J”14
(b)
jB1
J23
jB2
J23
52
54
56
di (m)
58
60
62
Fig. 6. di dependence of J’2,4.
J”1,4 < 0
0
|S11| (dB)
-40
-60
-80
-100
1.96
J”1,4 = 0
0
-20
-40
-60
J”1,4 > 0
-20
-40
-60
-80
-80
-100
-100
2
1.96
2
1.96
2
2.04
2.04
2.04
Frequency (GHz)
Frequency (GHz)
Frequency (GHz)
Fig.7. Frequency responses of the circuit model for measuring the J’’1,4.
J’24
jB2
50
-20
J25”
Fig.2. Circuit model of the n=5 BPF with cross-coupling.
(a)
48
jB5 J56
0
J14”
Meanderline
Interval (di )
|S11| (dB)
J’13
|S11| (dB)
J’24
2.04
2
Frequency(GHz)
-5
When the size of the filter decreases, the cross-coupling
between the resonators tends to appear, which causes
attenuation poles. Fig.2 shows the circuit model of the n=5 BPF
with cross-coupling. There are two kinds of cross-coupling,
namely cross-coupling passed over one resonator (J’i,k) and
cross-coupling passed over two resonators (J”m,n), respectively.
We can neglect the higher order coupling because the coupling
effect is extremely smaller than that of J’i,k and J”m,n.
At first, we found the conditions for appearances of the
attenuation poles by simulation. In order to realize the
cross-coupling section, we reformed the meanderline interval
and shape of the CPW resonators. Fig. 3 (a) shows the circuit
model for measuring the J’2,4. Fig. 4 shows the frequency
responses of the Fig.3 (a). When J’ 2,4 is negative value, namely
electric coupling (C coupling), one attenuation pole appears on
lower frequency than that of the pass band. On the other hand,
when J’ 2,4 is positive value, namely magnetic coupling (M
coupling), one attenuation pole appears on the opposite side.
Fig. 5 shows the EM-simulation pattern for the cross-coupling
measurement. In order to realize the J’i,k, we reformed the
meanderline interval (di) of the CPW resonators. Fig. 6 shows
the di dependence of J’2,4.
We can measure and control the J”m,n in the same manner as
J’i,k. Fig. 3 (b) shows the circuit model for measuring the J”1,4.
Fig. 7 shows the frequency responses of the circuit model for
measuring the J”1,4. In order to realize the J” 1,4, we reformed
the meanderline shape (ds) of the CPW resonators. Fig. 8 shows
the ds dependence of J” 1,4. We confirmed that the J’i,k value
almost dose not change by changing ds.
J’2,4 < 0
0
jB3
J34
jB4
Fig. 3. Circuit model for measuring the J’2,4 (a) and J”1,4 (b).
IV. DESIGN AND SIMULATION OF CROSS-COUPLED BPF
As shown in Sec. III, using J’’m,n is particularly effective for
miniaturized cross-coupled BPF, because two attenuation poles
appears on both sides of the pass band by only one J’’m,n. At first,
we designed standard Chebyshev CPW BPF (see Fig. 1(a)),
which has center frequency (f0)=2GHz, w=15MHz and n=5.
From Figs. 6 and 8, we decided di=58m and ds=210m as no
cross-coupling condition. Fig. 9 shows the frequency responses
774
3
1.5
-10
EM
Simulation
-20
Circuit
Model
-30
-40
-60
Ｍ（Magnetic）
Coupling
1
J"1,4 (×10-5 S)
0
-50
2
-70
0.5
-80
1.96 1.97 1.98 1.99 2 2.01 2.02 2.03 2.04
frequency (GHz)
Fig.10. Frequency response of the n=5 cross-coupled CPW BPF.
0
-0.5
Meanderline shape (ds)
-1
Ｃ（Electric）
-1.5
-2
(f0=2GHz, w=15MHz). The filter size is 2.5mm×10mm. Fig.
15 shows the simulation results of the n=4 /4 BPF with no
cross-coupling. Simulated performance is in good agreement
with the circuit model.
S11,S21 [dB]
of the EM simulation result. Simulated performance is in good
agreement with the circuit model. Fig.10 shows the frequency
response of the n=5 cross-coupled CPW BPF. We decided di
=58m and ds =400m in order to make two attenuation poles
with ±14MHz from the center frequency. The results of w and
the position of attenuation poles are in good agreement with the
circuit model. Fig. 11 shows the simulated pattern of the n=7
cross-coupled BPF. Filter size is 6mm ×10mm. Fig. 12 shows
the simulation result of the BPF. In the figure, the responses of
the n=11 Chebyshev BPF are also plotted. This BPF has the
skirt steepness of 20dB/MHz (40dB attenuation) and offband
minimum rejection of 45dB, which is the same skirt
characteristic of n=11 standard Chebyshev BPF.
0
100
Size 6×10mm
ds
Coupling
200
300
ds (m)
400
500
600
di =58m
Fig. 8. ds dependence of J”1,4.
0
-10
EM
Simulation
-20
Circuit
Model
ds = 400m
S11,S21 [dB]
-30
Fig. 11. Simulation pattern of the n=7 cross-coupled BPF.
-40
-50
0
-60
-10
-70
-20
Fig. 9. Frequency responses of the n=5 Chebyshev BPF.
V. DESIGN AND SIMULATION OF QUARTER WAVELENGTH BPF
For further miniaturization, we designed and tested the
quarter wavelength (/4) resonator BPF by using our present
design theory. Fig. 13 (a) shows the circuit model of the /4
BPF. /4 resonator is connected with admittance inverter
(K-inverter) and J-inverter. Fig.13 (b) shows the CPW
configuration. The meander-shape short stubs realize k-inverter.
Fig. 14 shows the simulation layout of the n=4 /4 BPF
-30
S11,S21 [dB]
-80
1.96 1.97 1.98 1.99 2 2.01 2.02 2.03 2.04
frequency (GHz)
n=7 Crosscoupled BPF
n=11
Chebyshev BPF
-40
-50
-60
-70
-80
1.96 1.97 1.98 1.99 2 2.01 2.02 2.03 2.04
frequency (GHz)
Fig. 12. Simulation result of the n=7 cross-coupled BPF.
774
4
0
(a)
K12
λ/4
(b)
J23
λ/4
K34
λ/4
J-Inverter
J45
-5
λ/4
K-Inverter
λ/4　Line
Interdigital Gap
Experimental results
Simulation results with
contact loss
-10
|S11|, |S21| (dB)
J01
Meander-Shape
Short Stub
Circuit model
-15
-20
-25
-30
Fig. 13. Equivalent circuit model (a) and CPW configuration
of the /4 BPF (b).
-35
-0.3
-0.2
-0.1
0
0.1
Frequency (GHz)
0.2
0.3
Fig. 16. Frequency responses of the n=3 highly packed meanderline YBCO
Chebychev CPW BPF at 24K.
Size : 2.5mm×10mm
VII. CONCLUSION
Fig. 14. Layout of n=4 /4 CPW BPF.
0
EM
Simulation
-10
We can design and control the frequency and number of the
attenuation poles of the miniaturized BPF by reforming the
meanderline interval and shape. n=7 cross-coupled CPW BPF is
packed within 6mm × 10mm square substrate. Simulated
performance was in good agreement with the designed one. This
BPF has the skirt steepness of 20dB/MHz (40dB attenuation)
and offband minimum rejection of 45dB, which is the same skirt
characteristic of n=11 Chebychev BPF. Moreover, for further
miniaturization, we designed the /4 CPW BPF by using our
present design theory. The size of the n=4 /4 BPF is 2.5mm×
10mm.
Circuit
Model
S11,S21 [dB]
-20
REFERENCES
-30
[1]
-40
[2]
-50
[3]
-60
1.96 1.97 1.98 1.99 2 2.01 2.02 2.03 2.04
frequency (GHz)
[4]
Fig. 15. Frequency responses of the n=4 /4 CPW BPF.
[5]
VI. EXPERIMENTAL RESULT
Fig. 16 shows the frequency responses of the n=3
meanderline YBCO Chebyshev CPW BPF at 24K. This BPF
has no cross-couplings and there are no trimmings. These
characteristics include the residual loss due to the contact
between the YBCO film and air coplanar metal probe. In Fig. 16,
dashed lines shows the simulation results considered with the
contact loss. The observed frequency responses such as the
value of the insertion loss and the bandwidth are similar to that
of the simulation results with contact loss.
[6]
[7]
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