L u J Synthesis of Inline Mixed Coupled Quasi Elliptic Bandpass Filters Based...

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TMTT-2015-01-0083 1 AbstractThis paper proposes a general synthesis method for inline mixed coupled quasi-elliptic bandpass filters based on λ/4 resonators. Different from the conventional modeling with lumped and mixed inductive and capacitive coupling, the proposed mixed-coupling model here includes not only the coupling magnitudes, but also their paths’ phases inside the mixed-coupling. According to the presented formulation, there exists one lower side transmission zero for the capacitive- dominant mixed coupling. However, there are two transmission zeros in the upper stopband for the inductive-dominant case, and these two transmission zeros can be analytically synthesized with different coupling path ratios. The proposed synthesis method is then applied to design two 2 nd -order bandpass filters based on inductive-dominant coupled λ/4 resonators, resulting in two upper stopband transmission zeros. Furthermore, this synthesis method is extended to design two 4 th -order quasi-elliptic bandpass filters with both inline capacitive- and inductive- dominant mixed couplings. Finally, the designed filters are fabricated and measured to provide successful verification on the proposed mixed coupling model approach. Index TermsInline coupled filter, mixed coupling, quarter- wavelength resonator, quasi-elliptic bandpass filter and finite transmission zero. I. INTRODUCTION INITE transmission zeros are critical for filter synthesis to enhance the rejection ratios. One of prevalent methods for creating finite transmission zeros is the basic cross-coupling mechanism [1]. These cross couplings are equal in magnitude and out-of-phase with the mainline one at the transmission zero frequencies. Cross-coupling paths can be introduced either by resonant nodes [2][4], or non-resonant nodes [5], [6]. This mechanism is only valid with assumption of narrow-band non-dispersive mainline and cross couplings, and it is able to generate maximum N-2 finite transmission zeros without considering I/O ports (N is the filter order). Another popular mechanism to create finite transmission zeros is based on the mixed inter-resonator couplings, where capacitive- or inductive-dominant mixed-coupling is dispersive. In the filter core-passband synthesis, it provides required capacitive- or inductive-dominant couplings. Meanwhile, these capacitive Manuscript received November 7, 2014; revised January 23, 2015, May 8, 2015 and August 3, 2015; accepted on August 5, 2015. S. Zhang and R. Weerasekera are with Institute of Microelectronics, Singapore. S. Zhang is also with Skyworks Solutions, Singapore. (e-mail: [email protected]) L. Zhu is with the Department of Electrical and Computer Engineering, Faculty of Science and Technology, University of Macau, Macau SAR, China. and inductive components annihilate with each other at certain frequencies, and resulting in finite transmission zeros. Mixed-coupling between open-loop λ/2 resonators was discussed in [7], and its inductive and capacitive components are enlaced with each other. An earlier work [8] employed the stepped impedance resonators (SIRs) to separately control inductive and capacitive components in mixed inter-resonator couplings. Separated inductive coupling using iris and capacitive coupling using strips were also introduced between two cavity resonators [9] and the substrate integrated waveguide (SIW) resonators [10][12] for implementation of compact inline quasi-elliptic bandpass filters. For the other planar implementations, quasi-elliptic bandpass filters based on λ/4 resonators and separated J and K mixed-couplings were illustrated in [13][18]. However, most of pioneered works had in general modeled the mixed-coupling as in Fig.1 (a) with a lumped inductor, L m , and a capacitor, C m , intuitively representing for inductive and capacitive couplings, respectively. Explicit formulation presented in [7], [11] had explained that existence of one lower-side transmission zero for the capacitive-dominant coupling, and one upper-side transmission zero for the inductive-dominant coupling. Synthesis of Inline Mixed Coupled Quasi-Elliptic Bandpass Filters Based on λ/4 Resonators Songbai Zhang, Member, IEEE, Lei Zhu, Fellow, IEEE, Roshan Weerasekera, Senior Member, IEEE F C m L m C C L L (a) J K θ j θ k θ 1, θ 2, θ u θ l θ j θ k θ u θ l Port 1 Port 2 Z r Z r θ 1, Z r θ 2, Z r (b) Fig. 1. (a) Conventional lumped model for mixed inter-resonator coupling, (b) proposed mixed coupling model for λ/4 resonators with coupling path phases.

Transcript of L u J Synthesis of Inline Mixed Coupled Quasi Elliptic Bandpass Filters Based...

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Abstract—This paper proposes a general synthesis method for

inline mixed coupled quasi-elliptic bandpass filters based on λ/4

resonators. Different from the conventional modeling with

lumped and mixed inductive and capacitive coupling, the

proposed mixed-coupling model here includes not only the

coupling magnitudes, but also their paths’ phases inside the

mixed-coupling. According to the presented formulation, there

exists one lower side transmission zero for the capacitive-

dominant mixed coupling. However, there are two transmission

zeros in the upper stopband for the inductive-dominant case, and

these two transmission zeros can be analytically synthesized with

different coupling path ratios. The proposed synthesis method is

then applied to design two 2nd-order bandpass filters based on

inductive-dominant coupled λ/4 resonators, resulting in two

upper stopband transmission zeros. Furthermore, this synthesis

method is extended to design two 4th-order quasi-elliptic

bandpass filters with both inline capacitive- and inductive-

dominant mixed couplings. Finally, the designed filters are

fabricated and measured to provide successful verification on the

proposed mixed coupling model approach.

Index Terms—Inline coupled filter, mixed coupling, quarter-

wavelength resonator, quasi-elliptic bandpass filter and finite

transmission zero.

I. INTRODUCTION

INITE transmission zeros are critical for filter synthesis to

enhance the rejection ratios. One of prevalent methods for

creating finite transmission zeros is the basic cross-coupling

mechanism [1]. These cross couplings are equal in magnitude

and out-of-phase with the mainline one at the transmission zero

frequencies. Cross-coupling paths can be introduced either by

resonant nodes [2]–[4], or non-resonant nodes [5], [6]. This

mechanism is only valid with assumption of narrow-band

non-dispersive mainline and cross couplings, and it is able to

generate maximum N-2 finite transmission zeros without

considering I/O ports (N is the filter order). Another popular

mechanism to create finite transmission zeros is based on the

mixed inter-resonator couplings, where capacitive- or

inductive-dominant mixed-coupling is dispersive. In the filter

core-passband synthesis, it provides required capacitive- or

inductive-dominant couplings. Meanwhile, these capacitive

Manuscript received November 7, 2014; revised January 23, 2015, May 8,

2015 and August 3, 2015; accepted on August 5, 2015.

S. Zhang and R. Weerasekera are with Institute of Microelectronics, Singapore. S. Zhang is also with Skyworks Solutions, Singapore. (e-mail:

[email protected])

L. Zhu is with the Department of Electrical and Computer Engineering, Faculty of Science and Technology, University of Macau, Macau SAR, China.

and inductive components annihilate with each other at certain

frequencies, and resulting in finite transmission zeros.

Mixed-coupling between open-loop λ/2 resonators was

discussed in [7], and its inductive and capacitive components

are enlaced with each other. An earlier work [8] employed the

stepped impedance resonators (SIRs) to separately control

inductive and capacitive components in mixed inter-resonator

couplings. Separated inductive coupling using iris and

capacitive coupling using strips were also introduced between

two cavity resonators [9] and the substrate integrated

waveguide (SIW) resonators [10]–[12] for implementation of

compact inline quasi-elliptic bandpass filters. For the other

planar implementations, quasi-elliptic bandpass filters based

on λ/4 resonators and separated J and K mixed-couplings were

illustrated in [13]–[18]. However, most of pioneered works had

in general modeled the mixed-coupling as in Fig.1 (a) with a

lumped inductor, Lm, and a capacitor, Cm, intuitively

representing for inductive and capacitive couplings,

respectively. Explicit formulation presented in [7], [11] had

explained that existence of one lower-side transmission zero

for the capacitive-dominant coupling, and one upper-side

transmission zero for the inductive-dominant coupling.

Synthesis of Inline Mixed Coupled Quasi-Elliptic

Bandpass Filters Based on λ/4 Resonators

Songbai Zhang, Member, IEEE, Lei Zhu, Fellow, IEEE, Roshan Weerasekera, Senior Member, IEEE

F

Cm

Lm

C C

L L

(a)

J

K

θj

θk

θ1,

θ2,

θu

θl

θj

θk

θu

θl

Port 1 Port 2

Zr

Zr

θ1, Zr

θ2, Zr

(b)

Fig. 1. (a) Conventional lumped model for mixed inter-resonator coupling, (b)

proposed mixed coupling model for λ/4 resonators with coupling path phases.

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To the best of our knowledge, for the first time in this paper,

mixed-coupling is modeled not only with magnitudes of

constituted capacitive and inductive couplings, but also their

respective different coupling path phases as illustrated in Fig

1(b). Compared with the conventional model in Fig. 1(a), there

are two coupling paths between ports 1 and 2 in Fig. 1(b). The

upper path composes of two 𝜃1 sections, a J inverter and its

two associated electric lengths 𝜃𝐽. On the lower path, there are

two 𝜃2 sections, a K inverter and its two associated electric

lengths 𝜃𝐾 . Overall Fig. 1(b) portrays that two λ/4 resonators

are mixed coupled together with separated J and K inverters.

Depending on different positions of ports 1 and 2, there exists

different phase difference between these two coupling paths.

By introducing this coupling path with phase difference, a

single lower side finite transmission zero appears for the

capacitive-dominant inter-resonator mixed coupling, which is

identical with the conventional model in Fig. 1(a). Different

from lumped modeling in Fig. 1(a), two upper-side

transmission zeros emerge for the inductive-dominant

mixed-coupling case in Fig 1(b), and the pertained pair of

transmission zeros can be analytically derived and controlled

with different choices of coupling path phases.

The remainder of this paper is organized as follows. In

Section II, in-band mixed-coupling for filter synthesis is

discussed first. Transmission zeros due to the mixed-coupling

are formulated, and then mathematically proved the existence

of one lower-side and two upper-side transmission zeros for the

capacitive-/inductive-dominant mixed couplings, respectively.

In Section III, two 2nd

-order planar bandpass filters with

inductive-dominant mixed-coupled λ/4 resonators are designed

to experimentally verify two upper-side transmission zeros.

This synthesis methodology is further extended to design two

4th

-order inline quasi-elliptic filters in Section IV. Lastly,

Section V concludes this paper.

II. MIXED COUPLING FORMULATION

A. In-Band Mixed Inter-Resonator Coupling

As shown in Fig. 1(b), two λ/4 resonators are simultaneously

coupled with separated J and K inverters. These two inverters,

represent electrical and magnetic couplings, are out-of-phase

for the passband synthesis [19]. The overall inter-resonator

coupling coefficient 𝑀𝑖𝑗 is calculated in following (1).

b

J

x

KFBW

ijm

ijM (1)

where 𝑚𝑖𝑗 is the normalized entry in coupling matrix, FBW is

the fractional bandwidth. K and J are the inductive and

capacitive inverters, their signs are rather relative. Inductive

inverter K is defined positive hereafter, and the capacitive J is

thus chosen as negative.𝑥 = 𝜋𝑍𝑟 4⁄ and 𝑏 = 𝜋𝑌𝑟 4⁄ are λ/4

resonator’s reactance and susceptance slopes, respectively [3].

𝑍𝑟 and 𝑌𝑟 are the characteristic impedance and admittance of

λ/4 resonators in Fig. 1(b). (1) can be further simplified as (2),

) ˆˆ4)(

4JK(

Y

J

Z

KM

rr

ij

(2)

Here, the normalized J and K inverters are defined as

rZKK /ˆ andrYJJ /ˆ . J and K inverters can then be

synthesized based on our previous work in [20] for the physical

realization.

B. Mixed Coupling and Finite Transmission Zeros

In Fig. 1(b), the upper path is coupled with the capacitive J

inverter, and lower path is coupled with the inductive K

inverter. ABCD matrix for the upper capacitive coupling path is

calculated in (3) at the bottom of this page. Admittance matrix

element 𝑌21,𝑢 for the upper network is thus calculated in (4),

uur

uZJ

jJY

2222,21cossin

(4)

Meanwhile, ABCD matrix for the lower half inductive coupling

path is calculated in (5) at the bottom of this page.𝑌21,𝑙 in

admittance matrix is derived in (6).

llr

lKZ

jKY

2222,21cossin

(6)

The upper capacitive and lower inductive coupling paths are

connected in parallel, so the overall normalized 𝑌21 with

respective to resonator’s admittance 𝑌𝑟 between ports 1 and 2

in Fig. 1(b) is calculated as follows.

r

lu

r Y

YY

Y

YY

,21,212121

ˆ

uurJZ

J

rY

ujJ

J

urjY

uJ

rjZ

J

uj

uuJ

rZ

J

rY

uurjY

urjZ

ujJ

Jj

uurjY

urjZ

u

UABCD

cossin)(2cos

2sin2

2sin22cos

cossin)(

cossin

sincos

0

/0

cossin

sincos

(3)

llrr

lrl

llr

llrr

llr

lrl

llr

lrl

L

KYK

ZKjY

K

j

jKK

jZKY

K

Z

jY

jZ

Kj

jK

jY

jZ

ABCD

cossin)(sincos

cossin

cossin)(

cossin

sincos

0/

0

cossin

sincos

222

222

(5)

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llK

Kj

uuJ

Jj

2sin2cos2ˆ

ˆ

2cos2sin2ˆ

ˆ

(7)

To create transmission zeros, magnitude of 21Y should be

zero, thereby its numerator in (8) is equal to zero.

)ˆ(numerator ˆ2121 |Y|Y ,n

uK

uKJ

lJ

lKJ 2cosˆ2sinˆ2ˆ2sinˆ2cos2ˆˆ (8)

Before analyzing (8) in general, a special case is worthy of our

attention. Assuming that (a) both J and K inverters are

non-dispersive, and (b) the electrical lengths of upper and

lower coupling paths in Fig. 1(b) are equal to each other, e.g.

u = l = 0 . Thus, transmission zeros are constrained as

02tan

ˆ

ˆ

J

K (9)

Fig. 2 illustrates transmission zeros configuration. For a λ/4

resonator filter with central frequency 0f locates at 4/0 ,

its 1st spurious response appears around 03 f where 4/30 .

Thus, only transmission zeros below 03 f are discussed

hereafter. According to (9), if the mixed coupling is

capacitive-dominant, i.e., KJ ˆˆ , the mixed coupling in (2)

becomes negative. As a result, a single transmission zero

appears at lower side of passband in 1ˆ/ˆ JK region in Fig. 2.

However, if the mixed coupling is inductive-dominant, in-band

coupling in (2) is positive. Accordingly, two transmission

zeros appear in 1ˆ/ˆ JK region in Fig. 2, and they are

symmetrical with respect to 2/0 . Now, analysis here

proves existence of two upper-side transmission zeros for the

inductive-dominant mixed coupling. However, both practical J

and K inverters are dispersive, and positions of two ports in

Fig. 1(b) are also not restricted in middle of λ/4 resonators.

Hence, exact transmission zeros positions are subjected to the

general condition in (8), which will be discussed further in the

following section.

III. MIXED-COUPLED 2ND

-ORDER FILTERS

Based on the previous discussion, two inductive-dominant

2nd

-order Chebyshev bandpass filters are exemplified with

different port locations. Both filters are designed with 20 dB

in-band return loss with fractional bandwidths of 3.7%, and

central frequency of 2.5 GHz. The dielectric substrate used in

this work is Roger’s RT/Duriod 6010 with εr=10.8, tanδ =

0.002 and thickness = 1.27 mm. The strip width of λ/4

resonators is uniformly chosen as 0.4 mm, and its characteristic

impedance corresponds to 𝑍𝑟 =73.7 Ω. The coupling

coefficient M12 based on 2nd

-order Chebyshev lowpass

prototype is presented in (10),

061.05445.06648.0

%7.3

21

12

gg

FBWM

(10)

Hence, the required mixed coupling is derived according to (2),

048.04

061.04

ˆˆ12

MJK (11)

The J inverter in Fig. 1(b) is realized with the anti-parallel

coupled line in Fig. 3(a). A quasi-lumped metallic via in Fig.

3(b) functions as the K inverter in Fig. 1(b). Their physical

dimensions are explicitly illustrated in Fig. 3(a) and 3(b),

respectively. Their broadband normalized values: J and K , and

their associated electrical lengths: 𝜃𝐾 and 𝜃𝐽 , are fullwave

extracted and shown in Fig. 3(c) [20]. From Fig. 3(c), K

=0.108, J =0.06, 𝜃𝐾 =7.660, and 𝜃𝐽 =19.05

0 at 2.5 GHz. This

inductive-dominant mixed coupling calculated in (11) satisfies

the theoretical inter-resonator coupling requirement M12=0.061

in (10). Furthermore, the positions of two upper-side

Fig. 2. Transmission zeros configuration emerged in presented filter based on

mixed and equal-phase coupled λ/4 resonators.

L=2.0 mm

S=0.7 mm

W=0.4 mm

de-embed de-embed

Zr=73.7 Ω Zr=73.7 Ω

de-embed de-embed

Wstub=0.6 mm

Lstub=0.9 mmLvia=0.6 mm

D=0.4 mm

Zr=73.7 Ω Zr=73.7 Ω

(a) (b)

(c)

Fig. 3 Schematics of (a) an anti-parallel coupled J inverter, and (b) a

quasi-lumped K inverter. (c) Fullwave extracted normalized J and K inverter

values and associated electrical lengths.

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transmission zeros are determined based on (8) and Fig. 3(c).

Fig. 4 (a) and (b) graphically illustrate two upper-stopband

transmission zeros with different k, which is defined as

electrical length ratio of upper to lower paths in Fig. 1(b).

l

uk

(12)

Fig. 4(a) depicts the graphs of normalized admittance for

determining the transmission zeros with k ranged from 0.42 to

0.56. The pair of transmission zeros emerge at k=0.43, and split

afterwards. As k increases from 0.43 to 0.56, the first

transmission zero fZ1 shifts downwards, and 2nd

transmission

zero fZ2 shifts more aggressively to the higher frequency. As k

increases above 0.7 as plotted in Fig. 4(b), transmission zero fZ1

continues to slightly shift downwards. However, transmission

zero fZ2 shifts backward to lower frequency. In this context,

these two upper transmission zeros can be derived and

controlled with different port positions in Fig. 1(b).This result

also addresses the two upper transmission zeros in [15], [18].

To realize the external coupling structure between I/O ports

and resonators, the tapped line structure proposed in [21] is

applied as used in [13]. However, the I/O tapped line positions

(ports 1 and 2’s positions in Fig. 1(b)) are primarily determined

by required external quality factor 𝑄𝑒, thus, it results in limited

freedom for controlling length ratio k, and associated two

upper-side transmission zeros. To circumvent this problem, a

tri-port coupled-line in Fig. 5(a) is used. Its equivalent circuit

was developed based on [22], and illustrated in Fig. 5(b).

Electrical length in Fig. 1(b) is determined by coupled line

length 𝜃 , and external quality factor 𝑄𝑒 depends on the

coupling gap and transformer ratio n in Fig. 5(b). Hence, length

ratio k and external quality factor 𝑄𝑒 can be de-coupled and

separately designed.

These two 2nd

-order bandpass filters, noted as Filter A and

Filter B, are shown in Fig. 6(a) and 6(b), respectively. Both

filters have identical in-band frequency responses; therefore,

(a)

(b)

Fig. 4. Admittance graphs under different length ratios for determining

transmission zeros (a) 56.042.0 k , and (b) 9.15.0 k .

Port 1 Port 2

Port 3

Port 1 Port 3

Port 2

θ θ

1:n

(a) (b)

Fig. 5. (a) Tri-port coupled line section, and (b) equivalent circuit [22] .

(a) (b)

(c)

(d)

Fig. 6. Physical filter layout with different coupling length ratios, (a) k=0.5,

and (b) k=0.45. Fullwave simulated and measured frequency responses for (c)

Filter A and (d) Filter B.

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they have the same inductive-dominant coupling M12. The

constituted J and K inverters are illustrated in Fig. 3(a) and (b).

However, Filter A and Filter B have different length ratios

contributed by the tri-port feeding structure in Fig. 5(a). In our

design, the length ratios are chosen as 0.5 and 0.45 for the

Filter A and Filter B, respectively. According to the Fig. 4(a),

the theoretical transmission zeros appear at 3.5 and 6.8 GHz for

Filter A, 3.8 and 5.3 GHz for Filter B. Apart from the

associated electrical lengths 𝜃𝐽 and 𝜃𝑘 in relevance to J and K

inverters, compensated lengths 𝜃1=110 or 1.4 mm for upper

capacitive coupling path and 𝜃2=52.340 or 6.75 mm for the

lower inductive coupling path in Fig. 1(b) are introduced to

realize effective λ/4 resonators for Filter A with length ratio k

=0.5. Similarly, 𝜃1=8.90 or 1.15 mm and 𝜃2=54.4

0 or 7.0 mm

are inserted for upper and lower coupling paths in Filter B,

whose length ratio k=0.45, for the same purpose.

Fig. 6(a) and 6(b) show the optimized filter layout with noted

dimensions. Insets in Fig. 6(c) and 6(d) illustrate two identical

simulated in-band frequency responses for Filter A and Filter

B, and they are consistent with measured results. Measured

in-band insertion and return losses are 1.05 dB and 21.4 dB for

Filter A, and 0.90 dB and 17.6 dB for Filter B. The measured

transmission zeros are found at 3.47/6.77 GHz and 3.64/5.12

GHz for Filter A and Filter B, respectively. These measured

and simulated two transmission zeros locations for both filters

with different feeding length ratios have justified our proposed

idea in the design.

IV. MIXED-COUPLED 4TH

-ORDER FILTERS

In this section, the proposed mixed-coupling filter synthesis

method is applied to design two 4th

-order bandpass filters,

namely, Filter C and Filter D, as shown in Fig. 7(a) and 8(a).

Both filters are purposely design with the same in-band

specification, i.e., central frequency at 2.45 GHz, 20 dB

in-band return loss, and 7% fractional bandwidth. The

inter-resonator coupling M12 is chosen as inductive-dominant,

where1212

ˆˆ JK . Meanwhile, M34 is chosen as capacitive-

dominant, where3434

ˆˆ JK . The strip width of synchronously-

tuned resonators is set as 0.3 mm, thus its characteristic

impedance 𝑍𝑟 equals to 80.4 Ω. According to the 4th

-order

Chebyshev low-pass prototype [19] and (2),

0638.02920.19314.0

%7

21

12

gg

FBWM

(13)

and,

05.04

0638.04

| ˆˆ| 12

MJK (14)

05.0ˆˆ JK is chosen for the inductive-dominant M12 stage,

and 05.0ˆˆ KJ is chosen for the capacitive-dominant M34

stage.

Fig. 7(a) illustrates the final optimized Filter C with detailed

dimensions. Herein, the J12 realized with anti-parallel coupled

line with the dimensions of L=2.2 mm, S= 0.7mm and W=0.3

mm. At the filter central frequency 2.4 GHz, 12J equals to 0.06.

For the quasi-lumped K12 inverter with Lstub=1.1 mm, Wstub=0.6

mm and via diameter D=0.4 mm, 12K equals to 0.104.

Meanwhile, the dimensions for J34 inverter are derived as

L=2.1 mm, S=0.2 mm and W=0.3 mm, so we can extract34J

=0.14. The quasi-lumped inverter K34 has Lstub of 0.75 mm,

Wstub of 0.6 mm and metallic via diameter of 0.4 mm. The

extracted 34K =0.082 at 2.4 GHz. The mixed-couplings 0.044 (

12K -12J ) and 0.058 (

34J -34K ), slightly deviated from 0.05

calculated in (14). The coupling M23 in Filter C is implemented

with a modified parallel coupled line, its magnetic coupling

strength is much smaller than its electric counterpart, and it is

thus modeled as capacitive-only coupling J23.

Simulated, measured and ideal 4th

-order Chebyshev filter

frequency responses for Filter C are compared in Fig. 7(c).

In-band fullwave simulated frequency responses are well

matched with the ideal 4th

-order counterpart. The measured

in-band insertion and return losses are 2.4 and 10.6 dB,

respectively. The lower-side transmission zero fZ1 by

capacitive-dominant M34 locates at 2.16 and 2.13 GHz in

simulated and measured results, respectively. It slightly

deviates from the theoretical calculated 2.1 GHz. The

(a)

Input

Ji,1J1,2

K1,2

J2,3

J3,4

K3,4 J4,oOutput3 421

(b)

(c)

Fig. 7. (a) Physical layout of 4th-order Filter C, (b) mixed-coupling topology,

and (c) comparison between simulated and measured frequency responses.

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simulated 2nd

transmission zero fZ2 at 2.80 GHz is consistent

with measured 2.86 GHz. However, the 2nd

transmission zero

at 4.75 GHz due to inductive-dominant M12 stage disappears,

and it may be interpreted by the fact that the length ratio of

coupling path deviates from targeted k=0.43 in Fig. 7(a) M12

stage. In other word, the port 2 in Fig. 1(b) for M12 stage could

not be clearly identified due to the distributed nature of J23

stage. Thus, it somehow destroys the synthesized length ratios

for both M12 and M34 stage.

To solve this problem, an improved filter, named as Filter D

in Fig. 8(a) is proposed. The middle M23 stage is now realized

by a modified anti-parallel coupled line with an embedded

lumped inter-digital capacitor. After intensive analysis, there

are three main advantages from this capacitor. (a) The

anti-parallel coupled line without extra inter-digital capacitor

in Fig. 8(a) itself is a mixed coupling. Its electric and magnetic

strengths are comparable and cancel each other, resulting in

coupling strength too weak to realize a 7% fractional

bandwidth. Hence, the extra inter-digital capacitor enhances its

capacitive component inside M23, and improves the net

coupling strength. (b) The phase difference for the mixed

coupling stage M12 and M34 can now be flexibly controlled so

as to freely adjust transmission zeros positions using the

method discussed in Section III. (c) This capacitive-dominant

mixed coupling M23, modeled as J23 and K23, is also capable to

create one extra lower-side transmission zero fZ2, thereby

enhancing lower-side rejection skirt.

The fabricated Filter D and its corresponding coupling

topology are depicted in Fig. 8(a) and 8(b), respectively, where

the specified coupling parameters are given as 12J = 0.065 and

12K = 0.11 in the M12 stage, 34J =0.164 and

34K =0.114 in the

M34 stage. The inductive-dominant M12 creates two finite

transmission zeros at fZ3=2.75 GHz and fZ4=4.55 GHz in the

simulated frequency response. Meanwhile, the capacitive-

dominant M34 stage creates a lower-side transmission zero

fZ1=2.2 GHz. Moreover, the lumped inter-capacitor embedded

in M23 not only preserves the coupling path ratios for both M12

and M34 stages, but also brings an additional transmission zero

at fZ2= 2.26 GHz. After testing the fabricated filter, the

fullwave simulated, measured, and ideal 4th

-order Chebyshev

frequency responses for Filter D are plotted and compared in

Fig. 8(c). Good agreement between them has evidently verified

our proposed phase-dependent mixed-coupling formulation for

transmission zeros design.

Unfortunately, there are always a few uncontrollable

parasitic effects as commonly existed in the implementation

and measurement of planar bandpass filters, such as fabrication

tolerance in etching process, transition discontinuity between

the feeding line and SMA connector, inaccurate value of

permittivity listed in the datasheet, nonzero conductor

thickness and so on. As a result, the measured 10 dB return

losses of 4th

-order filters, as shown in Fig. 6(c) to Fig. 8 (c), do

not perfectly achieve the targeted 20 dB in design.

V. CONCLUSION

In this paper, a general synthesis method for the inline

mixed-coupled quasi-elliptic bandpass filters is proposed. The

mixed inter-resonator coupling is modeled in such a way that

both magnitudes and phase differences of constituted

capacitive and inductive couplings are made use of in finite

transmission zeros synthesis. Two 2nd

-order filters with

identical inductive-dominant coupling and different length

ratios are analytically synthesized. Next, two 4th

-order

quasi-elliptic bandpass filters with both inline capacitive- and

inductive-dominant mixed couplings are presented, designed

and fabricated. The multiple finite transmission zeros in

measured frequency responses of the fabricated filters have

well justified our proposed mixed-coupling formulation and

transmission zeros synthesis.

ACKNOWLEDGMENT

The authors are grateful to Mr. Li Yang and Dr. Dong Chen

from University of Macau for their kind help on circuit

fabrication and measurements.

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(a)

Ji,1J1,2

K1,2

J3,4

K3,4

J4,oJ2,3

K2,3

Input Output1 32 4

(b)

(c)

Fig. 8. (a) Physical layout of 4th-order Filter D, (b) mixed-coupling topology,

and (c) comparison between simulated and measured frequency responses.

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Songbai Zhang (S’11–M’14) received the B.

Eng. and Ph.D degrees in Electrical and

Electronics Engineering from Nanyang

Technological University (NTU), Singapore, in

2010 and 2014, respectively. From Jul. 2013 to Jan. 2015, he was with the

Institute of Microelectronics, Agency for

Science, Technology and Research (A*Star), Singapore. His research includes RF/microwave

passive devices: filters and antennas, advanced

3D-IC package and RFICs. Since Feb. 2015, he is with Skyworks Solutions as a Senior RFIC

Design Engineer, involved in mobile transceiver

frontend power amplifier and antenna switch module design. Dr. Zhang was a recipient of the Ministry of Education Scholarship,

Singapore, from 2006 to 2010, and the NTU Research Scholarship from 2010

to 2014. He was the best student paper recipient of the 2013 International Wireless Symposium, Beijing. He also served on as a reviewer for IEEE

TRANSACTION ON MICROWAVE THEORY AND TECHNIQUES and IEEE

MICROWAVE AND WIRELESS COMPONENTS LETTERS.

Lei Zhu (S’91–M’93–SM’00–F’12) received

the B.Eng. and M.Eng. degrees in radio engineering from the Nanjing Institute of

Technology (now Southeast University),

Nanjing, China, in 1985 and 1988, respectively, and the Ph.D. degree in electronic engineering

from the University of Electro-

Communications, Tokyo, Japan, in 1993. From 1993 to 1996, he was a Research

Engineer with Matsushita-Kotobuki Electronics

Industries Ltd., Tokyo, Japan. From 1996 to 2000, he was a Research Fellow with the École Polytechnique de Montréal,

Montréal, QC, Canada. From 2000 to 2013, he was an Associate Professor

with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. Since August 2013, he has been a

Professor with the Faculty of Science and Technology, University of Macau,

Macau, China. Since September 2014, he has been serving as the Head of Department of Electrical and Computer Engineering, University of Macau. His

research interests include microwave circuits, guided-wave periodic structures,

antennas, and computational electromagnetic techniques. Dr. Zhu was the Associate Editors for the IEEE TRANSACTION ON

MICROWAVE THEORY AND TECHNIQUES (2010-2013) and the IEEE

MICROWAVE AND WIRELESS COMPONENTS LETTERS (2006-2012). He served as a General Chair of the 2008 IEEE MTT-S International Microwave

Workshop Series on the Art of Miniaturizing RF and Microwave Passive

Components, Chengdu, China, and a Technical Program Committee Co-Chair of the 2009 Asia–Pacific Microwave Conference, Singapore. He has been

serving as the members of IEEE MTT-S Fellow Evaluation Committee and

IEEE AP-S Fellows Committee since 2013 and 2015, respectively. He was the

recipient of the 1997 Asia–Pacific Microwave Prize Award, the 1996 Silver

Award of Excellent Invention from Matsushita-Kotobuki Electronics Industries Ltd., and the 1993 First-Order Achievement Award in Science and

Technology from the National Education Committee, China.

Roshan Weerasekera (S’01–M’04–SM’12)

received the B.Sc. degree from the University of

Peradeniya, Peradeniya, Sri Lanka, in 1998 and the M.Sc. and Ph.D. degrees in electronic system

design from the Royal Institute of Technology,

Stockholm, Sweden, in 2002 and 2008, respectively.

From October 2001 to December 2003, he

was a Lecturer in the Department of Electrical and Electronic Engineering, University of

Peradeniya, and from 2008 to 2011, he was a

Research Associate with Lancaster University, U.K., within a 3-D Flash memory integration

project (ELITE) under a European Union FP7 research grant. Currently, he is

with the Institute of Microelectronics (IME), Agency for Science, Technology and Research (A*STAR), Singapore. His research interests include the

2D/2.5D/3D heterogeneous system design for applications such as data-center

servers, portable computing platforms; and integrated bio-sensor platforms for point-of-care systems.