optimizing single element microstrip hairpin low pass filter with

Transcription

OPTIMIZING SINGLE ELEMENT MICROSTRIP HAIRPIN
LOW PASS FILTER WITH SHARP REJECTION
NOR HAFIZA BINTI RAMLI
UNIVERSITI TEKNOLOGI MALAYSIA
PSZ 19:16 (Pind. 1/97)
UNIVERSITI TEKNOLOGI MALAYSIA
BORANG PENGESAHAN STATUS TESIS
JUDUL: OPTIMIZING SINGLE ELEMENT MICROSTRIP HAIRPIN LOW PASS FILTER
WITH SHARP REJECTION (PENGOPTIMUMAN PENAPIS LULUS RENDAH PIN
RAMBUT MIKROJALUR UNSUR TUNGGAL DENGAN HENTIAN TAJAM)
SESI PENGAJIAN : 2006/2007-1
Saya
(HURUF BESAR)
mengaku membenarkan tesis (PSM/Sarjana/Doktor Falsafah)* ini disimpan di Perpustakaan
Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut:
1. Tesis adalah hakmilik Universiti Teknologi Malaysia.
2. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan pengajian
sahaja.
3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara institusi
pengajian tinggi.
4. **Sila tandakan ( )
SULIT
(Mengandungi maklumat yang berdarjah keselamatan atau
kepentingan Malaysia seperti yang termaktub di dalam
AKTA RAHSIA RASMI 1972)
TERHAD
(Mengandungi maklumat TERHAD yang telah ditentukan
oleh organisasi/badan di mana penyelidikan dijalankan)
TIDAK TERHAD
√
Disahkan oleh
_________________________________
(TANDATANGAN PENULIS)
___________________________________________
(TANDATANGAN PENYELIA)
Alamat Tetap:
LOT 2623, KG RHU SEPULUH,
21090, BDR PERMAISURI,
TERENGGANU DARUL IMAN
Tarikh: 29 OKTOBER 2006
CATATAN
:
*
**
ASSOC. PROF. DR MAZLINA BINTI HJ ESA
Nama Penyelia
Tarikh: 29 OKTOBER 2006
Potong yang tidak berkenaan.
Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/organisasi
berkenaan dengan menyatakan sekali sebab dan tempoh tesis ini perlu dikelaskan sebagai
SULIT atau TERHAD.
Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana secara
penyelidikan, atau disertasi bagi pengajian secara kerja kursus dan penyelidikan, atau
Laporan Projek Sarjana Muda (PSM).
OPTIMIZING SINGLE ELEMENT MICROSTRIP HAIRPIN
LOW PASS FILTER WITH SHARP REJECTION
A thesis submitted in fulfillment of the
requirements for the award of the degree of
Bachelor of Electrical Engineering (Telecommunication)
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
OCTOBER 2006
ii
CERTIFICATION OF SUPERVISOR
“I certify that I have read this thesis and in my opinion it is fully adequate in terms of
scope and quality for the purpose of awarding a Bachelor Degree of Electrical
Engineering in Telecommunication.”
Signature
: …………………………………..
Supervisor’s Name
: Assoc. Prof. Dr. Mazlina binti Haji Esa
Date
: 29 Oktober 2006
iii
DECLARATION
“I declare that this thesis entitled “Optimizing Single Element Microstrip Hairpin
Low Pass Filter with Sharp Rejection” is the result of my own research except as
cited in the references. The thesis has not been accepted for any degree and is not
concurrently submitted in candidature of any other degree.
Signature
: ……….......................................................
Name
: Nor Hafiza binti Ramli
Date
: 29 October 2006
iv
Special dedication
To my beloved mother, father, brothers and sisters,
All my friends and relatives,
All my teachers and lecturers,
For the support and care.
And not forgetting my lovely friend…
v
ACKNOWLEDGEMENT
AlhamduliLlah, I am grateful to ALlah S.W.T for the guidance and
knowledge bestowed upon me, for without it I would not have been able to come this
far.
I would like to express my sincere appreciation to my project supervisor,
Associate Professor Dr Mazlina binti Hj Esa for her advice, understanding, guidance
and support throughout the duration of the project. Without her valuable suggestions
and encouragement, this project would not have been a success.
A special thanks to my family and all my fellow friends for their brilliant
ideas, support and encouragement through out the duration of this project.
Lastly, my heart felt appreciation goes to all, who have directly or indirectly
helped me to make this project a success.
vi
ABSTRACT
The use of microstrip in the design of microwave components and integrated circuits
has gained tremendous popularity over more than three decades. Filtering application
is a critical part of the system as it helps segregating between wanted and unwanted
signal frequencies. The major challenge in designing a filter is to meet the
requirement of its specification for a particular application. The stepped-impedance
hairpin filter is one of the recently developed configurations with prominent
compactness. Hairpin filter configuration is one of the most popular configurations
used in the lower microwave frequencies due to its compactness. This thesis presents
the optimizations performed on a single element microstrip stepped-impedance
hairpin low pass filter by varying the number of finger elements, widths, and lengths
of the microstrip section. It was found that the hairpin filter with 5 fingers, 10.08 mm
microstrip line length, and 0.3 mm width of microstrip line section is the optimum
configuration which exhibits the sharpest rejection.
vii
ABSTRAK
Penggunaan mikrojalur dalam rekabentuk komponen gelombang mikro telah
meningkatkan popularitinya sejak lebih tiga dekad lalu. Aplikasi penapis adalah
bahagian sangat penting suatu sistem di mana ia dapat memisahkan antara frekuensi
isyarat yang dikehendaki dengan yang tidak. Cabaran terbesar merekabentuk penapis
ialah memenuhi spesifikasi yang dikehendaki bagi aplikasi tertentu. Penapis pinrambut galangan-langkah adalah satu daripada jenis konfigurasi baru penapis
mikrojalur dengan kepadatan yang ketara. Tesis ini membentangkan pengoptimuman
yang dijalankan terhadap penapis lulus rendah mikrojalur galangan-langkah unsur
tunggal. Ini meliputi pelarasan terhadap bilangan jari, lebar dan panjang bahagian
talian mikrojalur. Pemerhatian dibuat menggunakan perisian simulasi. Didapati
bahawa penapis pin-rambut dengan lima jari dan , talian mikrojalur dengan dimensi
10.08 mm panjang dan 0.3 mm tebal merupakan konfigurasi yang optimum dengan
hentian paling tajam.
viii
TABLE OF CONTENTS
TITLE
i
CERTIFICATION OF SUPERVISOR
ii
DECLARATION
iii
DEDICATIONS
vi
ACKNOWLEDGEMENT
v
ABSTRACT
vi
ABSTRAK
vii
TABLE OF CONTENTS
viii
LIST OF TABLES
xi
LIST OF FIGURES
xii
LIST OF SYMBOLS
xiv
LIST OF ABBREVIATIONS
xvi
LIST OF APPENDICES
xvii
CHAPTER
TITLE
PAGE
1
INTRODUCTION
1.1
Objective of the Project
1
1.2
Problem Statement
2
1.3
Project Background
2
1.4
Scope of the Project
3
1.5
Organization of the Thesis
5
ix
2
3
4
LITERATURE REVIEW
2.1
Introduction
6
2.2
Scattering Parameters
6
2.3
Properties of Microwave Filters
9
2.4
Hairpin Filter
12
2.5
Filter Approximation Method
13
2.6
Microstrip Technology
17
SIMULATION SOFTWARE USED
3.1
Introduction
20
3.2
Microwave Office 2004
20
3.3
Example of an 8 GHZ LPF Design
24
RESULTS AND DISCUSSION
4.1
Introduction
27
4.2
Configuration of SSIH LPF
27
4.2.1 Varying the Number of Finger Elemnets
of SSIH LPFs
29
4.2.2 Varying Microstrip Line Length
of SSIH LPF
36
4.2.3 Varying Microstrip Line Width
5
of SSIH LPF
47
4.2.4 Overall Discussions
54
CONCLUSIONS AND RECOMMENDATIONS
5.1
Introduction
55
5.2
Conclusion
55
x
5.3
Suggestion for Further Work
56
REFERENCES
57
APPENDIX
58
xi
LIST OF TABLES
Table
4.1
Caption
Page
Performance comparison of SSIH LPF with varying
number of fingers
36
4.2
Performance comparison of SSIH5 LPF with increasing L
41
4.3
Performance comparison of SSIH5 LPF with decreasing L
47
4.4.
Performance comparison of SSIH5 LPF with increasing W
53
xii
LIST OF FIGURES
Figure
Caption
1.1
Configuration of a 2-finger single element microstrip
stepped-impedance hairpin low pass filter
1.2
4
1.4
3
1.3
Page
4
Configuration of a conventional microstrip
stepped-impedance low pass filter having 3-section [1]
4
2.1
Two-port network showing network variables [1]
7
2.2
Frequency response of an ideal low pass filter [1]
10
2.3
Frequency response of an ideal high-pass filter [1]
11
2.4
Frequency response of an ideal band pass filter [1]
11
2.5
Frequency response of an ideal band stop filter [1]
12
2.6
Geometry of a hairpin filter where θ is the slide
factor and Sj, j+1 is the spacing between resonators [3]
13
2.7
A Butterworth low pass attenuation response [3]
14
2.8
A Chebyshev low pass attenuation response [3]
16
2.9
Figure of General Microstrip Structure
18
3.1
Microwave Office Window
22
3.2
Window of creating a circuit
22
3.3
Figure of Setting Frequency
23
3.4
Figure of Creating Graph
23
3.4
Creating a graph.
24
3.5
Adding measurement
25
3.6
Low pass filter EMSight
25
xiii
3.7
Simulated Circuit
26
3.8
Simulated responses
26
3.9
Simulated Circuit
29
4.1
Configurations of SSIH LPFs (a) 2-finger (b)
4-finger (c) 6-finger [2]
4.2
Simulated SSIH2 LPF (a) layout (b) insertion loss
(c) |S11| and |S12| responses
4.3
33
4.6
32
(c) |S11| and |S12| responses.
4.5
31
4.4
30
34
35
4.7
Simulated insertion losses for SSIH LPFs
37
4.8
SSIH5 LPF with L = 8.12 mm (a) layout (b) |S12|
4.9
4.10
45
4.16
44
4.15
43
4.14
42
4.13
40
Simulated insertion losses for SSIH5 LPF with
varying L = 8.12 mm, 10.12 mm, and 12.12 mm
4.12
39
4.11
38
45
46
xiv
4.17
varying L = 10.12 mm, 10.10 mm, 10.08 mm,
10.06 mm, and 10.04 mm
4.18
SSIH5 LPF with W = 0.1 mm (a) layout (b) |S12|
4.19
51
4.23
50
4.22
49
4.21
48
4.20
46
52
varying W = 0.1 mm, 0.2 mm, 0.3 mm,
0.4 mm, and 0.5 mm
|S12|
53
xv
LIST OF SYMBOLS
fH
- high cut off frequency
fL
- low cut off frequency
f0
- center frequency
εr
- dielectric constant
s
- Spacing between resonator
W
- Substrate width
h
- Substrate thickness
t
- Conducting strip thickness
λ0
- Free space wavelength
θ
- Electrical length
θt
- Electrical length of tapped-line
vp
- phase velocity
l
- Input and output length
c
- Speed of light
Zc
- Characteristic impedances
β
- Propagation constant
η
- Free space wave impedance
λg
- Guided wavelength
Γ
- Reflection Coefficient
α
- Attenuation constant
LAr
- pass band ripple
LAs
- Stop band attenuation
L
- Inductance
C
- Capacitance
εre
- effective dielectric constant
xvi
Ci
- Self-capacitances per unit length
Ci,i+1
- mutual capacitances per unit length
Z0ei,i+1 - even mode impedances
Z0oi,i+1 - Odd mode impedance
xvii
LIST OF ABBREVIATIONS
FBW
-
Fractional Bandwidth
RF
-
Radio Frequency
TEM
-
Transverse Electromagnetic Mode
VSWR
-
Voltage Standing Wave Ratio
MEMS
-
Microelectromechanical System
SSIH
-
Single-element Stepped Impedance Hairpin
xviii
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
Gantt Chart
58
B
Varying of the Finger Elements
59
C
Varying of Microstrip Line Length
61
D
Varying of Microstrip Line Width
64
CHAPTER 1
INTRODUCTION
This chapter presents the objective of the project, problem statement,
background of the project, scopes of work and the organization of the thesis.
1.1
Objective of the Project
The objective of this project is to optimize a single element microstrip
stepped-impedance hairpin low pass filter by adjusting the finger numbers, widths,
and lengths of the microstrip line section.
2
1.2
Problem Statement
Low pass filters have been widely used for suppressing of unwanted
harmonics and spurious signals [1]. However, the conventional hairpin filters can
only provide a gradual cut-off frequency response. In order to achieve a sharp cut-off
frequency, more sections are thus required. This will only increase the loss in the
passband region, thus increase the circuit size. A compact hairpin structure of
stepped-impedance configuration has been recently developed with only a single
element [2]. It exhibits properties that can overcome these problems. Investigations
are thus needed for optimizing the filter performance for sharp rejection properties.
1.3
Project Background
In this project, a single element hairpin microstrip low pass filter has been
optimized using the interdigital capacitor having Chebyshev response. In this project,
emphasize is given on to optimize the single element hairpin microstrip low pass
filter with Chebyshev response. This project also aimed to investigating the
characteristic of the response, performance of the filters and comparison between the
filters. The optimum size for the hairpin microstrip filter will be selected from the
simulated results.
3
1.4
Scopes of Work
The scopes of the project are as follows:
i)
Understanding of the microwave filter theory with focus on
Chebyshev response.
ii)
Learning the Microwave Office 2004 simulation software.
iii)
Investigate the single element microstrip stepped-impedance hairpin
low pass filter configuration by adjusting its dimensions and number
of finger elements.
iv)
Analysis of results and thesis writing.
The desired specification of the stepped-impedance hairpin low pass filter are
Chebyshev response, cut-off frequency of 1.5 GHz, return loss of better than -10 dB
in the low pass region, 0.1 dB ripple in the passband region, and a stop-band
attenuation of -20 dB. The configurations of the single element filter are illustrated in
Figures 1.1 to 1.3. The dimensions are L ≅ microstrip line, W ≅ width of L, Lc ≅
length of finger, Wc ≅ width of Lc, G ≅ gap between adjacent fingers. A 3-section
conventional stepped-impedance low pass filter is illustrated in Figure 1.3. W5, W6
and L5, L6 are widths and lengths of each filter section. WF and LF are that for the
feed line.
Figure 1.1 Configuration of a 2-finger single element microstrip stepped-impedance
hairpin low pass filter [2].
4
Figure 1.4 Configuration of a conventional microstrip stepped-impedance low pass
filter having 3-section [1].
5
1.5
Organization of the Thesis
This thesis consists of five chapters. Chapter 1 presents brief overview of the
project which includes the objective of the project, problem statement, project
background, scopes of the work and organization of the thesis.
Chapter 2 briefly presents some fundamentals of a microwave filter.
Butterworth and Chebyshev response approximations are also presented.
Chapter 3 briefly discusses the software used in this project, i.e. Microwave
Office 2004 software.
In chapter 4, all the simulation results obtain are presented and discussed.
Chapter 5 concludes the thesis, with recommendations for further work.
CHAPTER 2
MICROWAVE FILTER FUNDAMENTALS
2.1
Introduction
There are some important fundamentals related to the design of a microwave
filter. Firstly, the scattering parameter is presented. This is followed by types of
filters and the Butterworth and Chebyshev filter approximation methods.
2.2
Scattering Parameters
Scattering parameters are commonly referred to as S-parameters [1]. These
parameters relate to the traveling waves that are scattered or reflected when an N-port
network is inserted into a transmission line. S-parameters are important in
microwave designs because they are easier to be measured and worked with at high
frequencies compared to other types of network parameters. A two-port network is
shown in Figure 2.1.
7
Figure 2.1 Two-port network showing network variables [1].
In Figure 2.1, the relationship between input and output travelling waves can
be defined as [1]:

+ R 0 I1 


a 1=
1  V1
2  R0

b 2=

1  V2
+ R0 I2 

2  R0


(2.1b)
b 1=

1  V1
+ R 0 I1 

2  R0


(2.1c)
a 2=

1  V2
+ R0 I 2 

2  R0


(2.1d)
(2.1a)
The square of the magnitude of these variables can be viewed as travelling power
waves as follows:
|a1|2 = incident power wave at the input
|a2|2 = reflected power wave at the input
8
|b1|2 = incident power wave at the output
|b2|2 = reflected power wave at the output
These variables and the network’s S-parameters are related by the expressions [1]:
b1 = a1 S11 + a2 S12
(2.2)
b1 = a1 S11 + a2 S12
(2.3)
Hence, S-parameters can be obtained as [1]:
S11 =
S 21 =
b1
a1
b2
a1
S12 =
a2 =0
S 22 =
a2 =0
b1
a2
b1
a2
a1 = 0
(2.4)
a1 = 0
where S11 is the network’s input reflection coefficient and S21 is the forward voltage
transmission coefficient of the network when a1 and a2 are the terminations at Port 1
and 2, respectively. S22 is the network output reflection coefficient and S12 is the
reverse transmission coefficient of the network.
Generally, the S-parameters are of complex values. Since they are voltage
ratios, they may be expressed as decibel ratios as follows:
|S11| = 20 log |S11| ≅ input reflection coefficient, dB
(2.5a)
|S22| = 20 log |S22| ≅ output reflection coefficient, dB (2.5b)
|S21| = 20 log |S21| ≅ forward gain, dB
(2.5c)
|S12| = 20 log |S12| ≅ reversed gain, dB
(2.5d)
9
The input voltage standing wave ratio, VSWR, and |S11| are related by [1]:
VSWR
1 + S11
1 − S11
(2.6)
The output VSWR is related to S22 by a similar equation. The complex input
impedance is related to the input reflection coefficients by the expression [1]:
Z input = Z 0
1 + S11
1 − S11
(2.7)
The output impedance is similarly defined using S22.
2.3
Properties of Microwave Filters
A filter allows certain range of frequencies to pass through (the passband
region) but attenuates (or reduces) others (the stopband region) [1]. Ideally, there
should be no attenuation in the passband, and maximum attenuation in the stopband.
Practically, attenuation exists in the passband, however, this can be controlled by
improving the filter design. Similarly, the attenuation in the stopband region can be
controlled. Lumped element inductors and capacitors can be used as the filter
elements at lower frequencies. At microwave frequencies, however, transmission line
sections and waveguide elements are used instead. Filters are essentially frequency
selective elements with the filtering behaviour being governed by the frequency
dependent reactances provided by inductive and capacitive transmission line
sections.
10
Minimization of the losses in the passband of a filter is extremely important
since this helps to reduce the overall losses of a transmitter while improving the
noise figure when used with a receiver. Filters can be designed using the image
parameter or the insertion loss methods. The former method is simple, however, the
response in the passband and the stopband regions cannot be precisely controlled. In
the latter method, the design starts with a low-pass prototype based on a chosen
response. The insertion losses in the passband and stopband regions can be defined
and controlled based on the number of sections and the equivalent lumped elements.
There are several types of passive filters regularly used, described as follows:
(i) Low pass filter: This filter passes low frequencies, but attenuates frequencies
higher than the cutoff frequency. An example of its frequency response is shown in
Figure 2.2 for attenuation, α, versus normalised frequencies, Ω.
Figure 2.2 Frequency response of an ideal low pass filter [1]
(ii) High pass filter (HPF): This filter passes high frequencies well, but attenuates
frequencies lower than the cutoff frequency. An example of its frequency response
is shown in Figure 2.3.
11
Figure 2.3 Frequency response of an ideal high-pass filter [1]
(iii) Band pass filter (BPF): This filter allows certain frequency signals to pass
through while attenuates others. An example of its frequency response is given in
Figure 2.4.
Figure 2.4 Frequency response of an ideal band pass filter [1]
(iv) Band stop filter (BSF): This filter rejects certain frequencies but allows others
to pass through. An example of its frequency response is shown in Figure 2.5.
12
Figure 2.5 Frequency response of an ideal band stop filter [1]
2.4
Hairpin Filter
The hairpin resonator filter is one of the most popular microstrip filter
configurations used in the lower microwave frequencies [3]. It is easy to manufacture
because it has open-circuited ends that do not need any grounding. The configuration
is derived from the edge-coupled resonator filter by folding back the ends of the
resonators into a “U” shape. This reduces the length and significantly improves the
aspect ratio of the microstrip filter as compared to that of the edge-coupled
configuration. The geometry of the hairpin filter is given in Figure 2.6. Each
resonator of the filter is 180 degrees, hence, the length from the center to either end
of the resonator end is 90 degrees. From 90 degrees, θ degrees are “slid” out of the
coupled section into the uncoupled segment of the resonator (fold of the resonator).
This reduces the coupled line lengths, thus reduces the coupling between resonators.
13
2θ
90°- θ
Sj, j+1
Figure 2.6
Geometry of a hairpin filter where θ is the slide factor and Sj, j+1 is the
spacing between resonators [3].
There are many commercially available substrates with various dielectric
constants. The high dielectric constants are more suitable for lower frequency
applications in order to help minimize the size. The size of a filter can be further
reduced by using a high-dielectric thin substrate [3]. The length of the resonator is
inversely proportional to the square root of the dielectric constant. The relationship
of the width of the microstrip and the dielectric height h is not linear. Therefore, a
decrease in the dielectric height will mean a greater decrease in the width w of the
microstrip line. The relationship is governed by:
w
8e A
=
h e 2A − 2
…………………………… (2.9)
where
A=
Zo εr + 1 εr - 1 
0.11 
+
 0.23 +

60
2
εr + 1 
εr 
Zo ≅ characteristic impedance
εr≅ relative dielectric constant
14
2.5 Filter Approximation Method
There are 4 most common filter approximation methods; Butterworth,
Chebyshev, Bessel and Elliptic. This Section will only discuss Butterworth and
Chebyshev approximations that are most commonly and widely used method.
(a) Butterworth Approximation
This is also known as maximally flat due to the presence of a flat response at
the pass band. Figure 2.5 shows a typical Butterworth low pass filter attenuation
frequency response. The frequency ω1’ where the corresponding attenuation is LAr is
defined as the pass-band edge.
Figure 2.7
A Butterworth low pass attenuation response [3]
Butterworth attenuation is given by the simple closed form expression [3]:
LA( ω')
2N

ω'  

10 log1 + ε ⋅
 

 ω1 ⋅'  
…………………. (2.10)
15
where N equals to filter order, ω' equals to the desired frequency and ω`1 equals to
the cutoff frequency. In the passband, the attenuation is nil and therefore the return
loss is excellent. The above synthesis procedure is the basic of the Butterworth
prototype g-value. With ε = 1, the Butterworth g-values are given by:
gn
 ( 2n − 1)n

 2N 
2 sin
……………………… (2.11)
with n = 1, 2, 3…..N
g N+1 = 1………………………………………(2.12)
(b) Chebyshev Approximation
Chebyshev filter utilizes an equal ripple approximation in the pass band and
exhibit a monotonically increasing loss characteristic in the stop band [3]. It has an
error distribution over the entire pass band. Hence, it holds the peak amplitude of the
error to a minimum. Chebyshev filter or “equal ripple” has an advantage of requiring
less order compared to Butterworth filter with the same bandwidth. The filter has a
much sharper rate of cutoff and produces a more rectangular attenuation curve
similar to an ideal low pass filter. It also can produce better frequency response at
band pass and the slope at cut-off frequency nearing stopband ripple. Figure 2.6
shows a typical Chebyshev low pass filter attenuation frequency response.
16
Figure 2.8 A Chebyshev low pass attenuation response [3]
However if the reactive elements of a filter have appreciable dissipation loss
the shape of the pass-band response of any type of filter will be altered as compared
with the lossless case, and the effect will be particularly large in a Chebyshev filter.
With the cutoff attenuation defined as the ripple value, the Chebyshev amplitude
response is given by
LA( ω')
with

10⋅log1 +

ε
2
− 1 ω'


 ω'1 
ε ⋅cosh n⋅cosh 


 L 
antilog Ar  − 1

 10 
(2.13)
(2.14)
where LAr equals to the pass band attenuation. Prototype element values for the
Chebyshev filter are given as:
g0 = 1
g k +1 = 1
17
gk =
2a1
if k = 1
γ
4a k −1 a k
otherwise
bk −1 g k −1
where β, γ, ak and bk are given by the following equations:

 L 
β = ln coth  Ar 
 17.37 

 β 
γ = sinh  
 2n 
(2.15)
(2.16)
 (2k − 1)π 
ak = sin 
 2n 
(2.17)
 kπ 
bk = γ 2 + sin 2  
 n 
(2.18)
For k = 1,2…n.
2.6
Microstrip Technology
The general structure of a microstrip is illustrated in Figure 2.9 [1]. A
conducting strip of width W and thickness t is on top of a dielectric substrate that has
relative dielectric constant εr and a thickness h, and the bottom of the substrate is a
ground (conducting) plane.
18
Figure 2.9
Figure of General Microstrip Structure [4]
With microstrips, a portion of the electric fields are in the dielectric between
the strip and the ground plane while other fields exist in the region above the strip
with air as dielectric. At frequencies where the electrical distance in the dielectric
material between the strip and the ground plane is much less than a wavelength,
microstrip behaves as non-dispersive transverse electromagnetic (TEM) line.
Transmission characteristic of microstrips are described by two parameters,
namely the effective dielectric constant εre and characteristic impedance Zc. The
fundamental mode of wave propagation in microstrip is assumed pure TEM. These
two parameters of microstrips are determined from the value of two capacitances as
follows [1], [3]-[7]:
ε re =
Zc =
Cd
Ca
1
c Ca Cd
(2.19)
(2.20)
19
where Cd is the capacitance per unit length with the dielectric substrate present, Ca is
the capacitance per unit length with air as the dielectric constant and c is the velocity
of electromagnetic wave in free space (c ≈ 3.0×108 m/s).
For very thin conductors, more accurate closed-form expression for effective
dielectric constant and characteristic impedance are given by the equation [5]:
ε re =
ε r + 1 ε r − 1  10 
+
1 + 
u 
2
2 
−ab
(2.21)
where u = W/h and
 4  u 
 u +   
  u 3 
52  
1 
1
a =1+
ln 4 
ln 1 + 
+
 
49  u + 0.432  18.7   18.1  




 ε − 0.9 

b = 0.564 r
 εr + 3 
(2.22)
0.053
(2.23)
The characteristic impedance, Z o is given by:
Zo =
60
ε re
2
F
2 

ln  + 1 +   
u
 u  

(2.24)
where F is given by
  30.666  0.7528 
F = 6 + (2π − 6 ) exp  − 


  u 

(2.25)
20
Other important properties of the quasi-TEM mode of microstrip [5] are
guided wavelength, propagation constant, phase velocity, and electrical length given
by the following equations:
Guided wavelength, λ g
λ0
ε re
λ g=
(2.26)
where λ0 is the free space wavelength at operation frequency.
Propagation constant, β
β=
2π
λg
(2.27)
Phase velocity, v p
ω
β
(2.28)
θ = βl
(2.29)
vp =
and the electrical length, θ
CHAPTER 3
SIMULATION SOFTWARE USED
3.1
Introduction
Microwave Office 2004 is used in this project. The software is used to
simulate the hairpin filters.
3.2
Microwave Office 2004
The Microwave Office solution was designed with a single, object-oriented
database that is inherently synchronized with schematic, simulation, and layout data
The software has linear and nonlinear circuit simulators, electromagnetic (EM)
analysis tools, layout-vs.-schematic (LVS) checks, statistical design capability, and
parametric cell libraries with built-in design rule checking (DRC). The design
environment is shown in Figure 3.1.
To create a file project, click FileNew Project and button FileSave Project As at
menu. The created file is now saved.
22
(a) Create Circuit
From Project Browser, right click Schematic button and choose New Schematic…
after that, the user can rename the circuit, as shown in Figure 3.2.
Figure 3.1 Microwave Office Window
Figure 3.2
Window of creating a circuit
23
(b) Setting Frequency for Simulation
To set the frequency, the Project Options at Project Browser is double
clicked. Dialog box as Figure 3.3 will appear and the frequency can now be set.
(c) Graph
To see the frequency response of the circuit that has been designed, graph
adding is needed. From Project Browser, right click at Graph and choose Add Graph.
Pop up window like Figure 3.4 will appear. From this window, name and type of
graph can be determined.
Figure 3.4 Setting the frequency.
Figure 3.4 Creating a graph.
To determine the value of the graph, right click at graph name at Project Browser and
choose Add measurement. Pop up window as Figure 3.5 will appear.
24
Figure 3.5
Adding measurement.
(e) Simulation
The circuit is simulated by clicking on
3.3
button.
Example of an 8 GHz LPF Design
Some windows of an 8 GHz LPF design are shown in Figures 3.6 to 3.9.
25
Figure 3.6 Low pass filter EMSight
Figure 3.7 Simulated Circuit
26
Figure 3.8 Simulated responses
Figure 3.9 Simulated Circuit
CHAPTER 4
RESULTS AND DISCUSSION
4.1
Introduction
In this chapter, the simulated single element stepped-impedance hairpin
(SSIH) low pass filters are presented. The performances of the filters are then
discussed at length.
4.2
Configurations of SSIH LPF
The configurations of the SSIH LPFs shown in Chapter 1 were simulated in
Microwave Office environment. The geometries for three configurations are given
again in Figure 4.1 for reference purposes. The filters of dimensions L = 10.12 mm,
W = Wc = 0.3 mm, G = 0.3 mm and Lc = 1.78 mm [3] were then simulated by
adjusting the number of fingers, widths and lengths of t he microstrip line section of
the hairpin. The performances were then analysed.
28
(a)
(b)
(c)
Figure 4.1 Configurations of SSIH LPFs (a) 2-finger (b) 4-finger (c) 6-finger [2].
29
4.2.1 Varying the number of finger elements of SSIH LPFs
The SSIH LPF was simulated with varying number of finger elements from 2
to 6. The filters were named SSIH2, SSIH3, SSIH4, SSIH5 and SSIH6. The
simulated layout and responses are given in Figures 4.2 to 4.6. |S12| and |S21| perform
equally. It can be seen that all the filters behave as LPFs. As the number of fingers
increases, the slope at cut-off increases. These agree well with theory. The simulated
responses of all the filters are compared in Figure 4.7 and Table 4.1.
1
2
(a)
(b)
(c)
Figure 4.2 Simulated SSIH2 LPF (a) layout (b) insertion loss (c) |S11| and |S12| responses.
30
1
2
(a)
(b)
(c)
31
1
2
(a)
(b)
(c)
32
1
2
(a)
(b)
(c)
33
1
2
(a)
(b)
(c)
34
Figure 4.7 Simulated insertion losses for SSIH LPFs.
From Figure 4.7 and Table 4.1, it can be seen that SSIH5 LPF performs with the
sharpest slope and least transmission zeros at its two attenuation poles of 3 GHz and
5 GHz. SSIH2 and SSIH3 do not possess any distinct attenuation poles, being of
lower orders, hence high harmonics. The corresponding transmission zeros for
35
Table 4.1 Performance comparison of SSIH LPF with varying number of fingers.
No. of
frequency,
fingers
GHz
2
3
4
5
6
|S11|, dB
|S21|, dB
Attenuation
Transmission
pole, GHz
zero, dB
4.3
-3.1
-3.1
nil
nil
1.5
-26.428
-0.024596
nil
nil
2.927
-3.227
-3.227
4.5
-9.475
1.5
-21.487
-0.04649
2.478
-3.238
-3.238
4.5
-20.98
1.5
-23.487
-0.039745
2.14
-3.72
-3.72
3
-26.38
1.5
-17.686
-0.099866
5
-30.73
2.001
-3.038
-3.038
3.001
-22.8
1.5
-17.931
-0.099866
5.002
-15.25
6
-8.454
SSIH5 are -26.38 dB and -30.73 dB, respectively. The band rejection is also the
broadest. The filter operates at 2.14 GHz. It is observed that as the number of finger
elements increase, the fc decreases, while the attenuation poles increases and return
loss improves.
4.2.2 Varying microstrip line length of SSIH5 LPF
The SSIH5 LPF was then simulated with varying microstrip line lengths of
8.12 mm, 10.12 mm, and 12.12 mm. The simulated layout and responses are given in
Figures 4.8 to 4.10. The simulated responses of all the SSIH5 filters are compared in
Figure 4.11 and Table 4.2.
36
1
2
(a)
(b)
(c)
Figure 4.8 SSIH5 LPF with L = 8.12 mm (a) layout (b) |S12| (c) |S11| and |S12| responses.
37
1
2
(a)
(b)
(c)
Figure 4.9 SSIH5 LPF with L = 10.12 mm (a) layout (b) |S12|
38
1
2
(a)
(b)
(c)
39
Figure 4.11 Simulated insertion losses for SSIH5 LPF with
varying L = 8.12 mm, 10.12 mm, and 12.12 mm.
From Figure 4.11 and Table 4.2, SSIH5 LPF with L = 10.12 mm performs
with the sharpest slope and has least transmission zeros and broadest band rejection
region. The cutoff frequency is 2.326 GHz. All three SSIH5 have attenuation poles.
The two attenuation poles exist at 3.5 GHz and 5 GHz, with corresponding
transmission zeros of -32.07 dB and -29.92 dB, respectively. Increasing L will
increase the attenuation poles, reduces fc while improve the return loss in the
passband region, with L = 10.12 mm being the optimum value.
40
Table 4.2 Performance comparison of SSIH5 LPF with increasing L.
L, mm
frequency,
|S11|, dB
|S21|, dB
GHz
8.12
10.12
12.12
Attenuation
Transmission
pole, GHz
zero, dB
3.5
-25.12
2.431
-3.507
-3.507
1.5
-18.485
-0.081815
2.326
-3.789
-3.789
3.5
-32.07
1.5
-22.631
-0.046221
5
-29.92
2.08
-3.596
-3.596
3.992
-22.98
1.5
-14.303
-0.19326
3.497
-22.99
It can be inferred that SSIH5 with L = 10.12 mm is chosen as the optimum
configuration. For compacting the filter size, SSIH5 is then further simulated by
decreasing L by 0.2 mm i.e., the additional varying L are 10.10 mm, 10.08 mm,
10.06 mm, and 10.04 mm. The simulated layout and responses are given in Figures
4.12 to 4.16. The simulated responses of all the SSIH5 filters are compared in Figure
4.17 and Table 4.3.
From Figure 4.17 and Table 4.3, all SSIH5 LPFs have two attenuation poles
near the passband region. SSIH5 with L = 10.08 mm performs with the steepest
slope. The cutoff frequency is 2.273 GHz. It has two attenuation poles at 3.5 GHz
and 5 GHz, with corresponding transmission zeros of -28.95 dB and -36.86 dB,
respectively. The rejection band is also the broadest. It is interesting to note that all
the filters possess equally good low return losses.
41
1
2
(a)
(b)
(c)
42
1
2
(a)
(b)
(c)
43
1
2
(a)
(b)
(c)
44
1
2
(a)
(b)
(c)
45
1
2
(a)
(b)
(c)
46
varying L = 10.12 mm, 10.10 mm, 10.08 mm, 10.06 mm, and 10.04 mm.
Table 4.3 Performance comparison of SSIH5 LPF with decreasing L.
L, mm
frequency,
|S11|, dB
|S21|, dB
GHz
10.12
10.10
10.08
10.06
10.04
Attenuation
Transmission
pole, GHz
zero, dB
2.3
-3.556
-3.556
3.5
-31.9
1.5
-21.969
-0.05018
5
-29.97
2.284
-3.777
-3.777
3.5
-32.85
1.5
-21.073
-0.057326
5
-44.6
2.273
-3.713
-3.713
3.5
-42.46
1.5
-20.422
-0.062295
5.5
-35.09
2.35
-3.668
-3.668
3.5
-28.95
1.5
-23.709
-0.043212
5
-36.86
2.31
-3.709
-3.709
3.5
-29.89
1.5
-22.366
-0.04804
5
-37.66
47
4.2.3 Varying microstrip line width of SSIH5 LPF
The SSIH5 LPF with L = 10.08 mm is then further simulated for sharper
cutoff frequency response and compact size. Now, the dimension W is varied as 0.1
mm, 0.2 mm, 0.3 mm, 0.4 mm, and 0.5 mm.
1
2
(a)
(b)
(c)
Figure 4.18 SSIH5 LPF with W = 0.1 mm (a) layout (b) |S12| (c) |S11| and |S12| responses.
48
1
2
(a)
(b)
(c)
Figure 4.19 SSIH5 LPF with W = 0.2 mm (a) layout (b) |S12|
49
1
2
(a)
(b)
(c)
50
1
2
(a)
(b)
(c)
51
1
2
(a)
(b)
(c)
52
varying W = 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, and 0.5 mm.
Table 4.4. Performance comparison of SSIH5 LPF with increasing W.
W, mm
frequency,
|S11|, dB
|S21|, dB
GHz
0.1
0.2
0.3
0.4
0.5
Attenuation
Transmission
pole, GHz
zero, dB
4.5
-17.31
2.3
-3.075
-3.075
1.5
-8.7056
-0.64916
2.35
-3.253
-3.253
4
-37.12
1.5
-14.959
-0.16171
5.5
-34.07
2.07
-3.683
-3.683
3
-31.63
1.5
-19.501
-0.077068
5
-15.73
2.037
-3.152
-3.152
3
-29.7
1.5
-17.77
-0.10315
5
-17.18
1.953
-3.631
-3.631
3
-23.33
1.5
-18.627
-0.09348
5
-18.05
53
From Figure 4.23 and Table 4.4, all SSIH5 LPFs possess two attenuation
poles except when W is the narrowest. This is probably due to weak coupling
between adjacent fingers. It can be seen that the SSIH4 with W = 0.3 mm has the
steepest slope with the attenuation poles nearest to the passband region. The SSIH5
with W = 0.3 mm has two attenuation poles at 3 GHz and 5 GHz. It operates at 2.07
GHz. The corresponding transmission zeros are -31.63 dB and -15.73 dB,
respectively. It can be observed that an increase of W did not affect the number of
attenuation poles but improved the transmission zeros. The rejection band is also the
broadest. It is interesting to note that all the filters possess equally good low return
losses at 1.5 GHz from W = 0.3 mm.
4.2.4 Overall Discussions
The configuration of a single element microwave stepped-impedance hairpin
filter has been investigated and analysed. Firstly, the number of finger elements is
varied. The most optimum performance of the filter is with 5 finger elements.
Secondly, the length of the microstrip line is increased. The optimum performance is
achieved with length of 10.10 mm. Next, the length is decreased and the optimum
performance is achieved when the length is decreased to 10.08 mm. Finally, the
width of the microstrip line is varied in an increasing order. It was found that the
optimum performance is achieved with the width being 0.3 mm.
The final configuration which performed optimally has been achieved. The
optimum SSIH5 filter operates at 2.07 GHz with very low input return loss in the
passband region, indicating low reflections. The dimensions of the filter are: 5
fingers, 10.08 mm long microstrip line section, and 0.3 mm of microstrip line width.
The optimum configuration is the most compact but exhibits the sharpest slope but
broadest rejection band region. There are two attenuation poles with low
transmission zeros.
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
5.1
Introduction
This chapter concludes the thesis, and recommendations for future work are
given.
5.2
Conclusions
The objective of this project to optimize a single element microstrip hairpin
low pass filter with sharp rejection by successively varying the number of finger
elements, adjusting the widths, and lengths of the microstrip line section. These have
been achieved through simulations. Comparisons between the entire adjusted
elements of hairpin filter have been made.
55
It can be concluded that the optimum single element microstrip hairpin filter
has been successfully investigated. It possesses excellent behaviour in the passband
and rejection band regions. The -3 dB cutoff frequency is 2.07 GHz. The attenuation
poles appear at 3 GHz and 5.5 GHz, with corresponding transmission zeros of -31.63
dB and -15.73 dB, respectively. Sufficiently low return loss was observed at 1.5
GHz in the passband region, indicating well-matched filter at the input. The optimum
filter has 5 fingers, with dimensions of the microstrip line to be 10.08 mm long and
0.3 mm wide.
5.3
Suggestions for Further Work
Recommendations for future work are as follows:
i)
Fabricate the hardware of the optimised SIHH5 filter.
ii)
Design the hairpin filter for more compact size and better cutoff
frequency response such as elliptic function.
iii) Use other simulation softwares for simulating the designed filters.
Simulation of the equivalent filter circuit can be done too.
iv) Use of Microelectromechanical system (MEMS) technology for more
compact design structure.
57
REFERENCES
1. Jia-Shieng G. Hong and M. J. Lancaster, Microstrip Filters for
RF/Microwave Applications. A Willey-Interscience Publication, John Willey
& Sons, Inc. 2001.
2. Wen Hua Tu and Kai Chang, Compact Microstrip Low-Pass Filter With
Sharp Rejection, IEEE Microwave and Wireless Components Letters, Vol.
15, No. 6, June 2005
3. Carlota D. Salamat, Maria Abigail D. Lorenzo and Eusebio Jaybee B. Roxas
Jr., DESIGN OF A NARROWBAND HAIRPIN FILTER ON PTFE
LAMINATE, Communications Engineering Division, Advanced Science and
Technology Institute C.P. Garcia Ave., UP Technopark, Diliman, Quezon
City Philippines 1101
4. Fred Gardiol, Microstrip Circuits, Wiley Series in Microwave and Optical
Engineering, Switzerland: John Wiley & Sons, Inc. 1994
5. Hammerstad, E. O. and Jensen, O. Accurate models for microstrip computeraided design, IEEE MTT-S, 19080, Digest, pp. 407-409
6. KASA, Microwave Integrated Circuits, New York: Elsevier Science
Publishing Company, Inc. 1991
7. David M. Pozar. Microwave Engineering 2nd Edition. John Wiley @ Sons,
Inc. 1998.
8. Jim Jarky, Active Low Pass Filter Design, Application Report: AAP
Precision Analog, SLOA09B- September 2002
9. WANG SIN TAI, Microstrip Filter Design 2, (3004525) Cohort: TE 01/02,
University of Newcastle
10. Nisha Kunder, Low-Pass Filter Design Project, supervised by Dr. Ercument
Arvas, July 23rd, 2003
11. Jack Middlehurst, Practical Filter Design, Prentice Hall, 1993
12. Herrero and Willoner, Synthesis of Filters, Prentice Hall, Inc. Englewood
Cliffs, New Jersey, 1996
58
APPENDIX A:
GANTT CHART
GANTT CHART FOR PSM 1
GANTT CHART FOR PSM 2
59
APPENDIX B:
VARYING OF THE FINGER ELEMENTS
Configuration:
L = 10.12 mm, Lc = 1.78 mm
W = Wc = 0.3 mm, G = 0.2 mm
EM Structure
|S11| & |S21| responses
No. of finger = 2
1
2
No. of finger = 3
1
2
No. of finger = 4
1
2
|S11| & |S21|
60
EM Structure
No. of finger = 5
1
2
No. of finger = 6
1
2
|S11| & |S21|
61
APPENDIX C: VARYING OF MICROSTRP LINE LENGTH
Configuration:
Lc = 1.78 mm, No. of finger = 5
W = Wc = 0.3 mm, G = 0.2 mm
EM Structure
Microstrip line length = 8.12 mm
1
2
1
2
1
2
|S11| & |S21|
62
EM Structure
1
2
1
2
1
2
|S11| & |S21|
63
EM Structure
1
2
|S11| & |S21|
64
APPENDIX D: VARYING OF MICROSTRIP LINE WIDTH
Configuration:
L = 10.08 mm, Lc = 1.78 mm
G = 0.2 mm, No. of finger = 5
EM Structure
Microstrip line width = 0.1 mm
1
2
1
2
1
2
|S11| & |S21|
65
EM Structure
1
2
1
2
|S11| & |S21|

optimizing single element microstrip hairpin low pass filter with

Transcription

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