Study on MMIC Filter Composed of Microstrip Transmission Line

Bolin Ke, Chunhua Li Electronic Information Engineering College

Zhejiang Wanli University No.8, South Qian Hu Road Ningbo, Zhejiang Province

China kebolin@sina.com.cn http://dxxy.zwu.edu.cn

Abstract—Microstrip transmission line has some unique filter characteristics. This paper analyses filter characteristics of two kinds of parallel transmission line with specified length on basis of Y parameter theory. Loa-pass filter Matlab and Pspice software simulation proves the correctness of the analysis. Due to the advantages of simple structure and easy integration, parallel transmission lines can be widely used in the elements of MMIC (Monolithic Microwave Integrated Circuit).

Keywords-Monolithic Microwave Integrated Circuit, Parallel Transmission Line, Filter Characteristics, Filter

I. FORWARD When circuit frequency achieves radio frequency or even

microwave, circuit should be connected with microstrip transmission line that has two main functions. 1) if microstrip transmission line with specified characteristic impedance matching with output impedance of front-end circuit and input impedance of rear-end circuit is designed according to requirement, power loss can be minimized during signal transmission; 2) it is applied in input, output or stage matching of circuit on basis of impedance characteristics of microstrip transmission line. Microstrip transmission line is usually designed and realized according to these two points.

Microstrip transmission line is suitable for making planar structure transmission line of microwave integrated circuit. Compare with metallic waveguide, it has advantages of small size, light weight, wide frequency band], high reliability and low manufacturing cost, but it has disadvantages of more power consumption and less power capacity. In early 1960s, due to the development of microwave low-loss dielectric materials and microwave semiconductor device, microwave integrated circuit was formed and microstrip transmission line was widely used. Diversified microstrip transmission line arose successively, which usually made with thin film process. Dielectric substrates use materials with high dielectric constant and low microwave loss. Conductor should have characteristics of high conductivity, good stability and strong adhesion with substrate.

This paper discusses the method of controlling filter characteristics by using wiring layout of microstrip transmission lines, and configuring filter structure with these transmission lines. Obviously, filter designed in this way is on basis of distributed parameters instead of inductor and capacitor of lumped parameters, so it is especially applicable in

microwave frequency range. This method isn’t applicable to submicrowave frequency, because frequency is low and wring dimension related to wavelength parameters is too large to achieve.

This paper provides theoretical analysis on filter transmission characteristics of parallel transmission lines and proposes the concept of composing low-pass filter and wideband ban pass filter with specified parallel transmission lines, which will provide effective approach for practical application of parallel transmission lines in MMIC.

II. CIRCUIT STRUCTURE OF PARALLEL TRANSMISSION LINES WITH SPECIFIED LENGTH (PTLWSL)

The study object is parallel transmission line. According to its characteristics, theoretical analysis on parallel transmission line by using Y parameter is effective and practical.

Y parameter of transmission line with characteristic impedance of cZ and length of l (electrical length:θ ) is as follows:

θctgZjyyc

−== 2211 θcsc2112cZjyy ==

As shown in Fig. 1, Y parameters of parallel transmission lines with the same characteristic impedance of cZ and

respective length of 1l and 2l are as follows:

21

21

21

1221

2

2

1

1212211

sinsin)sin(

sinsinsincossincos

sincos

sincos

θθθθ

θθθθθθ

θθ

θθθθ

+−=

+−=

−−=−−==

c

c

cccc

Zj

Zj

Zj

Zjctg

Zjctg

Zjyy

(1a)

21

212112 sinsin

)sin(sinθθθθ +

==cZjyy

(1b)

As for two-port network whose source impedance and load impedance are real numbers, its equation of converting power gain is shown below:

2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 © 2010 IEEE

DOI 10.1109/iCECE.2010.1044

4299

2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 © 2010 IEEE

DOI 10.1109/iCECE.2010.1044

4299

2

21122211

221

)1)(1(

4

yyR

yR

yRR

yG

LsLs −++

=

(2)

Supposing Ls RR = and using Lc RZ 2= , equation of converting power gain for parallel transmission line is shown below:

2

221

22121

221

221

)sin(sin21)]sin(

22sinsin2[

)sin(sin)sin(sin4

θθθθθθ

θθθθ

+++−⋅

⋅+=

j

G

(3)

Supposing 221 2φθθ =+ 112 2φθθ =− (4)

After derivation and simplification, and writing attenuation, equation (5) is derived:

⎥⎦

⎤⎢⎣

⎡+=−=

12

22

14

cossin4sin

1lg10lg10φφ

φGAdB

(5)

Attenuation characteristics of parallel transmission line can be calculated with equation (5) according to the length of transmission line.

Fig.1 Parallel Transmission Line

If frequency rf is reference frequency and microstrip

wavelength is rλ , electrical length θ of transmission line with length l is as follows:

rr ffll ⋅==

λπ

λπθ 22

(6)

Once transmission line length 1l and 2l are determined,

according to the relation of φ and θ , equation (5) can be

directly expressed as the function ofrff

.

This paper chooses parallel transmission lines with two kinds of specified length such as rl λ25.01 = , rl λ25.12 =

and rL λ5.01 = , rl λ=2 as structural circuit. In view of simplification, parallel transmission lines with specified length are referred to as PTLWSL below. Attenuation characteristics of PTLWSL structural circuit can be analyzed according to equation (5).

A. I-type Structural Cell Circuit

PTLWSL with rl λ25.01 = and rl λ25.12 = is defined as I-type structural cell circuit. According to equation (4), (5) and (6), its attenuation equation is shown below:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⋅⋅

⋅+=−=

)(cos)2

3(sin4

)(sin1lg10lg10

22

4

rr

rdB

ff

ff

ff

GAππ

π

(7)

According to equation (7), ),2,1,0( ⋅⋅⋅== nnffr

,

0=dBA ; relation between attenuation characteristics dBA of

21+= n

ffr

and 31)12( ±+= n

ffr

, ∞=dBA and rff

repeats with a cycle of “2”. Among 2~0=rff

,

)32(~)

21(=

rff

and )23(~)

34(=

rff

are stop bands,

minimum attenuation is 13.6dB and curve of attenuation

characteristics is symmetric to rff

.

B. II-type Structural Circuit

PTLSL with rl λ5.01 = and rl λ=2 is defined as II-type structural circuit. Similar to the analysis on I-type structural cell circuit, its attenuation equation is shown below:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⋅⋅

⋅+=

)2

(cos)2

3(sin4

)2

(sin1lg10

22

4

rr

rdB

ff

ff

ff

A ππ

π

(8)

According to the above

equation: ),2,1,0(2 ⋅⋅⋅== nnffr

, 0=dBA ; relation

between attenuation characteristics dBA of 21+= n

ffr

&

43004300

31)12( ±+= n

ffr

, ∞=dBA and rff

also repeats with a

cycle of “2”. Among 2~0=rff

, )34(~)

32(=

rff

is stop

band, minimum attenuation is 8.5dB and curve of attenuation

characteristics is symmetric to rff

.

III. FILTER CHARACTERISTICS OF PTLWSL STRUCTURAL CASCADED CIRCUIT

According to equation (1a), (1b) and (4), Y parameters of two same structural circuit cascaded network are derived as follows:

)cos(coscos)coscos2(sin

12

22

2

12

22

2

2211

φφφφφφ

−−=

=

c

aa

Zj

yy

(9a)

)cos(coscoscossin

12

22

2

12

2

2112

φφφφφ

−−=

=

c

aa

Zj

yy

(9b)

Substitute equation (9a) and (9b) into equation (2), and substitute conditions of Ls RR = and Lc RZ 2= , through derivation and simplification, attenuation equation is shown below:

⎥⎦

⎤⎢⎣

⎡+==

14

22

14

22

cossinsincos

1lg10φφφφ

dBA (10)

According to comparison between equation (10) and (5),

one factor 1

22

2

coscos4

φφ

is added in the second term of logarithm

in equation (10).

IV. CONCLUSION This paper proposes the concept of filter network cascaded

by two parallel transmission lines with specified length. Such network has wide adjacent stop band as low pass filter and wideband filter characteristics as band pass filter, which is easy to design by properly choosing reference frequency. When realizing microstrip structure, it’s necessary to consider uncontinuity impact of microstrip and take some correction or compensation measures. For example, chamfered square elbow can be used at corner to correct length[6] of microstrip line and compensation T-type joint can be used to reduce reflection[7]. It’s necessary to seek measures that can reduce impact of parallel cross joint through experiment. In spite of that, the analysis in this paper provides theoretical basis for realizing this kind of filter network.

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