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
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,
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
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
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
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
ε
r=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
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
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
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
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
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 DIMENSIONSIn 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 f
0.
In order to determine the length of each stage, first we have to determine the effective
dielectric constant. To find the effective dielectric constant
𝜖
eff, we have to do someapproximations. 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(
𝜖
r).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
𝜖
r = 10 then the w/h ratio iscalculated by using the approximation method from [2] by assuming w/h<2
𝑤 ℎ
=
2∗𝑒𝐴 𝑒2𝐴−2
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]
10
Figure 2. ADS start line calculation of width, length and
𝜖
eff 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
𝜖
eff and length of each stage ofthe filter
𝜖
eff=
∈𝑟+1 2+
∈𝑟−1 2[(
1+12
ℎ 𝑤)
-1/2+0.04
(
1-
𝑤 ℎ)
2]
=
6.7 [2]11
The obtained
𝜖
eff value is verified using the graph shown in Fig.3. From this figure𝜖
eff isfound 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)
(
𝜆04
)
= (3+1) (0.717”) =2.86”.12
λ =
λo√𝜀𝑟
√
𝜀𝑟
1+0.63(𝜀𝑟−1)(𝑤ℎ)^0.1255
=2.88”
The normalized wavelength is given by [2] λ
λtem
=
√
𝜀𝑟
1+0.63(𝜀𝑟−1)(𝑤ℎ)^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]:
g
0=1.0000
g
1=1.5963
g
2=1.0967
g
3=1.5963
g
4=1.0000
These coefficients represent the lumped element’s values of the LC filter.
The normalized bandwidth is given by:
Normalized bandwidth (Δ)
=
fu−flf0
=
0.159
1.59
= 0.1
14
f
u =upper cutoff frequencyf
l =lower cutoff frequencyZ
0=50Ω
Z
0J
0, 1=
√
𝜋Δ 2gog1= 0.3137
Z
0J
1, 2=
𝜋Δ 2√g1g2=0.1187
Z
0J
2, 3=
𝜋Δ 2√g2g3=0.1187
Z
0J
3, 4=
√
𝜋Δ 2g3g4=0.3137
15
Determine the even and odd impedances of each trace pair (
Z
0 odd,Z
0 even) [1]Z
0 odd(J
i,
i+1) =Z
0(1- Z
0J
i, i+1+ (Z
0J
i, i+1)
2)
Z
0 even(J
i,
i+1) =Z
0(1+ Z
0J
i, i+1+ (Z
0J
i, i+1)
2The obtained even and odd impedances are tabulated in TABLE 3:
Stage Z
0 odd(
Ω) Z
0 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
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
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 =
𝑓√εeff𝑐|
at f0f0 = 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
21
|ωoω | = 1.05 |ωoω | - 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
22
Figure 9. ADS Schematic of coupled line bandpass filter.
The schematic is simulated and S11 (return loss), S21 (insertion loss) parameters are
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
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
ε
r of the substrate. A 10% variation inε
r 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
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\
28