CALIFORNIA STATE UNIVERSITY, NORTHRIDGE

MICROWAVE COUPLED LINE BANDPASS FILTER DESIGN

A graduate project submitted in partial fulfillment of the requirements

For the degree of Master of Science in

Electrical Engineering

By

Harish Polusani

May 2015

ii

The Graduate Project of Harish Polusani is approved:

______________________________ ______________

Professor. Farahnaz Nezhad Date

______________________________ ______________

Professor. Bruno Osorno Date

______________________________ ______________

Dr. Matthew Radmanesh, Chair Date

California State University, Northridge

iii

Acknowledgement

I would like to thank Dr.Matthew Radmanesh for his valuable guidance and support in

helping me to complete my project. I am grateful to him for giving me an opportunity to

work under him. Also, he is an inspiration to me for the hard work he puts in to his work

and also the way he tries to achieve perfection.

I also thank professor.Bruno Osorno and professor.Farahnaz Nezhad for being in my

committee and spending their valuable time to give a feedback about my project.

Finally I would like to express my love and respect to my parents for their support,

through the duration of my studies.

iv

TABLE OF CONTENTS

SIGNATURE PAGE…………………………………………………………………..….ii

ACKNOWLEDGEMENT ……….....................................................................................iii

LIST OF TABLES...............................................................................................................v

LIST OF FIGURES............................................................................................................vi

ABSTRACT......................................................................................................................vii

CHAPTER 1: INTRODUCTION………………………………………………………...1

1.1 DESIGN PROBLEM………………………………………………..….. 2

CHAPTER 2: DESIGN THEORY AND ANALYSIS……………………………………3

CHAPTER 3: DESIGN PROCEDURE…………………………………………………..7

3.1 PCB MATERIAL SELECTION………………………………………….7

3.2 CALCULATION OF STRIPLINE DIMENSIONS...................................8

3.3 CALCULATION OF INSERTION LOSS, CENTER FREQUENCY

AND BANDWIDTH…………………………………………………....20

3.4 ADS SIMULATION…………………………………………………….21

CHAPTER 4: CONCULSION..........................................................................................25

REFERENCES..................................................................................................................26

Appendix: A MATLAB CODE……………………………………………………..….27

Appendix: B PCB DATA SHEET……………………………………………………...28

v

LIST OF TABLES

Table 1.Filer architectures and their related quality factor. ................................................ 4

Table 2. Filer quality factor vs passband insertion loss. ..................................................... 5

Table 3.Even and odd mode characteristic impedance of filter stages. ............................ 15

Table 4.The Width (W) and Spacing(S) of stripline for each stage.................................. 20

Table 5.Comparison of results with desired specifications. ........................................................... 25

vi

LIST OF FIGURES

Figure 1. Characteristic line impedance as function of w/h ................................................ 9

Figure 2. ADS start line calculation of width, length and 𝜖eff of microstrip line. ............ 10

Figure 3. Effective di-electric constant as a function of w/h for various dielectric

constants ............................................................................................................................ 11

Figure 4. Normalized wavelengths vs. W/h with ϵ r as a parameter ................................ 12

Figure 5. Even and odd mode differential impedances of a microstrip line on Substrate

with εr =10 ......................................................................................................................... 16

Figure 6. ADS start line calculation of width, spacing and length of the microstrip

coupled line for Odd and even characteristic impedance. ................................................ 18

Figure 7. ADS start line calculation of width, spacing and length of the microstrip

coupled line for Odd and even characteristic impedance. ................................................ 19

Figure 8. Attenuation vs normalized frequency at 0.5 dB ripple. ..................................... 21

Figure 9. ADS Schematic of coupled line bandpass filter. ............................................... 22

Figure 10. The ADS simulated results of passband insertion loss (S21) and return loss

(S11). .................................................................................................................................. 23

Figure 11. The ADS designed layout of coupled line bandpass filter. ............................. 24

Figure 12. The final ADS design layout with dimensions. ............................................... 24

vii

ABSTRACT

MICROWAVE COUPLED LINE BANDPASS FILTER DESIGN

By

Harish Polusani

Master of Science in Electrical Engineering

Microwave frequency filters are suitable for satellite communication, wireless

communication and in military applications. For these applications, we need to design

filters that deliver high performance, at a low cost and small size. These requirements are

fulfilled by using high-quality materials. Printed circuit board (PCB) technology is

benefited by having high-quality factor materials. Printed circuit board is familiar and

practically easy to manufacture. This project presents the design of a paralleled line band

pass filter using PCB with higher dielectric permittivity (ORCER CER εr=10).

The coupled line band pass filter designed for this project has specifications with

midband frequency of 1.59 GHz and bandwidth of 0.159 GHz with Passband insertion

loss to be < 5 dB and return loss to be > 15 dB. This design was derived from standard

design theory, which is mentioned in the literature. Advanced design system software

(ADS) is used to simulate the design. The results of theoretical and simulated are

compared with the design goals, and the reasons for small variation among the results are

analyzed, and methods to improve the performance of filter are discussed in this project.

1

CHAPTER 1

INTRODUCTION

This paper includes the design of a coupled line band pass filter which meets the desired

requirements of center frequency at 1.59 GHz with a bandwidth of 0.159 GHz. Passband

insertion loss to be <5 dB and return loss to be >15 dB. These specifications are chosen

to make the filter design practical. The main purpose behind the design is to illustrate

some problems presently faced by RF filter designers. Radio frequency filters are mainly

used in satellite receivers, ground stations and military applications. These applications

have high demand because of the crowded spectrum, complex working environments and

higher performance. For many decades, manufacturing industries have been continuously

trying to reduce the cost and size of the filter.

It is not easy to design a filter using planar architecture; it involves complexity. The

selection of dielectric substrate used in the construction of PCB plays a major role in

design outcomes. If a high-quality substrate is used, then it results in low signal loss in

the passband.

The design illustrated here is a planar-coupled line filter type, which is more practical to

design and uses a most common design procedure compared to other PCB based

architectures. Using this planar architecture, we can easily meet our specification

requirements. Filters which are operating in the microwave frequency range must be

designed by using distributed transmission line structures. The dimensions for the

distributed transmission lines can be obtained by using formulas in literature or using

advanced simulation software. By taking all these factors into consideration and using

advanced tuning procedures, we can achieve our design specifications.

2

1.1 DESIGN PROBLEM

The goal of this project is to design a coupled line bandpass filter which is used for the

application in mobile communication where it requires insertion loss less than 1 dB.

Parameters Goal

Center frequency 1.59GHz

Bandwidth (10%) 0.159GHz

Insertion loss <5 dB

Return loss >15 dB

3

CHAPTER 2

DESIGN THEORY AND ANALYSIS

Nowadays, industries are experiencing continuous pressure to improve performance of

the filters. Recent papers on filters reveal that continuous development or improvement to

the design is required. By the use of advanced materials in designing the filters, their

performance can be improved. The use of this high-quality material in design will also

reduce the size and losses in the signal.

The textbook published by R. Ludwig and P. Bretchko [1] provides the overview of filter

design basics such as filter types and filter design theory. In his work author recommends

use of software tools as an advantage to tune the filter. Other references provide required

formulas to design a refined coupled lined filter without simulation tools [1].

Filter types described in the reference [1] can be Butterworth, chebyshev and linear

filters. Among these types chebyshev has an advantage of fast switching between

passband and stopband signal spectrum [1].

The selection of PCB substrate affects the performance of the filter, because the substrate

quality factor is inversely related to the passband insertion loss. If we choose a PCB with

a low quality factor, it results in a high passband insertion loss, which lowers the

performance of the filter. So selection of the material is an important step in the design of

a filter.

The quality factor is defined as the ratio of reactance to the resistance of the circuit

[4].The overall quality factor is obtained from the quality factor of the material and

quality factor associated with the circuit’s radiated emission [5].

4

The filter that is designed using common FR4 substrate will result in a high signal

loss>5dB. In order to reduce the signal loss, we should use high-quality materials with

quality factors over 300.

The quality factor of different filter architectures is shown in the Table 1 [4]

Filter architecture Quality factor

Lumped Element 10-50

Mircrostrip 50-200

Coaxial resonators 200-5000

Dielectric resonator 1000-10000

Waveguide 1000-50000

Table 1.Filer architectures and their related quality factor [4].

The corresponding insertion loss obtained from various quality factors is shown in the

Table 2 [4]

5

Quality factor insertion loss (dB)

10000 0.3

1000 0.5 to 1.0

300 1.4 to 2.3

100 4.0 to 6.0

Table 2. Filer quality factor vs passband insertion loss [4].

A cellular ground station requires a filter with passband insertion loss to be less than 1dB

(i.e., IL<1 dB). So in order to design a filter with low insertion loss of 1dB, we have to

choose the appropriate filter architecture which meets our requirement. The table 2

clearly shows it can be achieved by a filter with quality factor of 1000 or above.

Dielectric resonator falls within this category, due to its high-quality factor and low

signal loss.

The size of the filter designed by using dielectric resonator architecture inversely depends

on its permittivity constant (∈r). This means that if ∈r is high then the size of the designed

filter will be small. However, in spite of these advantages, it is more complex to design a

filter using a dielectric resonator architecture, due to high production costs [6].Other filter

types such as waveguides may also have advantages in performance, but they face issues

such as production cost and size. These issues can be overcome by using planar type

architecture.

6

The planar type implementation of the passband filter is the most common and most

practical design. The size and cost of the filter can be reduced by using planar type

architecture. Designing of such a filter provides the benefits of present advanced

materials.

The main aim of this project is to design a band pass filter which benefits from these

advanced materials. Recent papers on filters and advanced simulation softwares are used

to design a high tuned coupled line bandpass filter.

7

CHAPTER 3

DESIGN PROCEDURE

The coupled line bandpass filter is designed by using the coefficients published in the

Ludwig and Breutko book [1]. These coefficient sets represent the low pass Chebyshev

filters. Each of the coefficient sets represent capacitance and inductance of a lumped

element of a low-pass filter. Transforming these coefficients from lumped elements to

distributed elements, we can develop a bandpass filter with required specs. The obtained

bandpass filter from these coefficients has consecutive LC resonant pairs. The frequency

of each resonant LC pair is equal to filter center frequency.

Illustrated examples and equations from [1] [3] are used for converting filter coefficients

to distributed structures, these distributed structures of a coupled line filter consists of

two parallel transmission lines traveling across the PCB surface.

3.1 SELECTION OF PCB MATERIAL

Selection of PCB is the most important aspect in designing the filter. The properties of

these selected PCB have major impact upon the filter performance. In this design, we

used ORECER CER_10 PCB with 𝜖r =10. TACONIC COORPORATION provides

samples of PCB materials with required properties and dimensions. This PCB board

(ORECR CER-10) has a thickness of 1.57 mm with copper laminated on the surface of

both sides of the PCB with thickness of 0.007” (18 micrometer).

8

This PCB is selected due to its low dissipation factor (high-quality factor). A filter

designed with low dissipation factor material provides an advantage of low passband

insertion loss. The ORCER CER-10 has a dissipation factor of 0.0035. An Ideal PCB has

a zero-dissipation factor, which means no insertion loss. As this is a 3-stage filter, each

stage will have a pair of Micro-strip lines with a length that is approximately equal to

quarter wavelength (λ/4).

3.2 CALCULATION OF STRIPLINE DIMENSIONS

In calculating the strip line dimensions the procedure will be broken down into the

following steps for better understanding. In first step, we need to determine the lengths

for all stages of the coupled lined filter. As mentioned earlier, each stage length was

approximately equal to a quarter wavelength (𝜆

4) at f0.

In order to determine the length of each stage, first we have to determine the effective

dielectric constant. To find the effective dielectric constant 𝜖eff, we have to do some

approximations. In a first order of approximation, the thickness of the conductor is

neglected compared to height of the substrate. In such a case we can use, formulas that

depend only on width, height and dielectric constant(𝜖r).

The w/h ratio is calculated by using the equations given by [2] and the obtained value is

compared with the graphs provided in [1]. If Zo=50 ohms and 𝜖r = 10 then the w/h ratio is

calculated by using the approximation method from [2] by assuming w/h<2

𝑤

ℎ=

2∗𝑒𝐴

𝑒2𝐴−2

= 0.95

9

A =

𝑍𝑜

60√

𝜀𝑟+1

2

+

𝜀𝑟+1

𝜀𝑟−1(0.23+0.11

𝜀𝑟) = 2.151521

The obtained w/h ratio is verified by using the graph shown in Fig.1.From this graph we

obtain w/h=0.93 which is very close to the calculated value of 0.95

Figure 1. Characteristic line impedance as function of w/h [1]

The ADS simulation is also used to verify the calculated w/h ratio.

10

Figure 2. ADS start line calculation of width, length and 𝜖eff of microstrip line.

By using the width obtained in ADS and height from the PCB data sheet, we can

calculate w/h ratio as: 𝑤

ℎ=

1.473

1.570=0.93

This above obtained value is almost the same as the previous w/h values.

By using the equations provided in [2], [1] we can find 𝜖eff and length of each stage of

the filter

𝜖eff=∈𝑟+1

2+

∈𝑟−1

2[(1+12

ℎ

𝑤)-1/2 +0.04(1-

𝑤

ℎ)2 ]= 6.7 [2]

11

The obtained 𝜖eff value is verified using the graph shown in Fig.3. From this figure 𝜖eff is

found to be 6.7 which is the same as the calculated value.

Figure 3. Effective di-electric constant as a function of w/h for various dielectric

constants [1]

The total length of the third order coupled lined filter is given by:

Total filter length = (N+1) (𝜆0

4) = (3+1) (0.717”) =2.86”.

The above obtained filter length is verified by using the following equation [2]

12

λ = λo

√𝜀𝑟 √𝜀𝑟

1+0.63(𝜀𝑟−1)(𝑤

ℎ)^0.1255

=2.88”

The normalized wavelength is given by [2]

λ

λtem =√

𝜀𝑟

1+0.63(𝜀𝑟−1)(𝑤

ℎ)^0.1255

= 1.227

The above obtained normalized wavelength value is verified using the graph shown in

fig.4. From this figure normalized wavelength is found to be 1.225 which is very close to

the calculated value.

Figure 4. Normalized wavelengths vs W/h with ϵ r as a parameter [2].

13

The second step is to determine even and odd impedances of each trace pair by using

equations provided in [1]. By simulating the obtained impedances in ADS, we can

determine the width (W) and spacing(S) of each trace pair of a coupled line filter.

In order to make the calculations easier to understand, the filter coefficients,

characteristic line impedance, center frequency and bandwidth are expressed in terms of

J-parameters.

The calculation of K parameters for Chebyshev filter with ripple less than 0.5dB can be

obtained by using the coefficients from [1]:

g0=1.0000

g1=1.5963

g2=1.0967

g3=1.5963

g4=1.0000

These coefficients represent the lumped element’s values of the LC filter.

The normalized bandwidth is given by:

Normalized bandwidth (Δ) = fu−fl

f0 =

0.159

1.59 = 0.1

Where f0=√𝑓𝑢𝑓𝑙 =1.59 GHz

14

fu =upper cutoff frequency

fl =lower cutoff frequency

Z0=50Ω

Z0 J0, 1=√𝜋Δ

2gog1 = 0.3137

Z0J1, 2 =𝜋Δ

2√g1g2 =0.1187

Z0J2, 3 =𝜋Δ

2√g2g3 =0.1187

Z0J3, 4=√𝜋Δ

2g3g4 =0.3137

15

Determine the even and odd impedances of each trace pair (Z0 odd, Z0 even) [1]

Z0 odd (Ji, i+1) =Z0 (1- Z0 Ji, i+1+ (Z0 Ji, i+1)2)

Z0 even (Ji, i+1) =Z0 (1+ Z0 Ji, i+1+ (Z0 Ji, i+1)2

The obtained even and odd impedances are tabulated in TABLE 3:

Stage Z0 odd(Ω ) Z0 even(Ω)

0,1 39.2 70.6

1,2 44.76 56.64

2,3 44.76 56.64

3,4 39.2 70.6

Table 3.Even and odd mode characteristic impedance of filter stages.

16

The strip-line dimensions are obtained by using the graphs shown in figure 5 [3]

Figure 5. Even and odd mode differential impedances of a microstrip line on Substrate

with εr =10 [1].

17

The values of Spacing and Width correspond to the even and odd differential impedances

are noted from the above graph.

For Z0 odd =39.2 ohms and Z0 even =70.6 ohms the spacing and width are noted as.

S/d=0.42 => S=0.42xd => S=0.42x1.57=>S=0.659 mm =>S=25.944 mils

w/d=0.72=>w=0.72xd=>S=0.72x1.57=>S=1.130 mm =>S=44.481 mils

For Z0 odd =44.76 ohms and Z0 even =56.64 ohms the spacing and width are noted as.

S/d=1.2=> S=1.2xd => S=1.2x1.57=>S=1.88 mm=>S=74.173 mils

w/d=0.91=>w=0.91xd=>S=0.91x1.57=>S=1.428=>S=56.24 mils

18

The above stripline dimensions are verified by using the ADS line calculator tool.

Figure 6. ADS start line calculation of width, spacing and length of the microstrip

coupled line for Odd and even characteristic impedance.

19

Figure 7. ADS start line calculation of width, spacing and length of the microstrip

coupled line for Odd and even characteristic impedance.

20

Table 4.The Width (W) and Spacing(S) of stripline for each stage.

3.3 CALCULATION OF INSERTION LOSS, CENTER FREQUENCY AND

BANDWIDTH.

The center frequency of the filter can be calculated using equations provided in textbook

[1]. As we mentioned earlier in the design theory, the length of each stage of the filter is

equal to its quarter wavelength.

λ =𝑐

𝑓√εeff | at f0

f0 = 3𝑥10^8

0.0731√6.7 = 1.58 GHz

The insertion loss can be calculated by using the graph provided in textbook [3]

ω = 2π [fo + 0.05fo]

Stage Z0 odd(Ω ) Z0 even(Ω) Width(w) Spacing(s)

Width(W)

(calculation)

Spacing(s)

(calculation)

0,1 39.2 70.6 44.45 mils 25.206 mils

44.48 mils

25.944 mils

1,2 44.76 56.64 55.2 mils 74.938 mils

56.24 mils

74.173 mils

2,3 44.76 56.64 55.2 mils 74.938 mils

56.24 mils

74.173 mils

3,4 39.2 70.6 44.45 mils 25.206 mils

44.48 mils

25.944 mils

21

|ω

ωo| = 1.05

|ω

ωo| - 1 = 0.05

By using the graph shown in fig.8.The insertion loss can be noted as approximately equal

to 1.2 dB at n=3.

Figure 8. Attenuation vs normalized frequency at 0.5 dB ripple [1].

3.4 ADS SIMULATION

The values obtained by calculations were entered into the ADS software for evaluation,

and the design is tuned using the ADS tools. By using the values calculated in startline

calculation tool in ADS are inserted into the ADS schematic as shown fig.9.

22

Figure 9. ADS Schematic of coupled line bandpass filter.

The schematic is simulated and S11 (return loss), S21 (insertion loss) parameters are

plotted on the graph as shown in fig.10. The layout is shown in fig.11.

23

Figure 10. The ADS simulated results of passband insertion loss (S21) and return loss

(S11).

24

Figure 11. The ADS designed layout of coupled line bandpass filter.

a=57.48 mils b=716 mils c=735.6 mils d=44.45 mils

e=25.2 mils f=720.5 mils g=55.27 mils h=74.93 mils

i=55.2 mils j=720.5 mils k=735.6 mils l=44.45 mils

m=74.93 mils n=716 mils o=57.48 mils

Figure 12. The final ADS design layout with dimensions.

25

CHAPTER 4

CONCLUSION

The results obtained in ADS are analyzed and tabulated. Results provide passband

insertion loss to be 1.048 dB .This loss of 1.048 dB is assumed to be due to skin effect,

conductor loss, and dielectric loss and radiated emission.

ADS simulation provided a Center frequency of 1.56 GHz, which has a difference of

0.03GHz from the specified target (1.59 GHz), a bandwidth of 0.17GHz which has a

small difference of 0.011GHz from the design goal of 0.159GHz.This difference in center

frequency is due to variation of electrical length at each stage of the filter, which is due to

changes in the εr of the substrate. A 10% variation in εr will affect the center frequency

by 5% [1] [3].

Table 5.Comparison of results with desired specifications.

Parameter Goal Hand Calculation MATLAB ADS

Passband insertion

loss (S21)

<5dB 1.2 dB 1.23dB 1.048 dB

Return loss (S11) >15dB N/A N/A 26.6 dB

Center frequency(f0) 1.59GHz 1.58GHz 1.58 GHz 1.56GHz

Bandwidth (BW) 0.159GHz 0.158 GHz 0.18GHz 0.17GHz

26

REFERENCES

[1] R. Ludwig and P. Bretchko, “RF Circuit Design: Theory and Applications”. Upper

Saddle River, New Jersey: Prentice-Hall, 2000.

[2] Matthew, Radmanesh, “RF & Microwave Design Essentials: Engineering Design and

Analysis” from DC to Microwaves, 2007.

[3] Pozar, David M, “Microwave Engineering”, 3rd

Edition, Wiley, 2005.

[4] I. Hunter, R. Ranson, A. Guyette, and A. Abunjaileh, “Microwave filter design from

a Systems perspective,” IEEE Microwave Magazine, vol. 8, no. 5, p. 71, Oct. 2007.

[5] J.-S. Hong and M. J. Lancaster,” Microstrip Filters for RF/Microwave Applications”,

chapter 3, New York, NY: John Wiley and Sons, 2001.

[6] C. Wang and K A. Zaki, “Dielectric resonators and filters,” IEEE Microwave

Magazine, vol.8, no. 5, pp. 115-127, Oct. 2007.

27

Appendix A

MATLAB CODE

%w width of the substrate calculated from the calcualtions and ADS

simulation or from graphs in reference[1] %h %height of the substrate from data sheet %s %thickness of the substrate from data sheet %Er%dielectric permitivity of the substrate K=input('enter dielectric permitivity of the PCB substate from

substate'); c=3*10^8;%speed of light f=input('center frequency in Hz');%center frequency %R=w/h; Z0=input('enter characteristic line impedance'); G=(Z0/60)*((K+1)/2)^0.5+((K-1)/(K+1))*(0.23+(0.11/K)) r=(8*exp(G))/(exp(2*G)-2)% r=w/h if(r<1) Ee = (K + 1)/2 + (K - 1)*((1 + 12/r)^-0.5 + 0.04*(1-r)^2)/2 else Ee = (K + 1)/2 + (K - 1)*((1 + 12/r)^-0.5)/2 end wavelenth=(3*10^8)/(Ee)^0.5/(4*f)*(39370.0787) %lenth of the filter

conveted to mils by multiplying with 1meter=39370.0787 miles l=((0.05966)*(K/(1+0.63*(K-1)*r^0.1255))^0.5)*39.3701%total length of

the filter is given by l normalizedwavelenth=(K/(1+0.63*(K-1)*r^0.1255))^0.5 %normalized

wavelenth ?/?tem z0=1.0000 %coefficients represents the lumped elements values z1=1.5963 z2=1.0967 z3=1.5963 z4=1.0000 bw=0.159*10^9 %bw represents bandwidth fbw=bw/f %fbw represents fractional bandwidth which should be 10% Z(1)=(3.14*fbw/(2*z0*z1))^0.5; display(Z(1)) Z(2)=3.14*fbw/(2*(z1*z2)^0.5); display(Z(2)) Z(3)=3.14*fbw/(2*(z2*z3)^0.5); display(Z(3)) Z(4)=(3.14*fbw/(2*z3*z4))^0.5; display(Z(4)) for j=1:4; Zodd = Z0*(1-Z(j)+(Z(j))^2) Zeven=Z0*(1+Z(j)+(Z(j))^2)

end %center frequncy can be derived from the wavlength formula fo=c/(0.0731*Eeff^0.5) b=fo/10 w= 2*3.14*1.05*fo NF=w-1%normalized frequency\ B=1.23% from graph from normalized frequency vs attuenation

28

Appendix B s

DATA SHEET

29