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JALL i
NOVEL COMPACT MICROSTRIP
BANDSTOP FILTERS AT MICROWAVE FREQUENCIES
By
ENG.TEJINDER KAUR
A DISSERTATION SUBMITTED TO PROGRAM IN ELECTRONICS DEPARTMENT IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
M.SC. IN ELECTRONICS ENGINEERING
At the
NATIONAL INSTITUTE FOR ASTROPHYSICS, OPTICS AND ELECTRONICS
TONANTZINTLA, PUEBLA
JULY 2007
Advisors:
DR. ALONSO CORONA CHAVEZ (GTM) DR. IGNACIO ENRIQUE ZALDIVAR HUERTA (INAOE)
©INAOE 2007
TONANTZINTLA, PUEBLA.
ALL RIGTHS RESERVED THE AUTOR HEREBY GRANTS TO INAOE PERMISSION TO REPRODUCE AND TO
DISTRIBUYE COPIES OF THIS THESIS DOCUMENT IN WHOLE OR IN PART .
i
Microwave Filters are essential components in the communications industry and are
fundamental elements in wireless and satellite technology. The need of filters has
become more apparent as spectrum crowding increases with the development of new
systems. In this thesis, novel compact microstrip resonators and bandstop filters
configuration have been proposed for narrow band applications such as, wireless
communication and satellite systems at 1.5 GHz and 10 GHz.
At 1.5 GHz, several novel microstrip resonators have been proposed and at this
frequency successfully obtained the ultra compact size of the resonator from
conventional resonator. At this frequency, Chebyshev bandstop filters have been
designed using proposed resonators and experimentally measured. The first filter
consists of a 3 pole Chebyshev bandstop filter at 1.5 GHz using T-shape straight
resonators. The second type of structure is 3 poles Chebyshev bandstop filter using ultra
compact meandered T-shape resonators.
Also at 1.5GHz a novel Trisection bandstop filter with an extra transmission zero have
been proposed with narrow bandwidth, this work is unique as this topic is not known to
have been presented anywhere else in the review literature.
At 10 GHz novel compact high-Q (quality factor) microstrip resonators have been
explored with application such as wireless and satellite communication. These
resonators use micromachining technology to remove selective parts of the substrate to
increase the quality factor and hence filter performance. Also, miniaturization techniques
were applied to decrease the overall resonator size. The full design procedure and
simulation results are presented of several resonators and Chebyshev filter, along with
experimental results of fabricated resonators on HR-Si.
ii
Los filtros de microondas son dispositivos de suma importancia en la industria de las
telecomunicaciones. La necesidad de filtros ha llegado a ser más aparente como
espectro que llena los aumentos con el desarrollo de nuevos sistemas. En este trabajo
de tesis, se presenta el diseño y fabricación de filtros de banda angosta utilizando
estructuras de microcinta con aplicaciones a 1.5 GHz y 10 GHz. Los filtros aquí
presentados tienen aplicaciones potenciales en los sistemas de comunicación
inalámbrica y satelital.
Para una frecuencia de 1.5 GHz se han propuesto varios resonadores de tipo
microcinta. En esta frecuencia se obtuvo con éxito un tamaño ultra compacto de un
resonador convencional. Asimismo se diseñan y fabrican dos filtros rechaza-banda de
banda angosta tipo Chebyshev de tres polos utilizando estructuras del tipo microcinta.
El primer filtro se diseña y fabrica en base a resonadores en forma de T. El segundo
filtro se diseña y fabrica mediante la utilización de resonadores en forma serpenteada.
Se presenta también el diseño de un filtro tipo Triplet rechaza-banda de banda angosta,
el cual es un diseño único en su tipo y no reportado aún en la literatura.
Finalmente, se describe de manera detallada el diseño y fabricación de un filtro
rechaza-banda del tipo Chebyshev con un alto factor de calidad (Q) para la frecuencia
de 10 GHz. Esta estructura se fabrica en un substrato de silicio de alta resistividad (HR-
Si), y mediante el uso de técnicas de micro-maquinado se realiza un proceso selectivo
de grabado del substrato lo cual permite incrementar el factor de calidad así como
mejorar los parámetros del filtro.
iii
This thesis work has been done in two year course of master’s in Electronics. I would
like to thank my parents, Sqn. Ld. (Retd.) Mr. B.S Kataria and Mrs. Mohinder Kaur,
my brother Mr. Karanveer Singh and sisters and my jijus; Mrs. Narinder Kaur, Mrs.
Parminder Kaur, Miss Harpreet Kaur, Mr. Ranjit Singh and Mr. Ranjeet Singh, for
there complete support during this period of my study. I am grateful to my Assessor Dr.
Alonso Corona Chávez for his supervision and for his full support during master’s
course, which result in finishing this incredible thesis work in time. I am also thankful to
my Co-Assessor Dr. Ignacio Enrique Zaldivar Huerta for his help and assist in this
work. I want to thank to the Ministry of Foreign Affairs of Mexico and INAOE for
sponsoring my master’s course.
Special gratitude for following persons who helped me a lot during these two years of
master’s course:
The team of Microelectronics and MEMS laboratory of INAOE to support in
fabricating proposed device and Mechanical department (INAOE) for their help.
Thanks to my professor Dr. Ignacio Llamas for his help and support Thanks to Engg. Victor of General Administration Department of Computers who
helped me in maintaining my computer. Special thank to my very special friend David Chillon (bachas) for his help and
full support during hard and good time and also in translating resume into
Spanish.
iv
ABSTRACT (ENGLISH AND SPANISH)……………………………………………………i-ii
ACKNOWLEDGMENT…………………………………………………………………………iii
PREFACE…………………………………………………………………………………….… ix
CHAPTER 1: BASIC MICROWAVE THEORY
1.1 INTRODUCTION ............................................................................................ 1
1.2 TRANSMISSION LINE THEORY............................................................4
1.2.1 TRANSMISSION LINE EQUATIONS…………………………………....4
1.2.2 TYPES OF TRANSMISSION LINES……………………..……………. 8
1.2.3 MICROSTRIP LINE………………........................................................9
1.2.4 COPLANAR WAVEGUIDE…………………………………………..…13
1.3 THE SCATTERING PARAMETERS (S-PARAMETER)........................ .14
1.4 VECTOR NETWORK ANALYZER (VNA)……………………..……..….19
REFERENCES………………………………….……..……………………………20 CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN
2.1 BASIC INTRODUCTION TO MICROWAVE RESONATORS………..…….....22
2.1.1 BASIC PROPERTIES OF SERIES RLC RESONANT CIRCUIT…….24
2.1.2 BASIC PROPERTIES OF PARALLEL RLC RESONANT CIRCUIT...26
2.1.3 QUALITY FACTOR (Q)………….......................................................28
2.2 GENERAL FILTER DESIGN...................................................................…...31
v
2.2.1 TRANSFER FUNCTIONS…………………………………………….….31
2.2.2 LOWPASS PROTOTYPE FILTERS AND ELEMENTS……………….36
2.2.3 FREQUENCY AND ELEMENTS TRANSFORMATION….................38
2.2.4 IMMITTANCE INVERTERS………………………………….................43
REFERENCES…………….………….…………………………….………………........ 47 CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
3.1 MICROMACHINED MICROWAVE FILTERS...................... ………..…….....50
3.1.1 MEMBRAN SUPPORTED FILTERS……………...…………………….50
3.2 BANDSTOP FILTERS……………...................................................................54
3.2.1 L-RESONATOR BANDSTOP FILTER…...………………………….….55
3.2.2 MICROMACHINED BANDSTOP FILTER………………………..…….57
3.2.3 HIGH Tc SUPERCONDUCTING BANDSTOP FILTER
FOR RADIO ASTRONOMY FRONT ENDS…….………………………59
3.2.4 A SUPERCONDUCTING MICROSTRIP BANDSTOP
FILTERS FOR AN L-BAND RADIO TELESCOP RECEIVER............61
3.3 QUASI ELLIPTIC FILTERS.............…............................................................63
3.3.1 HIGH PERFORMANCE HTS PESUDO-ELLIPTIC
BANDSTOP FILTER........................................................…………....63 REFERENCES…………...……………………………………….………………66
CHAPTER 4: DESIGNING OF RESONATORS AND 3-POLE CHEBYSHEV BANDSTOP FILTERS AT1.5 GHz AND10 GHz
4.1 ELECTROMAGNETIC (EM) SIMULATOR ................................................... 70
4.2 MICROSTRIP RESONATORS AT 1.5GHz....................................................71
vi
4.2.1 MICROSTRIP RESONATOR (λ/2) ……………………………………..71
4.2.2 INTERDIGITAL T-SHAPE STRAIGHT RESONATOR ……….….….74
4.2.3 NOVEL ULTRA COMPACT INTERDIGITAL
MEANDERED RESONATOR …………………………….………...……75 4.3 3-POLE CHEBYSHEV BANDSTOP FILTER ON DUROID SUBSTRATE AT
1.5GHz................................................……………………………………….....79
4.3.1 3-POLE CHEBYSHEV BANDSTOP FILTER USING INTERDIGITAL T-SHAPE STRAIGHT RESONATORS…………….…………….…….80
4.3.2 3-POLE CHEBYSHEV BANDSTOP FILTER USING ULTRA
COMAPCT INTERDIGITAL MEANDERED RESONATORS ..…….86 4.4 MICROSTRIP RESONATORS AT 10 5GHz.......................................................90
4.4.1 MICROSTRIP CONVENTIONAL λ/2 ..RESONATOR.……..….……92
4.4.2. MICROSTRIP PATCH RESONATORS………………...……….…….94 4.4.3 MICROSTRIP PATCH RESONATORS WITH AIR WINDOW.….. .…96
4.5 3 POLE CHEBYSHEV BANDSTOP FILTER ON HR-SI SUBSTRATE AT 10 GHz……………………………………………………………………………101 4.6 DESIGNING OF COPLANAR WAVEGUIDE (50Ω) ………...……….….……….105
REFERENCES………….……………………………………….… ……………...………..109 CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTER AT 1.5GHz
5.1 FILTERS WITH SINGLE PAIR OF TRANSMISSION ZERO (QUASI ELLIPTIC RESPONSE)………………………………………...……………..112
5.1.1 APPROXIMATION SYNTHESIS PROCESS OF QUASI- ELLIPTIC…………………………………………………………..…..113
5.2 TRISECTION FILTERS………………………………….………………………….116
5.2.1 MICROSTRIP TRISECTION FILTERS……………………………….118 5.3 DESIGNING PROCEDURE OF NOVEL TRISECTION BANDSTOP FILTER AT
1.5 GHz………………………………………………………………………………..119
vii
REFERENCES…………………………..……………...…………………………………..140 CHAPTER 6: FABRICATION PROCESS OF MICROMACHINED FILTERS
6.1 MASK……………………………………………………..……………………………141 6.2 TYPES OF ETCHING TECHNIQUES……………………………………………..145
6.2.1 CAVITY DIMENSIO…………………………...………………………..147
6.3 FABRICATION PROCESS………………………………………………………….148
6.3.1 EXPERIMENT- I: LITHOGRAPHIC PROCESS USING SiO2 LAYER ON SILICON AS SUPPORTIVE LAYER…………………………….150
6.3.2 EXPERIMENT-II: LITHOGRAPHIC PROCESS USING SiO2, SILICON
NITRIDE(SiH4+NH3)ON SILICON AS SUPPORTIVE SUBSTRATE………………...…………………………..159
REFERENCES……………………………………………………….…………..…………..166
CHAPTER 7: EXPERIMENTAL RESULTS
7.1 EXPERIMENTAL RESULTS OF CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz…………………………………………………………….……………167
7.1.1 3 POLE CHEBYSHEV BANDSTOP FILTER AT1.5GHz USING INTERDIGITAL T-SHAPE STRAIGHT RESONATORS ON DUROID SUBSTRATE………………………………………………………….…168
7.1.2 3 POLE CHEBYSHEV BANDSTOP FILTER USING ULTRA COMPACT INTERDIGITAL MEANDERED RESONATORS AT 1.5GHz…..….173
7.2 TRIPSECTION BANDSTOP FILTER WITH AN EXTRA TRANSMISSION ZERO
USING ULTRA COMPACTINTERDIGITAL MEANDERED RESONATORS
AT 1.5GHz…………………………………………………………………………….178
7.3 INTERDIGITAL T- SHAPE PATCH RESONATOR ON SILICON SUBSTRATE AT 10GHZ …………………………………………….………………………………….183
viii
CHAPTER 8: CONCLUSION AND FUTURE WORK
8.1 CONCLUSION……………………………………………………………….…………186 8.2 FUTURE WORK ……………………………………………………….…..………….189 APPENDIX-I…………………………………………………………………..……………….190 APPENDIX-II……………………………………………………………………..……………192 LIST OF FIGURES……………………………………………………………………………194 LIST OF TABLES…………………………………………………………………...…..…..203 PUBLICATIONS………………………………………………………………………………205
ix
Filters are essential components in the communications industry and are
fundamental elements in wireless and satellite technology. There is constant
need for microwave filters with higher selectivity and lower losses filters in
communication systems as spectrum crowding increases with the development
of new systems. Further, subsystems miniaturization may require high
performance filters to occupy the same packages as high frequency integrated
circuits or least employ packages that are similar and handled the same way in
production. Microwave and millimeter-wave circuits as well as modules are
based on planar technologies using microstrip lines, coplanar waveguide or finite
ground coplanar waveguides since they provide compact, light weight and low
loss solutions, and are combined using wide variety of interconnects such as via
holes, and air bridges. Silicon micromachining technology has been used to build
low-loss lumped elements, filters, resonators and couplers. Currently, Radio
Frequency Micro Electronics Mechanical System (RF-MEMS) has been an
attractive field for both science research and industry due to its promising
application in future civil and military wireless communication and remote
controlling and sensing systems. RF-MEMS implicates that the devices and
structures realized via microsystem technologies, or RF-MEMS are technology
used for fabrication of miniaturized RF and Microwave device.
Bandstop filters are used to reject unwanted frequencies; the Chebyshev
bandstop filters proposed in this thesis have applications in radio astronomy,
satellite communications, mobile base stations as multiplexers and diplexer to
separate transmitted and received signals, front-end filters that protect receivers
from adjacent channel interference and output filters that limit the bandwidth of
transmitter noise.
x
Filters can be configured as Chebyshev, Butterworth, Quasi-Elliptic, cascaded
quadruplets, Trisection with extra transmission zero. In the literature, extensive
work has been found on Bandstop filters with Chebyshev and Quasi-Elliptic
configuration but no work was found on Trisection Bandstop filters; which makes
the proposal of a novel configuration of Bandstop Trisection filter with extra
transmission zero in this thesis highly valuable and propositive. For applications
where very steep cutoffs are needed on only one side of the reject band,
Trisection Bandstop filters are ideal candidates as they required only three
resonators, for such response. As apposed to Quasi-Elliptic filter which would
require many poles to obtain the higher selectivity needed. To have both sides
with high selectivity, two Trisection bandstop filters can be cascaded.
Applications for Trisection filters can be found in Multiplexers to separate
transmitted signals from received signals at mobile base station, satellite
communication systems and radio telescope.
At millimeter wave frequencies, membrane support high filters play an important
role in high performance systems. At higher frequencies (above 30GHz) the size
of the filters reduces due to which it becomes feasible to support thin silicon
membranes (1-2µm thick). But at lower frequencies (< 30GHz) the size of the
filters would be too large and becomes mechanically impossible to support them
on silicon membranes. Thus, in this thesis a novel way to achieve high Q filters
and mechanical strength is proposed by partially removing selective parts of the
silicon substrate. This work is novel as there is no work found in literature review
with selective removal of substrate to increase Q and also to obtain compact
structure of the resonator.
In this thesis work on novel designs of microstrip resonators and bandstop filters
at L and X band are shown. It includes all experimental and simulation results
and also the complete fabrication process of the filter at X band using
xi
Micromachining technology. At L band the central frequency selected is 1.5 GHz
and at X band is 10GHz. This thesis is divided into nine chapters:
First chapter presents the basic review of microwave theory, its applications and
microwave engineering.
Second chapter, explains general designing theory of microwave filters which
are going to be used in designing of proposed filters in chapter 4 and 5.
Third chapter presents literature review of the work done related to microwave
filters using different technologies of fabrication.
Fourth chapter describes the designing procedure of novel resonators and
Chebyshev bandstop filters at 1.5GHz and 10GHz along with the simulation
results. At 10GHz compact resonators with selective removal of the silicon
substrate using micromachining technology are proposed.
Chapter fifth shows the designing of advanced filter topologies using trisections
with a single transmission zero.
Chapter sixth presents the detailed micromachining fabrication procedure for
the device at 10GHz,
Chapter seventh gives experimental results of all the proposed filters at 1.5GHz
and resonator at 10GHz.
Chapter eight illustrates the conclusion of all the experimental and simulation
results obtained. And gives details related to the work proposed for future.
CHAPTER 1: BASIC MICROWAVE THEORY 1
1.1 INTRODUCTION In this chapter, brief description of basic microwave theory is presented. The
main objective of this introduction is to revise the basic aspects of microwave
applications, microwave engineering, transmission line theory and the
important parameter (S-Parameter) to measure the performance of the
resonators and filters in terms of Q value and bandwidth.
The range of the electromagnetic spectrum from 300 MHz to 300 GHz is
commonly referred to as the microwave range. Microwave signals with
wavelength of millimeters are called millimeter waves.
The RF/ Microwave have applications in following areas:
Communication
Radar
Navigation
Radio astronomy
Sensing
Medical instrumentation
To recall the spectrum of microwave signals and its applications, Figure 1.1
presents the electromagnetic spectrum with some applications.
CHAPTER 1: BASIC MICROWAVE THEORY 2
Figure 1.1: Electromagnetic Spectrum (Taken from © 2005 SURA www.sura.org Copyrighted
images used with permission. Rev2C 6-June-2005)
The standard radar frequency letter-band nomenclature according to IEEE
Standard 521-1984 is shown in table1.1. From this table its clear which range
of frequency belongs to which respective band. Microwave technology has
been used extensively by the broadcast and cable television industries, as
well as in other telecommunications applications, since the early 1950’s.
CHAPTER 1: BASIC MICROWAVE THEORY 3
Band
Designator
Frequency
(GHz)
Wavelength
in Free Space
(cm)
L band 1 to 2 30.0 to 15.0
S band 2 to 4 15 to 7.5
C band 4 to 8 7.5 to 3.8
X band 8 to 12 3.8 to 2.5
Ku band 12 to 18 2.5 to 1.7
K band 18 to 27 1.7 to 1.1
Ka band 27 to 40 1.1 to 0.75
V band 40 to 75 0.75 to 0.40
W band 75 to 110 0.40 to 0.27
AM Broadcast
Band
535-1605
kHz
Shortwave
radio
3-30MHz
FM Broadcast
band
88-108MHz
VHF TV (2-4) 54-72 MHz
UHF TV (5-6) 76-88MHz
UHF TV (7-
13)
174-216
MHz
UHF TV (14-
83)
470-
890MHz
Microwave
ovens
2.45GHz
(a) Standard Radar Frequency Letter-Band
Nomenclature (IEEE Standard 521-1984)
(b) Typical Frequencies
Table 1.1: (a) Standard Radar Frequency Letter-Band Nomenclature (IEEE Standard 521-
1984), (b) Typical Frequencies
For applications with wavelengths from 1m to 1mm, low frequency circuit
analysis techniques can not be used and for that transmission-line theory is
used. In transmission-line theory, the voltage and current along a
transmission line can vary in magnitude and phase as a function of position
which is discussed in next section.
CHAPTER 1: BASIC MICROWAVE THEORY 4
1.2 TRANSMISSION LINE THEORY
The uniform two-conductor transmission line is an essential element in the
realization of many transmission line circuits. In transmission-line theory, the
voltage and current along a transmission line can vary in magnitude and
phase as a function of position. Many different types of microwave
transmission lines have been developed over the years. In an evolutionary
sequence from rigid rectangular and circular waveguide, to flexible coaxial
cable, to planar stripline to microstrip line, microwave transmission lines have
been reduced in size and complexity.
1.2.1 TRANSMISSION LINE EQUATIONS
A transmission line can be approximated by a distributed-parameter network
with the circuit parameters distributed throughout the line, transmission line
always have at least two conductors. The current flowing in the two-wire line
and the potential difference between the two conductors is function of
distance z and time t. Figure 1.2(a) shows the voltage and current definition
of transmission line of short length Δ z and the effect of a short length of the
line Δ z is depicted in Figure 1.2(b).
The series impedance and shunt admittance per unit length of this line are
given by equation (1-1) and (1-2), respectively.
LjRZ ω+= (1-1)
CjGY ω+= (1-2)
Where,
CHAPTER 1: BASIC MICROWAVE THEORY 5
♦ R is the resistance in both conductors per unit length in Ω /m
♦ L is the inductance in both conductors per unit length in H/m
♦ G is the conductance of the dielectric media per unit length in S/m
♦ C is the capacitance between the conductors per unit length F/m
(a) Voltage and current definition (b) Lumped element equivalent circuit
Figure 1.2: Voltage and current definition and Equivalent circuit of an element of a
transmission line with a length of Δ z (a) Voltage and current definition, (b) Lumped element
equivalent circuit.
The potential drop across a section of line of length Δ z is given by equation
(1-3):
zz ILjR
dzdV )( ω+−= (1-3)
The current across the same section is given in equation (1-4):
zz VCjG
dzdI )( ω+−= (1-4)
CHAPTER 1: BASIC MICROWAVE THEORY 6
The negative signs in equations (1-4) signify that both the voltage and current
on the line decrease with increasing z [1].
The propagation constant of the line is given by equation (1-5)
ZY=γ (1-5)
Equation (1-5) is usually written in terms of its real and imaginary parts as:
( )( )CjGLjRj ωωβαγ ++=+= (1-6)
Where, α = attenuation constant of the line per unit length (Nepers /meter)
β = phase constant per unit length (radians / meter)
At very high frequency or for transmission lines with very small losses:
Rlj >>ω (1-7)
GCj <<ω (1-8)
And α and β approximated by:
0=α (1-9)
LCωβ = (1-10)
CHAPTER 1: BASIC MICROWAVE THEORY 7
From linear combination of forward and backward traveling waves as shown
in Figure 1.3, the wave equation is given by equation (1-11) and (1-12)
describing Vz and Iz
zzz BeAeV γγ += − (1-11)
( )zz
oz BeAe
ZI γγ −= −1 (1-12)
Where, Z o = Characteristic impedance of the line:
YZZ o = (1-13)
If equation (1-7) and (1-8) satisfies, then characteristic impedance is given by
equation (1-14) [3]:
CLZ o = (1-14)
CHAPTER 1: BASIC MICROWAVE THEORY 8
Figure 1.3: Diagram of transmission line with load showing incident, reflected-transmitted
waves.
1.2.2 TYPES OF TRANSMISSION LINES
Many different types of microwave transmission lines have been developed
over the years. In an evolutionary sequence from rigid rectangular and
circular waveguide, to flexible coaxial cable, to planar stripline to microstrip
line, microwave transmission lines have been reduced in size and complexity.
The microstrip transmission line is the technology employed in the current
hyperthermia applicator studied.
Types of transmission lines are shown in Figure 1-4. Parallel plate, Coaxial
and Strip lines are examples of homogeneous dielectric and have pure TEM
mode and microstrip line is example of inhomogeneous dielectric Quasi-TEM
mode.
CHAPTER 1: BASIC MICROWAVE THEORY 9
Figure 1-4: Types of Transmission Lines
1.2.3 MICROSTRIP LINE
Some relations specific to microstrip will now be discussed here. Microstrip
line is one of the trendiest planar transmission lines, the main advantages of
microstrip lines are:
♦ It can be fabricated by photolithographic process
♦ It is easily integrated with other passive and active microwave devices.
CHAPTER 1: BASIC MICROWAVE THEORY 10
(a) The general geometry of a Microstrip line.
(b) Electric and magnetic field lines
Figure 1-5: (a) the general geometry of a Microstrip line, (b) Electric and magnetic field lines
The geometry of a typical microstrip line can be seen in Figure 1-5(a). A
conductor of width (W) with thickness (t) is printed on a thin, grounded
dielectric substrate of thickness d and relative permittivity (εr); the field lines
are shown in Figure 1-5(b).
CHAPTER 1: BASIC MICROWAVE THEORY 11
CHARACTERISTICS OF MICROSTRIP
a) DC as well as AC signals may be transmitted.
b) Active devices, diodes and transistors may readily be incorporated (shunt
connections are also quite easily made).
c) In –circuit characterization of devices is straightforward to implement.
d) Line wavelength is reduced considerably from its free space value,
because of the substrates high εr. Hence, distributed component
dimensions are relatively small.
e) The structure is quite rugged and can withstand moderately high voltages
and power level.
Microstrip involves an abrupt dielectric interface between the substrate and
the air above it. Any transmission line that is filled with a uniform dielectric can
support a single, well- defined mode of propagation, at least over a specified
range of frequency (TEM for coaxial lines, TE for waveguides, etc.)
Transmission lines that do not have such a uniform dielectric filling cannot
support a single mode of propagation; microstrip is within this category.
Although this is true the bulk of energy is transmitted along microstrip with a
field distribution which is quite closely resembles TEM; it is usually referred to
as Quasi-TEM [4]. i.e., the speed of light (c) is different in air and dielectric the
boundary-value conditions at the air-dielectric interface can not be met with a
pure TEM wave and the exact fields constitute a hybrid TM-TE wave.
Because the dielectric substrate is electrically very thin ( )λ<<d , for this
application, the fields are quasi-TEM. Because the fields are quasi-TEM,
good approximations for the phase velocity, propagation constant and
characteristic impedance can be obtained from the static solution.
CHAPTER 1: BASIC MICROWAVE THEORY 12
The phase velocity in microstrip line is given by equation (1-15):
r
cvε
= (1-15)
And the propagation constant is given by equation (1-16):
eooreok εεμμωεβ == (1-16)
Where, eε is the effective dielectric constant and is given by:
⎟⎟⎠
⎞⎜⎜⎝
⎛+
−+
+=
Wdrr
e /1211
21
21 εε
ε (1-17)
The effective dielectric constant eε is the dielectric constant of an equivalent
homogenous medium that replaces the air and dielectric layers.
The characteristic impedance of a microstrip line can be calculated using
equation (1-18), when width W and substrate thickness d are known
( )[ ] ⎪⎪⎭
⎪⎪⎬
⎫
≥
≤
⎪⎪⎩
⎪⎪⎨
⎧
+++
⎟⎠⎞
⎜⎝⎛ +
=
1/
1/
444.1/ln667.0393.1/120
48ln60
dforW
dforW
dWdW
dW
Wd
Z
e
ro
επ
ε (1-18)
If all microstrip based circuits consisted of a proper width straight feed line
terminating in a load, there would not be much need to worry about
compensating for discontinuities. Even in this ideal case, the transition from
CHAPTER 1: BASIC MICROWAVE THEORY 13
microwave source to microstrip line and from the microstrip to load can be the
source of large reflections. Typical microstrip discontinuities are junctions,
bends, step changes in width and the coaxial cable to microstrip junction. If
these discontinuities are not compensated, they introduce parasitic reactance
that can lead to phase and amplitude errors, input and output mismatch, and
possibly spurious coupling. The strength of a particular discontinuity is
frequency dependent, where the higher the frequency, the larger is the
discontinuity [1].
1.2.4 COPLANAR WAVEGUIDE
Coplanar waveguide can be thought of as slotline with third conductor
centered in the slot region. Coplanar waveguide consists of a centre strip with
two ground planes located parallel to and in the plane of the strip. Figure 1-
6(a) depicts the schematic diagram of this transmission line (coplanar
waveguide) and Figure 1-6(b) shows the electric and magnetic fields in the
quasi- static situation.
Because of the presence of additional conductor, this type of structures can
support even or odd quasi-TEM modes, depending on whether the E-fields in
the two slots are in the opposite direction, or the same direction. Coplanar
waveguide is particularly useful for fabricating active circuitry, due to the
presence of the center conductor and close proximity of ground planes [3].
CHAPTER 1: BASIC MICROWAVE THEORY 14
(a) Schematic diagram of coplanar waveguide
(b) Field patterns in coplanar waveguide
Figure 1-6: (a) Schematic diagram of coplanar waveguide, (b) Field patterns in coplanar
waveguide
1.3 THE SCATTERING PARAMETERS (S-PARAMETER)
S-parameters are important in microwave design because they are easier to
measure and to work at high frequencies than other kinds of two port
parameters. They are conceptually simple, analytically convenient and
capable of providing detailed insight into a measurement and modeling
problem. However, it must be kept in mind that, like all other two port
CHAPTER 1: BASIC MICROWAVE THEORY 15
parameters, S-parameters are linear by default i.e., they represent the linear
behavior of the two ports [1].The following signal flow graph in two port
network in Figure 1.7, gives the situation for the S-parameter interpretation in
voltages.
Figure 1.7: Signal flow graph in two port network
Looking at the S-parameter coefficients individually from Figure 1.7, we have:
021_
1__
1
111 === a
VV
abS
porttowards
portatreflected
(1-19a)
021_
2__
1
221 === a
VV
abS
porttowards
portatreflected
(1-19b)
012_
1__
2
112 === a
VV
abS
porttowards
portatreflected
(1-19c)
CHAPTER 1: BASIC MICROWAVE THEORY 16
012_
2__
2
222 === a
VV
abS
porttowards
portatreflected
(1-19d)
Where, the wave variables , and , are recognized as normalized
versions of forward and backward traveling waves and Z
1a 1b 2a 2b
0 is the input
impedance.
The S11 and S22 are also called the reflection coefficients, whereas S12 and
S21 the transmission coefficients. These are the parameters directly
measurable at microwave frequencies.
an = 0 implies a perfect impedance match (no reflection from terminal
impedance) at port n. These definitions can be expressed in term of a matrix
as:
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡
2
1
22
12
21
11
2
1
aa
SS
SS
bb
(1-20)
Where the matrix containing the S parameters is referred to as the
scattering matrix or S- matrix.
The S parameters are in general complex, and it is convenient to express
them in amplitude and phase, i. e,
mnjmnmn eSS Φ= (1-21)
Their amplitude is given in decibels (dB), which are defined as:
mnSlog20 dB m, n = 1, 2 (1-22)
CHAPTER 1: BASIC MICROWAVE THEORY 17
Where, the logarithm operation is base 10. For characterizations, two
parameters are important:
LA = - mnSlog20 dB m, n = 1,2(m n) (1-23) ≠
LR = - mnSlog20 dB m=n = 1,2 (1-24)
Where, LA = Insertion loss between ports n and m.
LR = Return loss at ports n.
Instead of using the return loss, the voltage standing wave ration (VSWR)
may be used. The VSWR is defined as:
nn
nn
SS
VSWR−
+=
11
(1-25)
Whenever a signal is transmitted through a frequency – selective network
such as a filter, some delay is introduced into the output signal in relation to
the input signal. There are other two parameters that play role in
characterizing filter performance related to this delay.
1) PHASE DELAY: ω
τ 21Φ=p sec (1-26)
2) GROUP DELAY: ω
τd
dd
21Φ= sec (1-27)
♦ PHASE DELAY: the time delay for steady sinusoidal signal and is not
necessarily the true signal delay because a steady sinusoidal signal
CHAPTER 1: BASIC MICROWAVE THEORY 18
does not carry information; and is sometimes also called as Carrier
delay.
♦ GROUP DELAY: This represents the true signal (baseband signal)
delay, and is also referred to as Envelop delay.
In network analysis or synthesis, the reflection parameter S11 is expressed in
terms of terminal impedance Z01 and called as Input Impedance (Z in ), which
is the impedance looking into port1 and is given by equation (1-28).
1
11 I
VZ in = (1-28)
Where, Zin1 is the input impedance looking into port1.
S11 is given in equation (1-29):
011
01111 ZZ
ZZS
in
in
+−
= (1-29)
Similarly S22 is given by equation (1-30):
022
02222 ZZ
ZZS
in
in
+−
= (1-30)
2
22 I
VZ in = (1-31)
CHAPTER 1: BASIC MICROWAVE THEORY 19
Where, Zin2 is the input impedance looking into port2 of the network. Equation
(1-30) and (1-31) indicate the impedance matching of the network with
respect to its terminal impedance.
The properties of reciprocal and symmetrical network are:
♦ For reciprocal networks: S12=S21
♦ If the network is symmetrical: S11= S22
Hence, the symmetrical network is also reciprocal. For a lossless passive
network the transmitting power and the reflected power must equal to the
total incident power. The mathematical statements of this power conversion
condition are given in equation (1-32):
1
1
1
1
212
212
22221212
211
221
11112121
=+
=+
=+
=+
∗∗
∗∗
SS
SSSS
SS
SSSS
(1-32)
1.4 VECTOR NETWORK ANALYZER (VNA) A vector network analyzer (VNA) is an instrument which measures the
complex transmission and reflection characteristics of two-port devices in the
frequency domain by sampling the incident signal, separating the transmitted
and reflected waves, and then performing ratios that are directly related to the
reflection and transmission coefficients of the two-port. Frequency is swept to
rapidly obtain amplitude and phase information over a band of frequencies of
interest [6].
CHAPTER 1: BASIC MICROWAVE THEORY 20
VNA Antrisu (Wiltron model 360B Network Analyzer) as shown in Figure 1.8
was utilized to measure experimental response of proposed filters in terms of
S-parameters directly in our work.
Figure 1.8: Vector Network Analyzer Antrisu (model 360B Network Analyzer)
REFERENCES
[1] David M. Pozar, “Microwave Engineering second edition”, John Wiley
& Sons, Inc. © 1998.
[2] Danny Banks “Introduction to Microengineering MEMS Micromachines
MST”© DBanks1999. ueng@dbanks.demon.co.uk, 5 June 1999.
CHAPTER 1: BASIC MICROWAVE THEORY 21
[3] J.Helszain, “Microwave Engineering Passive, Active and Non-
Reciprocal Circuits.” ©1992 McGraw- Hill Book Company.
[4] T.C Edwards, M.B.Steer “Foundations of Interconnect and Microstrip
Design”, third edition, © 2000 John Wiley & Sons.Ltd.
[5] Franz Sischka, “Characterization handbook” 1SBASIC1.doc,
18.03.2002.
[6] Handbook of VNA Antrisu (model 360B Network Analyzer).
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 22
INTRODUCTION
This chapter presents the necessary theory to design resonators and
Chebyshev bandstop filters. This theory is going to be used in chapter 4 for
the design procedure of Chebyshev bandstop filters at 1.5 and 10 GHz.
Typical frequency response of microwave filters includes low-pass, high-pass,
bandpass, and bandstop characteristics; applications can be found virtually in
any type of microwave communication, radar, or test and measurement
system. Most microwave filter design is done with sophisticated
computer-aided design (CAD) packages based such as the Advanced Design
Systems (ADS), Microsoft office (AWR simulator), HFSS etc.
2. 1 BASIC INTRODUCTION TO MICROWAVE RESONATORS
Microwave resonators are used in a variety of applications like filters,
oscillators, frequency meters and tuned amplifiers. Resonators are key
elements in the realization of filters and oscillators, as their quality factor (Q)
determines the insertion loss and phase noise, respectively.
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 23
♦ Resonator is an electrical circuit that combines capacitance and
inductance in such a way that a periodic electric oscillation will reach
maximum amplitude.
Figure 2.1: LC circuit diagram
An LC circuit shown in Figure 2.1 consists of an inductor (L), and a capacitor
(C). When connected together, an electrical current can alternate between
them at an angular frequency. Angular frequency is shown in equation (2-1):
LC1
0 =ω (2-1)
Where, L is the inductance in henries, and C is the capacitance in farads. The
angular frequency has units of radians per second.
LC circuits are key components in many applications such as oscillators,
filters, tuners and frequency mixers. An LC circuit is an idealized model since
it assumes there is no dissipation of energy due to resistance.
Resonance effect: The LC circuit does not, by itself, resonate. The LC
circuit must be driven. The frequency at which the equality holds for
the particular circuit is called the resonant frequency.
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 24
The resonant frequency of the LC circuit (in radians per second) is given by
equation (2-2):
LCf
ππω
21
2== (2-2)
Near resonance, microwave resonators can usually be modeled by either a
series or parallel RLC lumped-elements equivalent circuit.
2.1.1 BASIC PROPERTIES OF SERIES RLC RESONANT CIRCUIT
A series RLC lumped resonant circuit is shown in Figure 2.2(a). Here R, L
and C are in series in an ac circuit. Inductive reactance (ZL) increases as
frequency increases while capacitive reactance (ZC) decreases with increase
in frequency. Figure 2.2(b), presents the input impedance magnitude versus
frequency [1].
(a)
(b)
Figure 2.2: Series RLC resonator and its response, (a) Series RLC circuit, (b) the input
impedance magnitude versus frequency.
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 25
At a particular frequency, these two reactances are equal in magnitude but
opposite in phase. The frequency at which this happens is the resonant
frequency for the given circuit resonant frequency for the given circuit.
The input impedance of series RLC resonant circuit, power dissipation by
resistor, average magnetic energy stored in inductor and average electric
energy stored in the capacitor are presented in table – 2.1 .
INPUT IMPEDANCE
POWER
DISSIPATED
BY RESISTOR
(R)
AVERAGE
MAGNETIC ENERGY
STORED IN THE
INDUCTOR (L)
AVERAGE ELECTRIC
ENERGY STORED IN THE CAPACITOR (C)
RIPloss2
21
=
LIWm2
41
=
CICVW ce 2
22 141
41
ω==
Vc = The voltage across the
capacitor.
CjLjRZin ω
ω 1−+=
Table 2.1: Formulas of Series RLC resonant circuit
At resonance, the input impedance is given by equation (2-3):
RI
PZ loss
in ==
2
2 (2-3)
This is purely real impedance. Hence, at resonance frequency ZL= ZC and
when the average stored magnetic and electric energies are equal, em WW =
implies that the resonant frequency 0ω , is defined as equation (2-4) [1].
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 26
LC1
0 =ω LC
fπ2
1= (2-4)
Where, f = Resonant frequency.
In a series ac circuit, ZC leads by 90 degrees while ZL lags by 90. Therefore
they both cancel each other out. Only opposition to current is coil resistance.
Hence in series resonance, at resonant frequency, current is maximum.
In summary:
1. At resonance, current is maximum. Circuit impedance is minimum. In
this state circuit is called acceptor circuit. 2. Below resonance frequency, ZL < ZC. Hence circuit is capacitive.
3. Above resonance frequency, ZL > ZC. Hence circuit is inductive.
2.1.2 BASIC PROPERTIES OF PARALLEL RLC RESONANT CIRCUIT
The parallel RLC circuit, shown in Figure 2.3(a), is dual of the series RLC
circuit and Figure 2.3(b) presents the input impedance magnitude versus
frequency graph.
(a)
(b)
Figure 2.3: Parallel RLC resonators and its response, (a) Parallel RLC circuit, (b) the input impedance magnitude versus frequency.
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 27
The input impedance of parallel RLC resonant circuit, power dissipation by
resistor, average magnetic energy stored in inductor and average electric
energy stored in the capacitor are presented in table – 2.2.
Here, a coil (L) and capacitor (C) are connected in parallel with an ac power
supply and R is the internal resistance of the coil. When ZL equals ZC, the
reactive branch currents are equal and opposite. Hence, they cancel each
other to give minimum current in the main line. Since total current is minimum,
in this state the total impedance is maximum. At resonance, resonant
frequency is similar to equation (2-4) [1].
input impedance power
dissipated by
resistor
(R)
average magnetic energy stored in
the inductor (L)
average electric energy stored in the capacitor
(C)
LIW Lm2
41
=
LVWm 2
2 141
ω=
CVWe2
41
=
R
VPloss
2
21
=11 −
⎟⎠⎞
⎜⎝⎛ −+=
CjLjRZin ω
ω
Table 2.2: Formulas of Parallel RLC resonant circuit
At resonance any reactive branch, current is not minimum, but each is given
separately by dividing source voltage (V) by reactance (Z). Hence, I = V / Z,
as per Ohm’s Law. In summary:
1. At resonance, line current is minimum. Total impedance is maximum.
In this state circuit is called rejecter circuit. 2. Below resonance frequency, circuit is inductive.
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 28
3. Above resonance frequency, circuit is capacitive.
2.1.3 QUALITY FACTOR (Q)
Q-factor is an important parameter of resonant circuit, which is defined as:
⎟⎠⎞
⎜⎝⎛
=
secondlossenergy
stored)energy (averageωQ (2-5)
The Q - factor compares the frequency at which a system oscillates to the
rate at which it dissipates its energy. It is particularly useful in determining the
qualitative behavior of a system. A higher Q indicates a lower rate of energy
dissipation relative to the oscillation frequency. The Quality factor of the
series tuned circuit is calculated as the ratio of the resonance frequency to
the bandwidth (in Hz) is given by equation (2-6):
0f
fΔ
ffQ s Δ
= 0 (2-6)
When the system is driven by a sinusoidal drive, its resonant behavior
depends strongly on Q. Resonant systems respond to frequencies close to
their natural frequency much more strongly than they respond to other
frequencies. A system with a high Q resonates with greater amplitude (at the
resonant frequency) than one with a low Q factor, and its response falls off
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 29
more rapidly as the frequency moves away from resonance. Thus, a radio
receiver with a high Q would be more difficult to tune with the necessary
precision, but would do a better job of filtering out signals from other stations
that lay nearby on the spectrum. The width of the resonance is given by
equation (2-7). Figure 2.4 illustrates the transfer characteristic of resonator
circuit to obtain bandwidth and Q-factor [2].
Qf
f 0=Δ (2-7)
Where, is the resonant frequency, 0f fΔ represent the bandwidth, is the width
of the range of frequencies for which the energy is at least half its peak
value.
Figure 2.4: Transfer characteristic of resonant circuit.
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 30
LOADED AND UNLOADED Q
The Q defined in the preceding section is a characteristic of resonant circuit
itself, in the absence of any loading effects caused by external circuitry, called
the unloaded Q.
In practice, a resonant circuit is invariably coupled to other circuitry, which will
always have the effect of lowering the overall, or loaded Q (QL), of the circuit.
If the resonator is a series RLC circuit Figure 2.2(a), the load resistor RL adds
in series with R, the effective resistance is given by (R+RL). If the resonator is
a parallel RLC circuit, Figure 2.3(a), the load resistor RL combines in parallel
with R, the effective resistance becomes [RRL / R+RL)].
Hence, the external Quality factor (Qe) is defined as:
⎪⎪⎩
⎪⎪⎨
⎧
=circuits parallelFor
circuits seriesFor
0
0
LRR
L
QL
Le
ω
ω
(2-8)
The loaded Q is expressed as:
QQQ eL
111+= (2-9)
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 31
2.2 GENERAL FILTER DESIGN
The main objective of this section is to describe about the basic concepts and
theories that form the foundation for the design of general RF/ microwave
filters and it also present equations and tables for obtaining elements values
of Chebyshev lowpass prototype filters which will be used in chapter 4 to
design Chebyshev bandstop filter.
FILTER: A passive filter is a device consisting of inductors and
capacitors arranged in a particular configuration (topology), so that a
group of specified frequencies is allowed to pass with little attenuation
while undesired frequencies are attenuated.
2.2.1 TRANSFER FUNCTIONS
The transfer function of two port filter network is a mathematical description of
network response characteristics, S21.
For lossless passive filter network transfer function is given as:
( ) ( )Ω+=Ω 22
221 1
1
nFjS
ε (2-10)
Where, ε is ripple constant, ( )ΩnF represents a filtering or characteristic
function and Ω is a frequency variable (rad / sec)
Ω represent a radian frequency variable of a lowpass prototype filter that has
a cut-off frequency at Ω = Ωc for Ωc = 1 (rad/ s).
The insertion loss response of the filter for equation (2-10) is computed by
equation (2-11).
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 32
( )( )
dBjS
L A 221
1log10Ω
=Ω (2-11)
Since 12
212
11 =+ SS for lossless, passive two-port network, the return loss
response of the filter is obtained by equation (2-12) [3]:
( ) ( )[ ]dBjSLR2
211log10 Ω−=Ω (2-12)
1. BUTTERWORTH (MAXIMALLY FLAT) RESPONSE
The amplitude–squared transfer function for Butterworth filters that have an
insertion loss LAr= 3.01dB at cut-off frequency Ωc = 1 (rad / s) is given by:
( ) njS 22
21 11Ω+
=Ω (2-13)
Where, n is the degree or the order of filter, which corresponds to the number
of reactive elements required in the lowpass prototype filter. This type of
response is also referred to as maximally flat because its amplitude-squared
transfer function defined in equation (2-13) has the maximum number of
(2n-1) zero derivatives at Ω = 0. Therefore, the maximally flat approximation
to the ideal lowpass filter in the passband is best at Ω = 0, but deteriorates as
Ω approaches the cutoff frequency Ωc. Figure 2.5, shows a typical maximally
flat response. The transfer function constructed from equation (2-13) is [3].
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 33
( )( )∏
=
−= n
iipp
pS
1
211
(2-14)
Figure 2.5: Butterworth (maximally flat) lowpass response
2. CHEBYSHEV LOWPASS FILTER
The Chebyshev filter response (Figure 2.6) exhibits the equal–ripple
passband (LAr) and maximally flat stopband with cut-off frequency
Ωc = 1 (rad / s).The amplitude–squared transfer function for this type of
response is presented in equation (2-15):
( ) ( )Ω+=Ω 22
221 1
1
nTjS
ε (2-15)
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 34
110 10 −=ArL
ε (2-16)
Were, ε is ripple constant is related to given passband ripple LAr in dB and
represent Chebyshev functions of first kind of order n. ( )ΩnT
Figure 2.6: Chebyshev lowpass response
3. ELLIPTIC FUNCTION RESPONSE
The response that is equal-ripple in both the passband and stopband is the
elliptic function response, as illustrated in Figure 2.7.
The transfer function for this type of response is:
( ) ( )Ω+=Ω 22
221 1
1
nFjS
ε (2-17)
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 35
With
( )
( )
( )( )
( ) ( )
⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪
⎨
⎧
≥
⎟⎠⎞
⎜⎝⎛
Ω−ΩΩ
Ω−ΩΩ
⎟⎠⎞
⎜⎝⎛
Ω−ΩΩ
Ω−Ω
=Ω
∏
∏
∏
∏
−
=
−
=
=
=
oddnforN
evennforM
F
n
i i
s
n
ii
n
i i
s
n
ii
n
32
1
122
2
21
1
22
2
122
2
2
1
22
(2-18)
Where, and ( )10 <Ω<Ω ii 1>Ω s represent some critical frequencies; M and
N are constants. Fn (Ω) will oscillate between 1± for 1≤Ω , and
( ) 11 =±=ΩnF [3].
Figure 2.7: Elliptic function lowpass response.
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 36
2.2.2 LOWPASS PROTOTYPE FILTERS AND ELEMENTS
Lowpass prototype filter is in general defined as the lowpass filter whose
element values are normalized to make the source resistance or conductance
equal to one denoted by =1, cut-off angular frequency (Ω0g c) =1 rad/s.
Figure 2.8 demonstrate two possible forms of n pole lowpass prototype for
realizing an all-pole filter response, including Chebyshev, Butterworth.
In Figure 2.8, for i = 1 to n represent either the inductance of series
inductor or the capacitance of shunt capacitor; n = number of reactive
elements. If is shunt capacitance or series inductance, then,
0g
1g 0g = shunt
capacitance or the series inductance.
Similarly series inductance becomes the load resistance or the load
conductance. Unless otherwise specifies these values are supposed to be
the inductance in henries, capacitance in farads, resistance in ohms and
conductance in mhos. This type of lowpass filter serves as prototype for
designing many practical filters with frequency and element transformation
[3].
1+ng
0g
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 37
Figure 2.8: Lowpass prototype filters for all- pole filters with ladder (a) A ladder
network structure, (b) its dual.
CHEBYSHEV LOWPASS PROTOTYPE FILTERS For Chebyshev prototype filters having the transfer function given in equation
(2-15) with passband ripples LAr a cut-off frequency (Ωc) =1 and the elements
values for two port networks shown in Figure 2.8 the g values can be
computed with formula given in reference [3]. Table-2.3 presents elements
values for Chebyshev lowpass prototype filters ( =1, Ω0g c = 1) for passband
ripples LAr = 0.04321 dB which will be used in this thesis work to design
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 38
3 pole Chebyshev filter and a triplet bandstop filter with an extra transmission
zero [3].
n
1g 2g 3g 4g 5g 6g 7g 8g 9g 10g
1 0.2 1
2 0.6648 0.5445 1.2210
3 0.8516 1.1032 0.8516 1
4 0.9314 1.2920 1.5775 0.7628 1.2210
5 0.9714 1.3721 1.8014 1.3721 0.9714 1
6 0.9940 1.4131 1.8933 1.5506 1.7253 0.8141 1.2210
7 1.0080 1.4368 1.9398 1.6220 1.9398 1.43680 0.8330 1.2210
8 1.0171 1.4518 1.9667 1.6574 2.0237 1.6107 1.7726 0.8330 1.2210
9 1.0235 1.4619 1.9837 1.6778 2.0649 1.6778 1.9837 1.4619 1.0235 1
Table 2.3: Elements values for Chebyshev lowpass filters (g0=1, Ωc = 1) for passband
ripples LAr = 0.04321 dB (taken from [3])
2.2.3 FREQUENCY AND ELEMENTS TRANSFORMATION In this section, we describe the procedure to design bandstop filter from
lowpass prototype filter, by means of frequency mapping, impedance scaling,
lowpass transformation and bandstop transformation.
1. FREQUENCY TRANSFORMATION To obtain characteristics and element values for practical filter based on the
lowpass prototype, which have a normalized source resistance / conductance
0g = 1 and cut-off frequency Ωc = 1, we have to apply frequency and element
transformations.
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 39
Frequency transformation or frequency mapping is required to map a
response of Chebyshev response in lowpass prototype frequency domain (Ω)
to that in frequency domain (ω) in which a practical filter response such as
lowpass, highpass, bandpass and bandstop are expressed. The frequency
transformation will have effect on all the reactive elements accordingly, but no
effect on the resistive elements [3].
In addition to frequency transformation mapping, impedance scaling
(equation 2-19) is also required to accomplish the elements transformation.
Impedance scaling will remove the 0g = 1 normalization and adjust the filter
to work for any value of the source impedance denoted by , impedance
scaling factor (
0Z
0γ ).
⎪⎪⎩
⎪⎪⎨
⎧
=e.conductanc thebeing gfor
.resistance thebeing gfor
00
0
00
0
0
YggZ
γ (2-19)
Where, 0
01
ZY = is the source admittance. In principle, applying the
impedance scaling upon filter network like in equation (2-20) has no effect on
the response shape [3].
0
0
γ
γCC
LL
→
→
0
0
γ
γ
GG
RR
→
→
(2-20)
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 40
2. LOWPASS TRANSFORMATION
The frequency transformation from lowpass prototype to practical lowpass
filter having cut-off frequency cω in the angular frequency axis ω is given by
equation (2-21).To obtain element transformation apply equation (2-21)
together with the impedance scaling (equation 2-22) [3].
ωω ⎟⎟
⎠
⎞⎜⎜⎝
⎛ Ω=Ω
c
c (2-21)
ecapacitanc thengrepresenti gfor
inductance thengrepresenti gfor
0
0
γω
γω
gC
gL
c
c
c
c
⎟⎟⎠
⎞⎜⎜⎝
⎛ Ω=
⎟⎟⎠
⎞⎜⎜⎝
⎛ Ω=
(2-22)
3. BANDSTOP TRANSFORMATION The frequency transformation from Chebyshev lowpass prototype to
Chebyshev bandstop is achieved by the frequency mapping given by
equations (2-23):
⎟⎟⎠
⎞⎜⎜⎝
⎛−
Ω=Ω
0
0
ωω
ωω
FBWc (2-23a)
Where, 210 ωωω = and fractional bandwidth (FBW) is given by equation (2-23b).
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 41
0
12
ωωω −
=FBW (2-23b)
Where, 12 ωω − is bandwidth.
The elements for LC resonators transformed to bandstop filter are shown in
Figure (2.10). For representing the inductance is given by equation (2-24a)
and for representing the capacitance is given by equation (2-24b):
g
g
gFBW
L
gFBWC
cp
cp
00
00
11
γω
γω
⎟⎟⎠
⎞⎜⎜⎝
⎛ Ω=
⎟⎟⎠
⎞⎜⎜⎝
⎛Ω
=
(2-24a)
00
0
0
1
γω
γω
gFBWC
gFBWL
cs
cs
⎟⎟⎠
⎞⎜⎜⎝
⎛ Ω=
⎟⎟⎠
⎞⎜⎜⎝
⎛Ω
=
(2-24b)
Basic element representation of equation (2-24) is shown in Figure 2.9(a)
Lowpass prototype to 3-pole bandstop transformation is shown in Figure
2.9(b) [3].
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 42
(a)
(b)
Figure 2.9: Lowpass prototype to 3 pole bandstop transformation (a) basic element
transformation, (b) a practical bandstop filter based on the transformation.
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 43
2.2.4 IMMITTANCE INVERTERS An inverter has a phase shift of or an odd multiple thereof. Immittance
inverters are either impedance or admittance inverters.
090±
IMPEDANCE INVERTER: A two-port network that has unique property at all
frequencies. If it’s terminated in impedance on one port, the impedance
seen looking in at the other port is where, K is real and is characteristic
impedance of the inverter. Impedance inverters also have a phase shift of
± 90 degrees pr and odd multiple thereof. If is inductive / conductive,
will become conductive / inductive, Impedance inverters are also known as K-
inverters.
2Z
1Z
2Z 1Z
2
2
1 ZKZ = (2-25)
ADMITTANCE INVERTER: In two port network, if admittance is
connected at one port, the admittance , seen looking in the other port is
where J is real and is called characteristic admittance of the inverter.
Admittance inverters also have a phase shift of ± 90 degrees pr and odd
multiple thereof and also known as J- inverters.
2Y
1Y
2
2
1 YJY = (2-26)
In this thesis we implemented admittance inverter to design Quasi-elliptic
bandstop filter from Chebyshev lowpass prototype filter:
By network analysis it can be seen that a series inductance with an inverter
on each side looks like shunt capacitance from its exterior terminals, as
inductance in Figure 2.10 (a). Likewise, a shunt capacitance with an inverter
on each side looks like a series inductance from its external terminals, as
demonstrated in Figure 2.10 (b) [4].
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 44
Figure 2.10: (a) Immittance inverter used to convert a shunt capacitance into as
equivalent circuit with series inductance. (b) Immittance inverter used to convert a series inductance into as equivalent circuit with shunt capacitance.
Inverters have the ability to shift impedance or admittance levels depending
on the choice of K or J parameters. Making use of these properties enables to
convert a filter circuit to an equivalent form that would be more convenient for
implementation with microwave structure. Using this technique we convert the
common lowpass prototype structure into the bandpass filter or bandstop filter
[3].
1. PRACTICAL REALIZATION OF IMMITTANCE INVERTERS
Another type of practical immittance inverter is a circuit mixed with lumped
and transmission line elements which are used in this thesis to design
Trisection (Triplet) bandstop filter at 1.5 GHz as shown in Figure 2.11.
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 45
` Figure 2.11: Immittance inverts comprised of lumped and transmission line element.
Where, are the characteristics impedance and admittance of line, and θ
denotes the total electrical length of the line. In practice, the line of positive or
negative electrical length can be added to or subtracted from adjacent lines of
the same characteristic impedance [1].
0Y
For the admittance inverter equation (2.27 a) applies:
L
in YJY
2
= (2-27a)
For the line equation (2.27 b) applies: 090
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 46
0YJ = (2-27b)
For lumped element implementation, the values, J, B, θ are calculated from
equation (2-28):
2tan0θYJ = (2-28a)
2
01 ⎟
⎠⎞⎜
⎝⎛−
=
YJ
JB (2-28b)
0
1 2tanYB−−=θ (2-28c)
CONCLUSION
In this chapter, types of resonators and some of the important parameters
that count up for designing of filter have been presented. The main objective
of presenting the general designing of filter is to describe about the basic
concepts and theories that form the foundation for the design of general RF/
microwave filters. The chapter also presents equations and tables for
obtaining elements values of Chebyshev lowpass prototype filters which will
be used in chapter 4 to design Chebyshev bandstop filter.
CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 47
REFERENCES
[1] David M. Pozar, “Microwave Engineering second edition”, John Wiley
& Sons, Inc. ©1998
[2] Héctor J. De Los Santos,”RF MEMS for Wireless Communication
Systems” © 2002 Héctor J. De Los Santos, MEMS Series.
[3] Jia-Sheng Hong and M.J.Lancaster, “Microstrip Filters for
RF/Microwave Applications”, © 2001 by Wiley Series in Microwave and
Optical engineering.
[4] Sonnet® User Manual Release 7.0 volume
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
48
INTRODUCTION
Microwave and millimeter-wave communication systems are expanding
rapidly as they offer many advantages over conventional wireless links. They
allow the use of very wideband radio links suitable for inter satellite and
personal communications. Filters play important roles in many
RF / microwave applications. They are used to separate or combine different
frequencies. The electromagnetic spectrum is limited and has to be shared.
Filters are used to select or confine the RF / microwave signals within
assigned spectral limits.
Emerging applications such as Wireless communication continues to
challenge RF/Microwave filters with ever more stringent requirements:
1. High performance
2. Smaller size
3. Lighter weight
4. Lower cost.
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
49
Depending on the requirements and specifications, RF / Microwave filters
may be designed as lumped element or distributed elements circuits [1].
At microwave frequency a lot of work has been done on bandpass filters
(Chebyshev, Butterworth, quasi elliptic etc) [2, 6] but very little work has been
done on Chebyshev bandstop filters, and bandstop filters with transmission
zero such as Quasi elliptic, Quadruplet and Triplets.
In this chapter, literature reviews of microwave filters including
micromachined filters are presented. The objective is to shown different
microwave filters, designed by using different technologies. In this chapter,
work related to bandstop filters will be presented due to two main reasons:
firstly, as there is very little work done in area of Bandstop filters at microwave
frequencies and secondly, this thesis work is based on novel bandstop filters.
The purpose of presenting the state of art of membrane support filters using
micromachining techniques is because in this thesis a novel configuration of
resonators with selective removal of substrate is proposed using
micromachining technology at X- band (chapter 4).
Finally, quasi-elliptic bandstop filter review will be presented in this chapter as
this relates to the novel work on Trisection (Triplets) bandstop filters with
extra transmission zero presented in chapter 5.
This chapter is divided in to three sub-sections, section (3.1) present some of
the work done on micromachined microwave filters. Section (3.2) shows
bandstop filters with different technologies. Section (3.3) present microwave
quasi elliptic bandstop filter.
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
50
3.1 MICROMACHINED MIRCOWAVE FILTERS
In this section a review of micromachined filters is presented, with the
objective of showing different micromachined microwave filters designed by
different technologies.
3.1.1 MEMBRANE SUPPORT FILTERS
Membrane supported striplines [7] and microstrips [8], [9] have become a way
of producing high performance millimeter wave circuits. High performance
planar micromachined filters at 37 and 60 GHz are presented in [9], the filters
consist of a 3.5% fractional bandwidth two pole Chebyshev filter with
transmission zeros at 37 GHz, which had a 2.3 dB port to port insertion loss.
The layout of an 8% fractional bandwidth quasi elliptic filter at 60 GHz
exhibiting an insertion loss 1.5 dB which is shown in Figure 3.1. A 2.7% and
4.3% fractional bandwidth four and five pole Chebyshev filters at 60 GHz,
which had an insertion loss of 2.8 and 3.4 dB respectively demonstrated in
Figure 3.2.
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
51
Figure 3.1: Layout of the 4 pole membrane quasi elliptic filter L1=820, L2=2180,
L3=645, L4=300, L5=675, w=500, G1=15, G2=200, G3=175, G4=625 (Dimensions
in microns), taken from [10]
All measurements of the filters presented in [9], include the losses of the
coplanar to microstrip transitions. These resonators are known to have Q’s in
the range of 400 to 500 at millimeter waves, from 30 GHz to 60 GHz. The
measured response of the 8% fractional bandwidth filter is presented in
Figure 3.2, the conductor width used is 500 µm and the ground to conductor
spacing is 250 µm, a single resonator exhibits a Q of 454 and the
metallization used is 1 µm of evaporated gold. The shielding is made using
via groves surrounding the filter. The insertion loss is 1.5 dB including the
transition and the whole filter is smaller than 4mm x 6mm.
A planar diplexer integrated on a single silicon substrate is presented in [7],
the diplexer channels have a Chebyshev response and have a 5% and 6.5%
relative bandwidth at 28 and 31 GHz, respectively. The layout of the diplexer
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
52
is shown in Figure 3.3, and consists of two capacitively coupled bandpass
filters with one port shared between the filters.
Figure 3.2: Measured response of the 4 pole membrane quasi elliptic filter, taken from [9]
The receive band filter is designed using a four pole Chebyshev prototype
with a centre frequency of 28 GHz, a relative bandwidth of 5.5%, and a ripple
of 0.1 dB. The transmit band filter is a three pole Chebyshev filter with a
centre frequency of 31.75 GHz, and a relative bandwidth of 5.5%, and a
ripple of 0.1 dB. The author claims that, bent diplexer structure has a better
performance than one having straight sections, because it helps to disturb
any possible parasitic modes of the micromachined structure.
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
53
Figure 3.3: Layout of the K-band diplexer, taken from [10]
The resonators used in the diplexer consist of 800 micrometers wide lines
with a ground plane height of 250 micrometers, and a shielding cavity height
of 800 µm. The distance from the edge of the conductors to the sidewalls of
the micromachined channel is 700 micrometers. The conductors are 2 µm
thick electroplated gold. A half wavelength resonator constructed of this
geometry has an unloaded quality factor of 460 at 29 GHz. The filter
response of the diplexer is shown in Figure 3.7.The diplexer outer dimensions
are 1.5cm x 1.6cm x 1.4mm thick. The insertion loss is 1.4 dB for the 28 GHz
band and 0.9 dB for the 31 GHz band, including all transition effects. The
measured isolation is better than –35 dB across the receive band, and better
than –50 dB in the transmit band.
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
54
Figure 3.4: Response of the K band diplexer, taken from [10]
3.2 BANDSTOP FILTERS In this section, the review of bandstop filters with the objective of showing
different bandstop microwave filters designed using different technologies is
presented. Very few papers have been found on bandstop filter design and
they all are presented in this section of literature review.
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
55
3.2.1 L - RESONATOR BANDSTOP FILTER The L-resonator bandstop filter configuration provides increased options in
the design of narrow bandstop filters using TEM transmission-line elements.
A design procedure is presented for narrow bandstop filters using TEM
transmission line L resonators in [11], which are intermediate of the gap and
parallel-coupled resonators. In this configuration, parallel coupling occurs
over a portion of the resonator length, with the remaining resonator length
forming a stub. The grounded end of the resonator may be in either the
coupled or stub portion of the resonator.
Figure 3.5: Bandstop filter with shunt-connected L resonators, taken from [11].
Figure 3.6, shows a five-resonator filter in another configuration which is also
suitable for narrow bandstop applications. Each resonator has a parallel-line
coupling with an electrical length of less than λ/4 at resonance, a shunt stub,
and an uncoupled portion of the through line to provide additional electrical
length between resonators as required. The stub portion of the resonator
(because of the shape),is called an “L-resonator”. Coupled and stub line
lengths can be arbitrarily chosen with some limitations, and can vary between
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
56
resonators. The theoretical response is shown in Figure (3.7) and is close to
that of the highpass prototype.
Figure 3.6: Bandstop filter with shunt-connected L resonators, taken from [11]
Figure 3.7: Theoretical loss and return loss of degree 5 elliptic-function
L-resonator bandstop filter, taken from [11].
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
57
3.2.2 MICROMACHINED BANDSTOP FILTER Membrane supported microstrip structures are formed by removing the silicon
substrate and suspending a microstrip line on a thin (1.4 μm) dielectric
membrane [12]. A ground plane is formed by another micromachined
substrate and attached to the top of the circuit. The bottom is also shielded
with a third substrate shown in Figure 3.8. These resonators show large
improvements in quality factor over conventional techniques, and more
importantly, allow for planar integration in complex systems. Resonators were
fabricated in suspended microstrip at 29, 37, and 62 GHz with quality factors
of over 450 with very close agreement between simulated and measured
results. For this structure, dielectric loss was eliminated with the air dielectric, the
radiation loss is minimized by shielding the structure on all sides using thick
via grooves to limit substrate modes, and ohmic loss is greatly reduced by
allowing for very wide transverse microstrip geometries. Micromachining
techniques are used to produce a micro packaged, air dielectric line with wide
transverse dimensions resulting in high-Q resonators at millimeter-wave
frequencies. The micromachined suspended microstrip transmission line is
based a three wafer process (Figure 3.8).
For the circuit wafer, a stress compensated 1.4μm membrane layer consisting
of SiO2 / Si3N4 / SiO2 (7000°A / 4000°A / 3000°A) is deposited on a high
resistivity 525 μm thick silicon substrate using thermal oxidation and low
pressure chemical vapor deposition. This process deposits the thin film on
both sides of the silicon wafer allowing for a membrane on the top side of the
wafer and a good etch mask for the silicon removal on the back side.
Complete dimensions and thickness are described in [12]. A single resonator
fabricated at 29GHz in a bandstop configuration (Figure 3.19). The measured
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
58
loaded Q was 190 with a coupling -4.6 dB giving an extracted unloaded Q of
460 at 28.7 GHz.
Figure 3.8: transverse section of the microstrip structure, taken from [12]
(a) Bottom view (b) Top view
Figure 3.9: Circuit wafer of 29 GHz microstrip resonator in bandstop configuration (a) Bottom view, (b) Top view, taken from [12].
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
59
Figure 3.10: Measured S11 of bandstop resonator including effects of transition, taken from [12].
3.2.3 HIGH TC SUPERCONDUCTING CPW BANDSTOP
FILTERS FOR RADIO ASTRONOMY FRONT ENDS
A superconducting coplanar waveguide (CPW) bandstop filter consisting of 8
coupled line sections at a center frequency of 1.53 GHz is shown in Figure
(3.14) [13]. A packaged 94.7% bandwidth low pass; Chebyshev design
yielded a filter with a center frequency of 1.58 GHz, less than 1.2 dB insertion
loss in the passband and better than 28 dB rejection at 20 Kelvin.
At a center frequency of 1.56 GHz 8 coupled lines constitute a 7 pole filter
having an insertion loss of less than 1.2 dB and a skirt selectivity of 1.53 with
band rejection better than 28 dB. The radio telescope receivers are already
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
60
cooled to 20 Kelvin to reduce the noise in the semiconductor electronics, high
Tc; materials are very attractive for this application.
Figure 3.11: The bandstop filter specification taken from [13]
Other work on high Tc bandstop filters have been reported by [14] who used a
6 bank optically switchable bandstop filter and Lancaster et al. [15] who
employed a lumped element approach. Figure 3.12 illustrate measurement
results, which show the reduced band rejection and the extra ripple near the
stopband. A band rejection of -28 dB is less than the desired - 40 dB due to
direct and parallel plate coupling from input to output.
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
61
Figure 3.12: Measurement of the bandstop filter, taken from [13]
3.2.4 A SUPERCONDUCTING MICROSTRIP BANDSTOP FILTER FOR AN L-BAND RADIO TELESCOPE RECEIVER
A seven-pole High Temperature Superconducting (HTS) microstrip bandstop
filter at L band Chebyshev bandstop filter shown in Figure 3.13(b) is
fabricated on a 2” LaAlO3 substrate to eliminate the strong interference at
1394MHz [16]. The filter has application in a radio astronomy receiver. The
zig-zag loop resonator and the zig-zag phase line are developed to reduce
the parasitic effect of the direct resonator-to-resonator coupling. The designed resonator has a large loop at the middle of the line, and the
lines are then folded inward in a zig-zag shape Figure 3.13 (a). On a 0.508
mm thick LaAlO3 substrate (relative dielectric constant =23.6), the overall size
of the zig-zag loop resonator is 6.92mm wide and 2.32mm long. The HTS line
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
62
width of the resonator is 0.2mm. The radiation from one resonator to the
others is reduced because the electric current at any two symmetrical
positions with regard to the centre of the resonator flows in opposite
directions. Both the strong electric field at the open ends and the strong
magnetic field at the middle of the resonator are reduced by the opposite
current flow in the inward zig-zag lines, allowing resonators to be placed in a
relative small area without substantial unwanted coupling .Figure 3.13(b)
shows the whole phase through line was folded to 4-leg zigzag line. All seven
resonators are implemented on 2” wafer [16]. The simulation results are also
shown in Figure 3.14. The measured centre frequency is 1394.02MHz.
(a)
(b) Figure 3.13: (a) Coupling structure between the resonator and 50-.microstrip line on a
0.508 mm-thick LaAlO3 substrate, (b) Layout of the 7-pole microstrip HTS bandstop filter on 0.508mm-thick LaAlO3 (44mm×26mm), taken from [16].
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
63
Figure 3.14: Measured (thick solid line S21 (dB); thick dash line S11 (dB)) and
simulated (thin solid line S21 (dB); thin dash line S11 (dB)) performance of the seven-pole HTS microstrip bandstop filter, taken from [16].
3.3 QUASI ELLIPTIC FILTERS
3.3.1 HIGH PERFORMANCE HTS PSEUDO-ELLIPTIC BAND-STOP FILTERS
Elliptic function band-stop filters play an important role in cellular front end
filtering. The filter shown in Figure 3.15 is 6th order pseudo-elliptic band-stop
design, the design techniques described can be extended to any order band-
stop filter and a large range of frequencies [17]. Design is an approximate
elliptic filter that shares the key properties of an elliptic function filter.
According to author, this pseudo-elliptic band-stop filter is of a form that is
easily realized in microstrip form. In both the elliptic and Chebyshev filters, the
reactance slope parameter of the resonators generally varies from one
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
64
resonator to the next. By constraining the optimization [17] complete lumped
element represent the filter shown in Figure 3.15.
A plot of the filter performance is seen in Figure 3.16 (including approximately
12 dB of gain). This filter was used to notch out the AMPS A prime frequency
band (845 MHz - 856.5 MHz) from the full AMPS B band (835 MHz - 849
MHz). This filter was designed as a 6th order band-stop.
The filter’s passband was 800 MHz to 900 MHz, and the measured rejection
on this design rejection was achieved while maintaining a pass band insertion
loss of less than 1 dB. The pass band return loss was measured to be >20
dB. The filter was cascaded with a low noise amplifier and the response is
shown in Figure 3.17.
Figure 3.15: Complete Band-stop Filter Assembly, taken from [17]
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
65
Figure 3.16: S-parameter plot of B band-stop filter (includes 12 dB LNA gain), taken
from [17].
Figure 3.17: S-parameter plot of AMPS-B micro enclosure, take from [17]
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
66
CONCLUSION In this chapter, the literature reviews relevant to the thesis was presented.
Firstly, the state of art of membrane support filters was exhibited, which is
related to the work of chapter 4. Secondly, the work published on advance
bandstop filter configurations was reported, which sets the basis of the work
of chapter 5.
REFERENCES
[1] Jia-Sheng Hong and M.J. Lancaster,”Microstrip Filters for RF/
Microwave Applications”©2001 by John Wiley & Sons, Inc.
[2] Jen-Tsai Kuo, Member, Ming-Jyh Maa, and Ping-Han Lu “A Microstrip
Elliptic Function Filter with Compact Miniaturized Hairpin Resonators”,
IEEE microwave and guided wave letters, Vol.10, No.3,March 2000.
[3] J.-T. Kuo and E. Shih, “Wideband bandpass filter design with three-line
microstrip structures” IEE Proc-Microw. Antennas Prop. , Vol. 149, No.
516, October/ December 2002
[4] Jen-Tsai Kuo,Tsung-Hsun Yeh, and Chun-Cheng Yeh “Design of
Microstrip Bandpass Filters With a Dual-Passband Response”, IEEE
transactions on microwave theory and techniques, Vol. 53, NO. 4, April
2005.
[5] G. L. Hey-Shipton, N. 0. Fenzi, K. F. Raihn, “HTS Diplexer & Low
Noise Amplifier RF Module,” 1997 IEEE MTT-S International
Microwave Symposium Digest, pp. 295-298.
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
67
[6] E. R. Soares, K. F. Raihn, A. A. Davis, R. L. Alvarez, P. J. Marozick, G.
L. Hey-Shipton, “HTS AMPS-A and AMPS-B Filters for Cellular
Receive Base Stations,” April 1998.
[7] Lee Harle and Linda P.B. Katehi, “A Vertically Integrated
micromachined Filter“, IEEE transactions on microwave theory and
techniques, Vol. 50, NO. 9, September 2002.
[8] Chen-Yu Chi and Gabriel Rebeiz, “Conductor loss limited stripline
resonator and filters”, IEEE transactions on microwave theory and
techniques, Vol 44, No 4, April 1996.
[9] Pierre Blondy, Andrew R. Brown, Dominique Cross and Gabriel M.
Rebeiz, “Low loss micromachined filters for millimeter wave
communication systems”, IEEE transactions on microwave theory and
techniques, Vol 46, No 12, December 1998.
[10] Andrew R. Brown and Gabriel M. Rebeiz, “A high performance
integrated K-band diplexer”, IEEE transactions on microwave theory
and techniques, Vol 47, No 8, August 1999.
[11] H. Clark Bell, “L-Resonator Bandstop Filters”, IEEE Transactions on
Microwave Theory and Techniques, Vol. 44, No. 12, December 1996.
[12] Andrew R. Brown, Pierre Blondy, and Gabriel M. Rebeiz “Microwave
and Millimeter-wave High-Q Micromachined Resonators” published in
the international journal of RF and Microwave Computer-Aided
Engineering, 1999, page 1.
[13] S. Wallage, J. b. Tauritz , G. H. Tan , P. Hadley and J. E. Mooij “High
Tc superconducting CPW bandstop filters for radio astronomy front
CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS
68
ends”, IEEE Transactions on applied superconductivity, Vol. 7, No. 2,
JUNE 1997.
[14] N.O. Fenzi, K.F. Raihn, G.V. Negrete, E.R. Soares, and G.L.Matthaei,
“An Optically Switched Bank of HTS Bandstop Filters,” In 1994 IEEE
MTT-S International Microwave Sympo sium Digest [12], pp. 195-198.
[15] M. J. Lancaster, J. C. Li, A. Porch, and N. G. Chew, “High
Temperature Superconducting Lumped Element Resonator,”
Electronic Letters, vol. 29, no. 19, pp. 1728-1729, Sept. 1993.
[16] Guoyong Zhang, Michael J. Lancaster, Frederick Huang, and Neil
Roddis “A Superconducting Microstrip Bandstop Filter for an L-Band
Radio Telescope Receiver” published in IEEE.
[17] Edward R. Soares “Design and Construction of High Performance HTS
Pseudo-Elliptic Bandstop Filters”, 1999 IEEE MlT-S Digest.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
69
INTRODUCTION
In this chapter, designing of novel structures of resonators and 3 pole
Chebyshev bandstop filters at 1.5GHz and at 10GHz are presented along
with there respective simulation response. Design of resonators starts with
conventional (λ/2) resonator which are miniaturized with the addition of
capacitive patch. At 1.5GHz this patch was modified into an interdigital
structure (interdigital T-shape straight resonator) to enhance the coupling to
the transmission line. Further more, these novel compact resonators were
used to design Chebyshev bandstop filters at 1.5GHz and 10GHz central
frequencies. All proposed resonators and filters were designed using
microstrip technology (for microstrip see chapter 1).
This chapter is divided into five sections. Section 4.1, gives a general
description about EM simulator [1] used for designing. Section 4.2, consists of
designing of λ/2 resonator, Interdigital T-shape straight resonator, and ultra
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
70
compact interdigital meandered resonator. Section 4.3, describes about the
two different designs of compact 3 pole Chebyshev bandstop filter at 1.5GHz
and its respective simulation response. Section 4.4, consists of the designing
procedure and simulation results of λ/2 resonator, patch resonator, and novel
compact patch resonators with selective removal of substrate at 10GHz.
Section 4.5, presents a 3 pole Chebyshev bandstop filter at 10GHz.
Section 4.6 describes, about λ/2 coplanar waveguide used to connect the X-
band devices to the probe station for measurement.
4.1 ELECTROMAGNETIC (EM) SIMULATOR
Electromagnetic simulator is a CAD tool used to obtain S parameters for all
the components to be modeled over the ranges of designable parameters
and frequencies for which these models are expected to be used.
Electromagnetic (EM) simulation solves the Maxwell equations with the
boundary conditions imposed upon the RF/Microwave structure to be
modeled. Most commercially available EM simulators use numerical methods
to obtain the solution. One principle error, which is common to all the
numerical methods, is due to the finite cell or mesh sizes. These EM
simulators divide a RF/microwave filter structure into subsections or cells with
2D or 3D meshing, and then solve Maxwell’s equations upon these cells.
Larger cells yields faster simulations, but at the expense of larger errors.
Errors are diminished by using smaller cells, but at the cost of longer
simulation times. The errors in the filter simulation are due to mesh sizes
errors. This can be done by repeating the EM simulation using different mesh
sizes and comparing the results, which is known as a convergence analysis
[2-3]. The most common EM techniques used by modern simulators are:
Method of Moments, Finite Element Method [9-11].The packages used for the
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
71
realization of this thesis is [1], which use the Method of Moments to solve the
electromagnetic structures.
4.2 MICROSTRIP RESONATORS AT 1.5GHz
In this section, the designing procedure of λ/2 resonator, Interdigital T-shape
straight resonator, novel ultra compact interdigital meandered resonators are
presented.
4.2.1 MICROSTRIP RESONATORS (λ/2)
To design the microstrip resonator at 1.5 GHz, duroid [table 4.1] substrate
and copper as conductor were selected. The designing parameters used for
microstrip resonators and filters at 1.5GHz are specified in table 4.1 and 4.2.
substrate
Thickness
(mm)
Relative
Permittivity (εr)
Dielectric tangent
loss (tan δ)
(Duroid RT/6010LM) 0.64 10.8 0.0023
Table 4.1: Specifications of substrate to design resonators at 1.5GHz [5]
Metal
Thickness (mm)
R dc (Ω/sq)
Skin effect
Copper 0.017 0.001021 2.618e-7
Table 4.2: Specifications of Copper to design resonators at 1.5GHz [7]
Initially, the length of microstrip resonator (λ/2) was calculated with respect to
central frequency and relative permittivity of the substrate using formula (4-1).
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
72
rofc
ελ = (4-1)
Where, λ is the wavelength (mm).
fo is the central frequency (1.5 GHz)
c is speed of light (3 x 108 m/sec).
εr is the relative permittivity of the substrate.
The wavelength of λ= 60.8mm and resonator (λ/2) = 30.4mm were obtained
using (4-1). The width of the resonator was chosen to be 0.6mm equivalent to
50Ω transmission line calculated using [12].
In order to calculate the unloaded Q of the resonator (described in chapter 2),
the resonators were weakly coupled to the input and output transmission lines
of 50Ω (0.1mm spacing between transmission line and resonator) as shown
in Figure 4.1. De-embedded [1] lines were used as feeds to remove the port
discontinuity and transmission line effects from the analysis results.
Figure 4.1: Microstrip resonator λ/2 on Duroid substrate at 1.5GHz.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
73
The simulation response of this resonator using copper is shown in
Figure 4.2. The Q-value of resonator with copper is 108 (with lossless
metal = 462) at central frequency of 1.5GHz. This Q is calculated with
equation (4-2) (explained in chapter 2).
BWfQ 0= (4-2)
1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58-50
-45
-40
-35
-30
-25
Δf = 0.0139 GHz
Mag
nitu
de (d
B)
Frequency (GHz)
S12
QU= 108Δf
Simulation result of λ/2 resonator on duroid substrate at 1.5GHz
fo=1.5GHz
Figure 4.2: S12 Response of microstrip resonator (λ/2) at 1.5 GHz.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
74
4.2.2 INTERDIGITAL T-SHAPE STRAIGHT RESONATOR
T-shape straight resonator is presented in Figure 4.3. For narrow bandwidth
filters, strong coupling is required between the resonators and the
transmission lines. Hence, this structure presents enhanced coupling having
an interdigital capacitor to couple to the main transmission line. It was
observed that with the addition of interdigital fingers, the overall length of the
resonator was reduced to 27.6mm. But due to the dissipation at the edges of
the patch the Q value decreases.
Figure 4.3: Interdigital T-shape straight resonator on Duroid using Copper at
1.5GHz.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
75
Figure 4.4, presents the Q value simulation results obtained for weakly
coupled T-shape resonator with transmission line. With copper the Q-value is
107 and with lossless metal, it is 378 at central frequency of 1.5 GHz.
1.40 1.45 1.50 1.55 1.60-50
-45
-40
-35
-30
-25
Δ f
Mag
nitu
de (d
B)
Frequency (GHz)
S12
QU= 107fo=1.5 GHz
Simulation result of interdigital T-shape resonator on duroid substrate with copper
Δ f = 0.014 GHz
Figure 4.4: S12 Response of Interdigital T-shape straight resonator (λ/2) on Duroid
using Copper at 1.5GHz.
4.2.3 NOVEL ULTRA COMPACT INTERDIGITAL MEANDERED
RESONATOR
Figure 4.5, shows the dimensional details of an ultra compact interdigital
meandered resonator. Its total length is 12.4mm, which is three times smaller
than conventional one (Figure 4.3). This miniaturization achieved by
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
76
meandering the T-shape straight resonator presented previously. The
meander line is 4.4mm long and width is 0.6mm.
Figure 4.5: Proposed novel ultra compact interdigital meandered resonator on
Duroid using Copper at 1.5 GHz.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
77
1.3 1.4 1.5 1.6 1.7
-55
-50
-45
-40
-35
-30
-25
-20M
agni
tude
(dB
)
Frequency (GHz)
S12
Simulation results of Novel ultra compact interdigital meandered resonator on Duroid substrate at 1.5GHz
QU= 100fo =1.5 GHzΔ f = 0.015
Δ f
Figure 4.6: S12 response of novel ultra compact interdigital meandered resonator
on Duroid using Copper at 1.5GHz.
The simulation result of this resonator is shown in Figure 4.6, using copper.
The Q-value with lossless metal obtained was 375 and with copper were 100
at central frequency 1.5 GHz. The Q value is expected to decrease due to the
meandering of lines, as corner edges make the current peak so higher losses
are present, and also radiation losses increases. Figure 4.7, shows the
comparison of proposed resonators at 1.5GHz in terms of size, it’s clearly
visible that the ultra compact meandered resonator is very compact.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
78
Figure 4.7: Comparison of proposed resonators with respect to size
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
79
Table 4.3 presents a summary of the obtained Q-values with copper and
lossless metal.
METAL TYPES of RESONATOR Q-VALUE ( unloaded)
Lossless Conventional (λ/2) 462
Interdigital T-shape straight resonator 378
Ultra compact interdigital meandered resonator
375
Copper Conventional (λ/2) 108
Interdigital T-shape straight resonator 107
Ultra compact interdigital meandered resonator
100
Table 4.3: Summary of Q-value obtained with Copper and lossless metals on Duroid
(εr= 10.8, thickness (t) = 0.64mm and tan δ = 0.0023) for all types of resonators
proposed at 1.5 GHz.
4.3 3 POLE CHEBYSHEV BANDSTOP FILTER ON DUROID
SUBSTRATE AT 1.5 GHz
In this section, the designing procedure of 3 pole Chebyshev bandstop filter is
presented. The main theory of band reject filters was presented in chapter 2.
Two filters are designed; the first one use the T-shape straight resonator
described in section 4.2.2 and other one uses the ultra-compact meandered
resonator described in section 4.2.3.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
80
4.3.1 3-POLE CHEBYSHEV BANDSTOP FILTER USING
INTERDIGITAL T-SHAPE STRAIGHT RESONATOR
Bandstop filters consist of serially coupled resonators to a transmission line.
Each resonator absorbs energy at a certain frequency and hence the
transmitted power from input and output is equivalent to the power that was
not trapped in the resonators. This turns out to be a bandreject filter
characteristic. The resonators can be electromagnetically coupled to the main
transmission line, or can be directly connected to it. A general bandstop filter
is shown in Figure 4.8 each resonator is coupled to the transmission line with
interdigital capacitors. The distance between adjacent resonators is λ/4.
To design the 3 pole Chebyshev bandstop filter shown in Figure 4.8, a
bandwidth (BW) of 10% was chosen. Initially the reactance slope parameters
were calculated using following gi values of Chebyshev lowpass prototype:
The element values of the chosen Chebyshev lowpass prototype for Ωc=1
are [4]:
Passband equal-ripple (LAr) = 0.04321dB
g0 = g4= 1, g1= g3= 0.8516 and g2= 1.1032
FBWgg
ZZ
Zxci
o
o
uoi Ω⎟⎟
⎠
⎞⎜⎜⎝
⎛=
2
i= 1, 2, 3 (4-3)
Where, is reactance slope parameter, Zix o is terminal impedance (50 ohms)
and Zu is the characteristic impedance.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
81
Figure 4.8: Three pole Chebyshev bandstop filter T-shape straight resonator on
Duroid at 1.5 GHz using copper.
The calculated normalized reactance slope parameter values are in (4-4).
74.11
9
74.11
3
2
1
=
=
=
o
o
o
ZxZxZx
(4-4)
To obtain similar normalized reactance slope parameter values of (4-4) in EM
simulator, the length of the interdigital capacitor (Li) was varied and coupling
gap (Cg) was kept fixed to 0.4mm, as shown in Figure 4.9.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
82
(a)
(b)
Figure 4.9: (a) Structure to obtain x1/ Zo and x3 / Zo value of Normalized reactance slope parameter in EM simulator by varying Li, (b) Structure to obtain x2 / Zo
value of Normalized reactance slope parameter in EM simulator by varying Li.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
83
dB
o
dB
o
o
i
ff
Zx
33 22 Δ=
Δ=
ωω
(4-5)
The different values of normalized slope parameter with respect to variable
length (Li) of the capacitor are shown in Figure 4.10. The different values of
capacitor length with the respective normalized slope parameter for first and
second resonators at 1.5 GHz are shown in Figure (4.10(a.b)). The desired
lengths of the capacitor (Li) were determined to be L1 = L3 =7.6 mm and
L2 = 6.9mm.
7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.06
8
10
12
14
16
Xi /
Zo
Length of capacitance (mm)
11.7
Normalized reactance slope parameter against length of capacitor
Figure 4.10: (a) Normalized reactance slope parameters obtained by varying
(Li) capacitance by for 1st and 3rd resonators.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
84
6.2 6.4 6.6 6.8 7.0 7.2
6
8
10
12
14X
i / Z
o
Length of capacitor (mm)
9
Normalized reactance slope parameter against length of capacitor
(b)
Figure 4.10: Illustrate the extracted normalized reactance slope parameter against
variable lengths (Li) of capacitor (a) Normalized reactance slope parameters obtained by varying (Li) capacitor by for 1st and 3rd resonators, (b) Normalized reactance slope parameters obtained by varying (Li) capacitance by for 2nd resonators.
Figure 4.11, shows the detail dimension used to design interdigital T-shape
3-pole Chebyshev bandstop filter at 1.5GHz and Figure 4.12, presents its
simulation results. From this graph it is seen that the bandwidth was 9.9%,
the return losses were -2.7dB and the insertion losses were below -20dB at
the centre frequency.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
85
Figure 4.11: Detail dimension of 3 pole Chebyshev bandstop filter using T-shape straight resonators at 1.5 GHz
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
86
1.3 1.4 1.5 1.6 1.7-35
-30
-25
-20
-15
-10
-5
0M
agni
tude
(dB)
Frequency (GHz)
S11_simulated S12_simulated
BW=9.9%fo= 1.49GHz
3 pole Chebyshev bandstop filter
Figure 4.12: Simulation response of 3 pole Chebyshev bandstop filter using interdigital
T-shape straight resonators using copper at 1.5GHz.
4.3.2 3 POLE CHEBYSHEV BANDSTOP FILTER USING ULTRA
COMPACT INTERDIGITAL MEANDERED RESONATOR AT
1.5 GHz
In this section, the designing of a 3pole Chebyshev bandstop filter using ultra
compact interdigital meandered resonator is described. The design procedure
is similar to the one described in section 4.3.1, the only changed is the type of
resonator and length of the interdigital capacitance used to calculate
reactance slop parameter. Figure 4.13, shows the layout of the filter using
ultra compact meandered resonators. The advantage of this filter is its
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
87
compact size (39.2mm x 13mm) as compared to the bandstop filter proposed
in section 4.31 (41mm x 28.2mm). The values of normalized reactance slope
parameters described in previous section were used to design this filter.
Figure 4.13: The 3 pole compact Chebyshev bandstop filter using ultra compact
interdigital meandered resonators at 1.5 GHz.
The required length of the capacitor with respect to the required normalized
slope parameter is L1= 6.1mm for the first and third resonators; and for
second resonator the length of the capacitor L2= 6.5mm. Figure 4.14 shows
the detail dimensions of the capacitor.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
88
Figure 4.14: Structure to calculate reactance slope parameter by varying length of
interdigital capacitor (Li).
Figure 4.15 (a) is photograph of the fabricated microstrip 3 pole Chebyshev
bandstop filter using ultra compact interdigital meandered resonators and
Figure 4.15 (b) shows the simulation response of this filter. The bandwidth
obtained by simulation was 8.6% with central frequency 1.506 GHz. Insertion
losses were below -20dB and return loss -2.7 dB at the centre frequency.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
89
4.15: (a) Photograph of the fabricated microstrip 3 pole Chebyshev bandstop filter
using compact interdigital meandered line resonator.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
90
1 .3 1 .4 1 .5 1 .6 1 .7-30
-25
-20
-15
-10
-5
0M
agni
tude
(dB)
F re qu en cy (G H z)
S 1 1 S 1 2
B W = 8 .6 %fo = 1 .5G H z
S im u la tion re su lt o f C om ap ct 3 p o le C he bysh ev b an ds to p filte r
(b)
Figure 4.15: (a) Photograph of the fabricated microstrip 3 pole Chebyshev
bandstop filter using compact interdigital meandered line resonator, (b) The simulation response of microstrip 3 pole Chebyshev bandstop filter using compact interdigital meandered line resonator at 1.5GHz.
4.4 MICROSTRIP RESONATORS AT 10GHz
In this section the designing of resonator at 10 GHz is described, which
follows the same procedure designed as mentioned in section 4.1 of this
chapter. The main idea of the resonators presented in this section is the
removal of silicon substrate beneath selective parts of the resonator using
micromachining technology to increase Q value. This proposal is very unique
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
91
as there is no literature found related to selective removal of substrate. This
proposal is very beneficial at lower end of the millimeter spectrum, since high
Q values are obtained with enough mechanical strength to support the
structure, something that could not be achieved by traditional membrane
support structures (chapter 2).
There are three types of resonators proposed to design filters at 10GHz, they
are:
(λ/2) resonator on silicon substrate.
Patch resonator on silicon substrate.
Patch resonator on silicon substrate with air window beneath the patch.
Patch resonator on silicon substrate with air window beneath the strip.
At 10GHz all proposed resonators and filter are fabricated on HR-Si using
Aluminum as conductor. Silicon substrate was used due to following
advantages.
Silicon is a mature technology
It has an excellent planarity for the flip chip and bounding technologies.
It is good thermal conductor.
Multi interconnect metal layer are easily achieved devices that can not
be realized on wafer can be realized on other material and then flip
chip can be attached.
Micromachining technology works on Silicon.
Integrability with active circuits.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
92
4.4.1. MICROSTRIP CONVENTIONAL RESONATORS (λ/2)
To design the microstrip resonator at 10 GHz we selected N type high
resistivity (HR) silicon substrate of resistivity 2000 Ω cm with 400 15µm
thickness, its orientation is <100>. Aluminum of resistivity 2.2µΩ-cm was
used as conductor. For comparison purpose, the resonators were simulated
with Aluminum and Silver. The design parameters are specified in tables 4.4
and 4.5.The cross section view of a microstrip circuit is shown in Figure 4.16.
It can be seen that SiO
±
2 layer was used to electrically isolate the HR-Si and
the metal to decrease the substrate losses [13]. The figure also shows the
grounded coplanar waveguide used to connect the device to a probe station.
Figure 4.16: Cross section view of microstrip
Layer Thickness (mm)
Relative Permittivity (εr)
Dielectric tangent loss (tan δ)
SiO2 0.0015 3.9 0.007
Substrate
(Silicon -HR )
0.4 11.9 0.01
Table 4.4: Specifications of substrate to design microstrip resonators at 10GHz [6, 7].
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
93
Metal Thickness (µm) R dc ⎟⎟
⎠
⎞⎜⎜⎝
⎛tσ
1
(Ω/sq)
Skin effect
( )⎟⎟⎠
⎞⎜⎜⎝
⎛
σπμ
Aluminum 2 0.13440 3.25e-7
Silver 2 8.104 x 10 -3 2.53 e-7
Table 4.5: Specifications of Copper and Silver metals to design microstrip
resonators at 10GHz [7].
The length of the microstrip resonator (λ/2) (shown in Figure 4.17) was
calculated with respect to central frequency and relative permittivity of the
substrate using formula (4-1). The wavelength λ = 8.7mm was obtained;
hence the resonator length (λ/2) is 4.35mm. By using full EM simulator [1] the
resonator length (λ/2) is optimized to 5mm, using a line width of 0.4mm. This
resonator was weakly coupled to the feed lines in order to obtain the
unloaded Q-factor. The response of this resonator (λ/2) is shown in Figure
4.18 giving a simulated Q is 43 using equation (4-2).
Figure 4.17: conventional resonator at 10GHz on HR-Si substrate using Aluminum.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
94
9.8 10.0 10.2 10.4 10.6 10.8-36
-34
-32
-30
-28
-26
-24
-22
-20M
agni
tude
(dB
)
Frequency (GHz)
S12_simulated
Δ f
fo=10.26GHz
Δ f=0.235QU= 43
S12 response of Conventional (λ/2) resonator on HR-Si at 10GHz
Figure 4.18: S12 Response of microstrip resonator (λ/2) at 10 GHz.
4.4.2. MICROSTRIP PATCH RESONATORS
In order to reduce the length of the resonator an extra capacitive patch was
added to it, hence increasing the capacitance to ground and thus reducing
the total length. The final layout of this resonator is shown in Figure 4.19(a).
As it can be seen, the overall length was decreased from 5mm (conventional
resonator) to 4.4mm. Figure 4.19(b) represents the simulation results of the
weakly coupled resonator. The obtained Qu is 40.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
95
(a)
9.9 10.0 10.1 10.2 10 .3 10 .4 10.5-29
-28
-27
-26
-25
-24
-23
-22
-21
-20
Δ f
Mag
nitu
de (d
B)
F requency (G H z)
S12_sim ula ted
fo = 10.2G H z
Δ f3dB = 0.255
Q U = 40
S12 Sim ulation response of Patch resonator on H R-Si at 10G H z
(b) Figure 4.19: (a) Layout of patch resonator on HR-Si substrate, (b) S12 Simulation
results of patch resonator representing at 10 GHz.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
96
4.4.3. MICROSTRIP PATCH RESONATORS WITH AIR WINDOWS
In this section, the approach to increase the Q-value of the resonator is
proposed by removing selective parts of the substrate beneath the resonator
using micromachining technology. Here two different patch resonators with
higher Q-value are proposed using micromachining technology.
The first proposed patch resonator with selective removal of silicon beneath
the patch is illustrated in Figure 4.20 and the second, resonator with air
window beneath the strip is shown in Figure 4.21. The patch resonator with
Silicon removal underneath the patch has a total length of 5.61mm
(Figure 4.20a). The simulation results of the weakly coupled resonator are
shown in Figure 4.20(b), the unloaded Qu is 114 using Aluminum.
Figure 4.20: (a)(i): Cross section view of Patch resonator having Air window
underneath the Patch
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
97
Figure 4.20: (ii): (a)
9.5 10.0 10.5 11.0-45
-40
-35
-30
-25
-20
Mag
nitu
de (d
B)
Frequency (GHz)
S12_ simulated
S12 Simulation Response of Silicon with air window beneath Patch of resonator using Aluminum
fo = 10.25 GHz
QU = 114
(b)
Figure 4.20: (a): (i) Cross section view of Patch resonator having Air window
underneath the Patch, (ii) 3-D view of Patch resonator on Silicon having Air window underneath the Patch (using Coventor), (b): S12 simulation result of patch resonator with high Q on air window beneath the patch on HR-silicon substrate at 10GHZ using Aluminum.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
98
The second proposed patch resonator with removal of silicon beneath the
strip, has a total length of 6.32mm is shown in Figure 4.21a. The simulation
results of the weakly coupled resonator are shown in Figure 4.21b, the
unloaded Qu is 171 using Aluminum.
Figure 4.21: (a) (i): cross section view of patch resonator with selective removal of
substrate beneath the strip of resonator,
Figure 4.21: (a) (ii): 3-D view of Patch resonator on Silicon having Air window beneath
the strip (using Coventor),
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
99
9.5 10.0 10.5 11.0-50
-45
-40
-35
-30
-25
-20M
agni
tude
(dB
)
Frequency (Ghz)
S12_ simulated
S12 Simulation response of patch resonator with air window betneath strip using Aluminum metal
fo= 10.3 GHz
QU = 171
(b)
Figure 4.21: (a): (i): cross section view of patch resonator with selective removal of substrate beneath the strip of resonator,
(ii): 3-D view of Patch resonator on Silicon having Air window beneath the strip (using Coventor),
(b): S12 simulation result of patch resonator with high Q on air window beneath the patch on HR-silicon substrate using Aluminum metal.
The choice of the resonator should depend on the type of application
requirements or upon the size and performance. The performance of these
two higher Q resonators is better than the conventional resonator presented
in section 4.4.1 which had a Qu is 43.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
100
Table 4.6 represents comparison of Q-values obtained when Aluminum was
used as conductor and when Silver was used as conductor. From table 4.6
the Silver metal gives better Q values as compared to Aluminum. With Silver
the Q value obtained for a conventional resonator is 46(with aluminum 43).
For the patch resonator on HR-silicon substrate is the Q is 49 (40 with
aluminum). With air window beneath the strip of patch resonator the Q valued
raised to 229 by using Silver metal (compared to 171 with Aluminum). For the
fabrication Aluminum was selected as conductor for fabrication as it is
compatible with CMOS processes used in the Microelectronics Laboratory at
INAOE.
229 Patch resonator Silicon with air window beneath
strip
117 Patch resonator Silicon with air window
underneath patch
49 Patch resonator Silicon
46 resonator Silicon Silver
171 Patch resonator Silicon with air window beneath
strip
114 Patch resonator Silicon with air window
underneath patch
40 Patch resonator Silicon
43 resonator Silicon Aluminum
Q-VALUE (unloaded)
RESONATOR TYPE SUBSTRATE METAL
λ/2
λ/2
Table-4.6: Comparison of Q-value of resonators proposed obtained with
Aluminum and Silver metal at 10GHz.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
101
4.5 3 POLE CHEBYSHEV BANDSTOP FILTER ON
HR-SILICON SUBSTRATE AT 10 GHz
In this section, design of compact 3 pole Chebyshev bandstop filter using
patch resonator is presented. The designing method is similar as described in
section 4.3.1. The chosen substrate was HR-Si (εr = 11.9 and thickness 0 0.4
μm) without any removal of Si and the resonator is shown in section 4.4.2.
The conductor used is Aluminum. The filter layout is shown in Figure 4.22.
Figure 4.22: Three pole Chebyshev bandstop filter using patch resonator at 10 GHz
using Aluminum as metal.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
102
The designing parameters used to calculate normalized reactance
slope parameter were:
Bandwidth (BW) = = 10%
Fractional bandwidth (FBW) = 0.1
The element values of the chosen Chebyshev lowpass prototype
for Ωc=1 are [4]:
Passband equal-ripple (LAr) = 0.04321dB
g0 = g4= 1, g1= g3= 0.8516 and g2= 1.1032
Equation (4-3), was used to calculate normalized reactance slope
parameters [4]. The 50 Ω main line has a width of 0.4mm (Figure 4.20). By
following the procedure already described in section 4.3.1, the gaps between
the 50 Ω line and the resonator were changed and simulated using [1] in
order to obtain the different reactance slope parameters. The normalized
reactance slope parameter is then extracted according to equation (4-5).
Figure 4.23, presents the structure to obtain normalized reactance slope
parameter in EM simulator by varying lengths (Li) of the capacitor coupled to
the patch resonator, keeping coupling fixed to 0.04mm between patch and
capacitor and also between resonator and transmission line. Its simulation
response is shown in Figure 4.24. The desired length of the capacitors are
L1 = L3 =1.07 mm and L2 = 0.53mm.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
103
(a)
(b)
Figure 4.23: Structure to calculate normalized reactance slope parameter by varying
length of capacitor (Li).
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
104
(a)
(b)
Figure 4.24: Extracted normalized reactance slope parameter against variable lengths (Li) of extra capacitance coupled to the patch resonator, (a): The reactance slope parameter by the extra capacitance introduced to patch of the resonator, (b): The reactance slope parameters obtained by varying extra capacitance length introduced towards strip of patch resonator.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
105
Figure 4.25, shows the simulation response of microstrip Chebyshev
bandstop filter on silicon substrate at 10GHz (Figure 4.22). As it can be seen
the bandwidth is 0.9GHz (9%) and the return loss is -1.5 dB throughout the
band and the insertion loss at center frequency is about -15dB.
8.0 8.5 9.0 9.5 10.0 10.5 11.0
-25
-20
-15
-10
-5
0
Mag
nitu
de (d
B0
F requency (G H z)
S11_sim ula ted S12_sim ula ted
fo
f0= 9 .72 G H zBW =0.9G hz
3 pole Chebyshev bandstop filter at 10GHz on silicon using Alum inum
Figure 4.25: Simulation response of microstrip Chebyshev bandstop filter on silicon
substrate at 10GHz using Aluminum.
4.6 DESIGNING OF COPLANAR WAVEGUIDE (50Ω)
In this section, coplanar waveguide designing and simulation is presented. A
conventional grounded CPW consist of dielectric substrate with conductors on
the top surface and bottom surface as shown in Figure 4.26(a). The CPW
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
106
used in this work is necessary for probe station measurements. The CPW to
microstrip transition was optimized by adjusting L1, L2, L3, L4 and G1, G2,
G3, G4. Figure 4.26(b), shows the simulation response of final structure
obtained with L1=0.45mm, L2=0.4mm, L3=2.6mm, L4=4.9mm and width
G1=0.04mm, G2= 0.07mm, G3=0.1mm and G4=0.2mm at the central
frequency (10GHz).
(a)
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
107
(b)
Figure 4.26: Proposed CPW to microstrip transition (a) Proposed CPW structure, (b) Transition frequency response.
Initially, all the steps were simulated separately for 50 Ω and after that all
were combined into one structure and input and output port impedance was
obtained to be 50 Ω. Small step were used in this CPW structure to maintain
the characteristic of lump elements through out the transmission line. The
return loss (S11) response is -23dB. Two via holes were micromachined on
each ground surface to connect bottom and top ground planes. The size of
via holes was 500 µm x 500 µm. The fabrication process is shown in
chapter 6.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
108
CONCLUSION
In this chapter, the design of novel resonators and Chebyshev bandstop
filters along with there respective simulation results have been presented.
The objective of designing resonators was to obtain compact size as well as
high Q value.
At 1.5GHz, three novel structures of resonators are presented and were
compared in terms of Q values and size to achieve the goal of compactness
and high Q. The first is conventional resonator (37mm) with copper Qu is 108
(lossless metal=462). Second is T-shape straight resonator (27.6mm)
structure which is 9.4mm smaller than conventional and its Q value with
copper is Qu is 107 (lossless metal=378), and the third is Ultra compact
interdigital meandered resonator (12.4mm), which is three times smaller than
the conventional resonator (37mm). The Q value with copper is Qu is100
(lossless metal=375).
At 1.5GHz, two 3 pole Chebyshev bandstop filters with 10% bandwidth have
been designed using the pervious resonators with good simulation responses.
At 10GHz, novel patch resonators layout have been proposed with selective
air windows beneath the patch and underneath the strip of the resonator
using micromachining technology. The total length of the conventional
resonator was 5mm with Qu is 43 and the patch resonators length was 4.4mm
with Qu is 40. The Q value obtained with patch resonator having air window
beneath the patch was Qu is 114 and with patch resonator having air window
underneath the strip is Qu is 171. Hence, by comparing the Q values it is clear
that we successfully increased the Q values from 40 (patch resonator) to
114(air window beneath patch) and 171(air window beneath strip). This
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
109
proposal is another special achievement in this thesis work as there is no
literature found on selective removal of substrate at lower frequency to obtain
higher Q values.
A Chebyshev bandstop filter is proposed using patch resonator on HR-Si at
10GHz with good simulation response.
REFERENCES
[1] “Sonnet 7.0b”, ©1989, 1991, 1993, 1995-2001 Sonnet Software, Inc.
[2] Jia-Sheng Hong and M.J.Lancaster, “Investigation of microstrip
pseudo-interdigital bandpass filters using a full-wave electromagnetic
simulator”, International Journal of Microwave and Millimeter-Wave
computer-Aided engineering, 7, 3, May 1997, 231-240.
[3] J.C.Rautio and G.Mattaei, “Tracking error sources in HTS filters
simulations”. Microwave & RF, 37, Dec,. 1998, 119-130
[4] Jia-Sheng Hong and M.J.Lancaster, “Microstrip Filters for
RF/Microwave Applications”, © 2001 by Wiley Series in Microwave and
Optical engineering.
[5] Data sheet, www.Rogerscorporation.com
[6] http://www.rfcafe.com/references/electrical/dielectric_constants_streng
ths.htm.
[7] Brain C.Wadell, “Transmission Line Design handbook”, © 1991 Artech
house, Inc.
CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz
110
[9] R.F. Harringdon, Field Communication by Moments Methods,
Macmillian, New York, 1968.
[10] J.C.Rautio and R.F Harrington,”An electromagnetic time-harmonic
analysis of arbitarary microstrip circuits”. IEEE Trans., MTT-35,
Aug.1987, 726-730.
[11] M.Koshiba, K.Hatata, and M.Suzuki, “Finite-element formulation in
terms of the electric-filed vector for electromagnetic waveguide
problems”, IEEE Trans.MTT-33, Oct.1985, 900-905.
[12] Paolo Delmastro “TRANSLIN software”, Artech house.
[13] J.A.Reynoso-Hernández, Raúl Rancel-Rojo, M.Aceves, I. Zaldivar,
L.E. Sánchez, and M.Herrera “ Influence of the SRO as passivation
Layer on the Microwave attenuation Losses of the CPWs Fabricated
on HR-Si”, IEEE microwave and wireless components
letter ,Vol.13,No.12,Dec.2003.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
111
INTRODUCTION
There has been an increasing demand for advance RF /microwave filters
other than conventional Chebyshev filters in order to meet stringent
requirement from RF/microwave systems, particularly from wireless
communications systems. In this chapter, the designing of advanced filter
topologies using trisections with single transmission zero is proposed which
gives higher selectivity at one side of the band. If double side selectivity is
required then two Trisection filters can be cascaded. In practice single side
selectivity is used in Diplexer designs where, Transmission and Receive
signals have to separate at mobile base stations, Satellite systems, etc.
No other work has been published (to the author’s knowledge) on Triplet
bandstop filters which makes this work highly valuable and propositive. The
principle of operation of these filters is based on the cross coupling of
non-adjacent resonators. In this chapter, the full designing procedure will be
explained and simulation results of the proposed structure are presented.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
112
This chapter is divided into three subsections, section 5.1, presents theory of
selective filters with transmission zeroes (Quasi-elliptic response), Section 5.2,
gives information about the working of Trisection filters with the help of
bandpass filter structures, section 5.3, describes about the designing
procedure of Triplet bandstop filter at 1.5 GHz based on optimization method.
5.1 FILTERS WITH SINGLE PAIR OF TRANSMISSION ZERO (QUASI ELLIPTIC RESPONSE)
The filter having only one pair of transmission zeroes at finite frequencies
gives much improved skirt selectivity, making it a viable intermediate between
the Chebyshev and elliptic function filters (Figure 5.1). The transfer function of
this type of filter is:
( ) ( )Ω+=Ω
nFS 22
221 1
1ε
(5-1)
110
1
10 −
=− RL
ε (5-2)
( ) ( ) ( )⎭⎬⎫
⎩⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛Ω+Ω+ΩΩ
+⎟⎟⎠
⎞⎜⎜⎝
⎛Ω−Ω−ΩΩ
+Ω−=Ω −−−
a
a
a
an nF
1cosh
1coshcosh2cosh 111
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
113
Figure 5.1: Comparison of frequency of the Chebyshev filter and the design filters with
single pair of attenuation poles at finite frequency (n=6)
Where Ω is the frequency variable that is normalized to the passband cut-off
frequency of the lowpass prototype filter, ε is ripple constant to a given return
loss 11log20 SLR = in dB, and n is the degree of the filter. The closer the
attenuation poles to the cutoff frequency (Ω=1), the shaper the filter skirt will
be and higher will be the selectivity.
5.1.1 APPROXIMATION SYNTHESIS PROCESS OF QUASI ELLIPTIC
The transmission zeroes of this type of filter may be realized by cross
coupling the pair of non adjacent resonators of the standard Chebyshev filter
the approximate synthesis method based on a lowpass prototype filter is
shown in Figure 5.2 [1], where the rectangular box represents ideal
admittance inverters with characteristic admittance J. The approximate
synthesis starts with the element values for Chebyshev filter using (5-1, 5-2).
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
114
γ
πng 2
sin21 = (5-1)
( ) ( )
( ) ( ) 2/,,.....2,11sin
232sin
212sin4
221 nmmi
ni
ni
ni
gg ii ==−
+
−−
=− πγ
π
(5-2)
Where,
⎟⎠⎞
⎜⎝⎛= −
εγ 1sinh1sinh 1
n (5-3)
( ) ( )
0
11
1
22
=
=
++=
−m
m
JS
J
VSWRpassbandtheS εε
(5-4)
In order to introduce transmission zero at aΩ±=Ω the required
value of Jm-1 is given by equation (5-5):
( ) 2'2
'
1
mma
mm
JgJJ−Ω
−=− (5-5)
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
115
Figure 5.2: Standard Chebyshev filter the approximate synthesis method based on a lowpass prototype filter
Introduction of Jm-1 mismatches the filter, and to maintain the required return
loss at midband it is necessary to change the value of Jm slightly according to
the formula given by equation (5-6).
1
'
1 ++=
mm
mm
JJJ
J (5-6)
Where, is interpreted as the updated J'mJ m. Equation (5-6) and (5-5) are
solved iteratively with the initial values of Jm and Jm-1 given in equation (5-2).
No other elements of Chebyshev filter are changed.
The method is simple, however quite useful in many cases for the design of selective
filters. It suffers from inaccuracy, and even can fail for very high selective filters that
require moving the attenuation poles closer to the cut-off frequencies of the passband.
This implies the use of more accurate synthesis procedure. Alternatively, one can use
a set of more accurate design tabulated data [1]. For less selective filters that require a
larger Ωa, the element values can be obtained using above approximation synthesis
procedure.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
116
5.2 TRISECTION FILTERS In this section the importance of working with Trisection filters is explained. As
there is no pervious report on Triple Bandstop, we are presenting the theory
available on bandpass Triplets. Trisection filter is basic unit for construction of
higher-degree cascaded trisection (CT) filters. To understand how it works
lets take case of the narrow-band, an equivalent circuit of Figure 5.3 (a) can
represent a trisection filter. The coupling between adjacent resonators are
indicated by the coupling coefficient M12 and M23 and the cross coupling is
denoted by M13. Qe1 and Qe3 are the external quality factors denoting the
input and output couplings.
Note: the resonators are not necessary synchronously tuned for trisection
filter and therefore each resonator resonates at different frequencies.
iiCL1 =ωoi=2πfoi is the resonator angular frequency of the resonator i for i=1,
2 and 3. To have asymmetric response of frequency trisection filters, the
physical configuration of the filter can be kept symmetric. Therefore, let
M12=M23, Qe1=Qe3 and ωo1=ωo3.
Figure 5.3: (a) Equivalent circuit of a trisection bandpass filters.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
117
Figure 5.3: (b) Associated lowpass prototype filter.
TRISECTION FILTER
CHEBYSHEV
TRANSMISSION ZERO
(c)
Figure 5.3: (a) Equivalent circuit of a trisection bandpass filter, (b) Associated lowpass prototype filter, (c) the comparison between ideal Chebyshev filter and Trisection filter
response.
The above coupled resonator circuit may be transferred to lowpass prototype
filter as shown in Figure 5.3(b). Each of the rectangular boxes represents a
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
118
frequency invariant immittance inverter, with J the characteristic admittance of
the inverter, here J12=J23=1 of the inverters along the main path of the filter.
The bypass inverter with a characteristic admittance J13 accounts for cross
coupling gi and Bi (i=1, 2, 3) denote the capacitance and the frequency
invariant susceptance of the lowpass prototype filter, respectively. g0 and g4
are the resistive terminations. With symmetric two-port circuit of Figure 5.3(b),
g0=g4, g1=g3 and B1=B3. Also g0=g4=1 be the normalized termination. The
scattering parameters of the symmetric circuit may be expressed in terms of
even and odd mode parameters of one-port circuit formed by inserting an
open or short circuited plan along its symmetric plan [1]. Figure 5.3 (c),
shows the comparison between Ideal Chebyshev filter and Trisection filter
response. The transmission zero makes very selective cut off at one side as
shown in figure 5.3(c), which makes the use of Trisection filters advantageous
for certain applications. If double side selectivity as required then two
Trisection filters could be cascaded.
5.2.1 MICROSTRIP TRISECTION FILTERS Microstrip trisection filters with different resonator shapes, such as open-loop
resonator and triangular patch resonator, can produce asymmetric frequency
responses with an attenuation pole of finite frequency on either side of the
passband.
When all the designing parameters are know gi, Jnm, Qe, Mmn, fo for the cross-
coupled resonator filter using formula given in [1], we can obtain an image
frequency response of the filter with finite frequency attenuation pole moved
to the low side of the passband.This kind of design parameters have dual
usage, and one may take the advantage of this to design the filter with the
image frequency response also. Having obtained the required design
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
119
parameters for bandpass filter, the physical dimensions of the microstrip
trisection filter can be determined using full EM simulator to extract the
coupling and external quality factor.
5.3 DESIGNING PROCEDURE OF NOVEL TRISECTION
BANDSTOP FILTER AT 1.5 GHz
In this section, the design procedure of Trisection filters is presented.
Photograph of proposed triplet filter is shown in Figure 5.4. The design
parameters for the filters are:
Bandwidth = 4.5%
Fractional bandwidth = 0.1
Central frequency = 1.5GHz
To design this filter the substrate was duroid [table 5-1] and copper was
chosen as conductor [table 5-2]. The substrate and metal specification used
in this work are given in table-5.1 and table-5.2.
Substrate Thickness (mm)
Relative Permittivity (εr)
Dielectric tangent loss (tan δ)
Substrate
(Duroid RT/6010LM)
0.64 10.8 0.0023
Table 5.1: Specifications of substrate to design microstrip resonators at 1.5GHz [5]
Metal Thickness
(mm) R dc
(Ω/sq) Skin effect
Copper 0.017 0.001021 2.618e-7
Table-5.2: Specifications of copper to design microstrip resonators at 1.5GHz [7]
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
120
Figure 5.4: Photograph of proposed novel Trisection Bandstop filter at 1.5GHz.
The design procedure steps are shown in Figure 5.5.
Figure 5.5: The steps follow to design Trisection filter.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
121
STEP1: Initially, the 3 pole Chebyshev bandstop filter with lumped
elements was designed using the procedure shown in chapter 4, as shown in
Figure 5.6.
The designing parameters to calculate normalized reactance slope
parameter were:
Bandwidth = 4.5%
Fractional bandwidth = 0.1
The element values of the chosen lowpass prototype for Ωc=1 are [4]:
For a Chebyshev filter with passband equal-ripple (LAr) = 0.04321dB
g0 = g4= 1, g1= g3= 0.8516 and g2= 1.1032
Equation (5-7) was used calculate reactance slope parameter [1].
FBWg
gZZ
Zxci
o
o
uoi Ω⎟⎟
⎠
⎞⎜⎜⎝
⎛=
2
i= 1, 2, 3 (5-7)
Where, is reactance slope parameter, Zix 0 is terminal impedance (50 ohms)
and Zu is the characteristic impedance. Consider = in equation (5-7)
which is to normalized impedance to calculate slope parameter.
uZ oZ
From equation (5-7) we obtained reactance slope parameter values given in
equation (5-8) for each resonator to be coupled to the main transmission line.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
122
74.11
9
74.11
3
2
1
=
=
=
o
o
o
ZxZxZx
(5-8)
At first instance, the coupling was achieved with lumped capacitances as it is
shown on Figure 5.6.
CAP
C=ID=
C1 pFC1
CAP
C=ID=
C2 pFC2
CAP
C=ID=
C1 pFC3
TLIN
F0=EL=Z0=ID=
1.5 GHz270 DegZ12 OhmTL1
TLIN
F0=EL=Z0=ID=
1.5 GHz270 DegZ12 OhmTL2
TLOC
F0=EL=Z0=ID=
1.5 GHzEL1 Deg50 OhmTL4
TLOC
F0=EL=Z0=ID=
1.5 GHzEL1 Deg50 OhmTL5
TLOC
F0=EL=Z0=ID=
1.5 GHzEL2 Deg50 OhmTL6
PORT
Z=P=
50 Ohm1
PORT
Z=P=
50 Ohm2
Z12=50
C2=0.6
C1=0.5
EL2=155
EL1=159
Figure 5.6: Chebyshev bandstop filter using lump elements.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
123
STEP 2: After designing Chebyshev bandstop filter using lumped
elements, cross coupling was done between non-adjacent resonators with
50Ω transmission line having 90 degrees electrical length as shown in Figure
5.7 and its response is presented in Figure 5.7(b). As it can be seen, the
response does not give the desired response, hence, optimization using AWR
[2] optimizer was done to obtain exact values of the capacitance and
transmission line dimensions as presented in step 3.The optimization goals
are shown in Figure 5.7 (c).
CAP
C=ID=
C1 pFC1
CAP
C=ID=
C2 pFC2
CAP
C=ID=
C1 pFC3
TLIN
F0=EL=Z0=ID=
1.5 GHz270 DegZ12 OhmTL1
TLIN
F0=EL=Z0=ID=
1.5 GHz270 DegZ12 OhmTL2
TLIN
F0=EL=Z0=ID=
1.5 GHz90 DegZ13 OhmTL3
TLOC
F0=EL=Z0=ID=
1.5 GHz158 Deg50 OhmTL4
TLOC
F0=EL=Z0=ID=
1.5 GHz158 Deg50 OhmTL5
TLOC
F0=EL=Z0=ID=
1.5 GHz150 Deg50 OhmTL6
PORT
Z=P=
50 Ohm1
PORT
Z=P=
50 Ohm2
Z13=50
C2=0.5
C1=0.5
Z12=50
Figure 5.7: (a) Cross-coupling of non-adjacent resonators of Chebyshev bandstop
filter with 50Ω transmission line of 90 degrees electrical length.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
124
Figure 5.7: (b) Response of initial trisection filter
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
125
Figure 5.7 :(c) Optimization goals to obtain required response.
Figure 5.7: (a) Cross-coupling of non-adjacent resonators of Chebyshev bandstop
filter with 50Ω transmission line of 90 degrees electrical length, (b) Response of initial trisection filter, (c) Optimization goals to obtain required response.
STEP 3: In this step the 50Ω transmission line cross-coupled to the
non- adjacent resonators was optimized to obtain improved response of the
Trisection bandstop filter with extra transmission zero. The optimized
Trisection filter is shown in Figure 5.8(a) and its optimized response is
presented in Figure 5.8(b). Here extra transmission zero response is clearly
visible towards higher frequency. The asynchronicity of the filter is clearly
seen as resonators 1 and 3 resonate at 1.49GHz where as resonator 2
resonate at 1.5GHz.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
126
CAP
C=ID=
C1 pFC1
CAP
C=ID=
C2 pFC2
CAP
C=ID=
C1 pFC3
TLIN
F0=EL=Z0=ID=
1.5 GHz270 DegZ12 OhmTL1
TLIN
F0=EL=Z0=ID=
1.5 GHz270 DegZ12 OhmTL2
TLIN
F0=EL=Z0=ID=
1.5 GHz90 DegZ13 OhmTL3
TLOC
F0=EL=Z0=ID=
1.49 GHz158 Deg50 OhmTL4
TLOC
F0=EL=Z0=ID=
1.49 GHz158 Deg50 OhmTL5
TLOC
F0=EL=Z0=ID=
1.5 GHz150 Deg50 OhmTL6
PORT
Z=P=
50 Ohm1
PORT
Z=P=
50 Ohm2
C1=0.95C2=1
Z12=50
Z13=200
Figure 5.8: (a) Cross-coupling of non-adjacent resonators of Trisection bandstop filter with 200Ω transmission line.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
127
(b)
Figure 5.8: (a) Cross-coupling of non-adjacent resonators of Trisection bandstop filter
with 200Ω transmission line of 90 degrees electrical length, (b) Response of Trisection filter with lump elements.
STEP 4: The optimized lumped elements Trisection filters presented in
step 3 were replaced with layout structures. The resonator used to design
Trisection bandstop filter is ultra compact interdigital meandered resonators
(described in chapter 4). For Trisection filter, asymmetry tuning was required
as stated earlier, here the two different frequencies chosen was1.5GHz for
the first and third resonators and 1.49GHz was chosen for second resonator.
Hence, with respect to these two resonating frequencies, the slope
parameters were implemented using method described below.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
128
The normalized reactance slope parameter 11.7 was chosen with respect to
the central frequency 1.5GHz of the resonator and normalized reactance
slope parameter 9 was selected for 1.49 GHz central frequency resonator.
Hence, Figure 5.9 gives the graph of normalized reactance slope parameter
of 1.5 GHz and 1.49 GHz and the typical response and extracted normalized
reactance slope parameters. The desired coupling (Li) are: L1 = L3 =6.3mm for
resonator first and third with central frequency 1.5GHz and L2 = 6.8mm length
of capacitor introduced to the second resonator with central frequency
1.49GHz.
6.0 6.2 6.4 6.6 6.8 7.0 7.2
4
6
8
10
12
14
16
18
Xi/Z
o
Length of capacitor (mm)
reactance slope parameter _Lossles
reactance slope parameter_copper
Normalized reactance slope parameter at 1.5GHz
11.6
Figure5.9: (a) The reactance slope parameter by varying the length of interdigital
capacitance at 1.5GHz,
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
129
6.0 6.2 6.4 6.6 6.8 7.0 7.2
4
6
8
10
12
14
16
18
Normalized reactance slope parameter at 1.49 GHz
Length of capacitor (mm)
Xi/Z
o reactance slope
parameter _Lossles
reactance slope parameter_copper
8.8
(b)
Figure5.9: (a) the reactance slope parameter by varying the length (Li) of interdigital capacitance at 1.5GHz, (b) The reactance slope parameters obtained by varying interdigital capacitance length (Li) at 1.49 GHz.
Figure 5.10 (a), shows the initial circuit of Trisection Bandstop filter replaced
with sub-circuits of original resonators and with interdigital capacitor with
transmission lines, its simulation response is presented in Figure 5.10(b). The
central frequency obtained was 1.5 GHz the transmission zero was obtained
at 1.49 GHz with return loss of -1.13dB and insertion loss of -15.6 dB at
central frequency, the drawback was the coupling transmission line between
resonator 1 and 3 was of impedance 200 Ω, which was not possible to
fabricate as the line would be extremely thin.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
130
Figure 5.10: (a) The initial circuit of Trisection bandstop filter replaced with sub-circuits of original resonators and transmission line inverter.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
131
(b)
Figure 5.10: (a) The initial circuit with transmission line inverter, (b) Response of filter with interdigital capacitor equivalent to transmission line of 200 Ω.
STEP 5: To over come the problem of 200 Ω transmission line,
transmission line inverter was implemented and the transmission line was
obtained in the form of interdigital capacitor of 0.95pF which was connected
to transmission line of electrical length 151.1 degrees at the left side and 11.5
degrees at the right side of interdigital capacitor. The calculation to obtain the
capacitive value of the inverter was done using formula given in [3]. The
circuit was optimized again to central frequency 1.5GHz with extra
transmission zero. Figure 5.11 (a), presents the steps and formulas used to
convert the 200Ω transmission line into 50Ω transmission line with a capacitor
[3]. The final circuit with transmission line inverter is shown in Figure 5.11(b),
and the circuit with interdigital capacitor, which is equivalent to the
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
132
transmission line 200 Ω is shown in Figure 5.11 (c) and its response is
present in Figure 5.11 (d).
Figure 5.11 (a) Steps and formulas used to convert transmission line of 200 Ω to
50 Ω transmission line using Admittance.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
133
TLIN
F0=EL=Z0=ID=
1.5 GHzTheta/2 DegImp OhmTL2
TLIN
F0=EL=Z0=ID=
1.5 GHz(Theta/2)-140 DegImp OhmTL3
MSUB
Name=ErNom=
Tand=Rho=
T=H=
Er=
SUB1 2.2 0 1 0.017 mm0.64 mm10.8
CAP
C=ID=
0.96 pFC1 PORT
Z=P=
50 Ohm1
PORT
Z=P=
50 Ohm2
Theta=303
Imp=50
Figure 5.11: (b) The final circuit with transmission line inverter
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
134
Figure 5.11: (c) The circuit with interdigital capacitor, which is equivalent to the transmission line 200 Ω
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
135
(d)
Figure 5.11: (a) Steps and formulas used to convert transmission line of 200 Ω to 50 Ω transmission line using Admittance, (b) The final circuit with transmission line inverter, (c) the circuit with interdigital capacitor, which is equivalent to the transmission line 200 Ω, (d) Response of filter with interdigital capacitor equivalent to transmission line of 200 Ω.
The practical structure of interdigital capacitor of 0.95pF which is connected
to the transmission line of electrical length 200 degrees (41.4mm) with
impedance 48Ω on both sides to obtain transmission zero response is shown
in Figure 5.12(a). The total length is 31.6mm, the length of each capacitor
finger is 30.8mm, and the gap between each capacitive finger is 0.4mm. The
electrical length of transmission line used to couple resonator 1 with
resonator 2 is 190 degrees (39.6mm) with impedance of 48Ω. Practical
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
136
structure of Trisection bandstop filter is shown in Figure 5.12 (b), its
simulation response is present in Figure 5.12 (c).
Figure 5.12(a): The interdigital capacitor which is connected to the transmission line.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
137
Figure 5.12(b): Dimensional detail of Photograph of proposed novel Trisection
bandstop filter at 1.5GHz.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
138
.71.4 1.5 1.6 1
-35
-30
-25
-20
-15
-10
-5
0
Mag
nitu
de (d
B)
Frequency (GHz)
S11 S12
fo= 1.5GHzBW=3.3%Return loss= -1.9dBinsertion loss= -15.7dB
(c) Simulation response of Triplet bandstop filter with extra transmission zero.
Figure 5.12: (a): The interdigital capacitor which is connected to the transmission line, (b): The practical structure of Triplet bandstop filter at 1.5GHz, (c): Simulation results of Triplet bandstop filter with extra transmission zero.
The transmission lines are meandered to miniaturize the length of the
transmission line as shown in Figure 5.12(b). The lengths of the transmission
line used here to couple resonators are as follows in terms of electrical length:
1) To connect resonator 1 to resonator 2 the transmission line electrical
length is 190o and impedance is 50 Ω.
2) To connect resonator 2 to resonator 3 the transmission line electrical
length is 190o and impedance is 50 Ω.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
139
3) To connect resonator 3 to one end of interdigital capacitor, the
transmission line electrical length is 200o and impedance is 50 Ω.
4) To connect resonator 1 to the interdigital capacitor the transmission
line electrical length is 200o and impedance is 50 Ω.
From simulation response shown in Figure 5.12(c) the central frequency
obtained was 1.57GHz and the bandwidth obtain was3.3%, transmission zero
was obtained on the higher frequency side. The experimental results of this
filter are presented in chapter 7.
CONCLUSION
In this chapter, the design procedure of Trisection filter has been presented.
The designing of a Novel Trisection bandstop filter with 4.5% bandwidth at
1.5 GHz has been proposed in this chapter using ultra compact T-shape
meandered resonator of 12.4mm x 10.6mm along with the simulation results.
The total size of Trisection bandstop filter is 72mm x 34mm. For Trisection
filters the asymmetric tuning of resonators was required to resonate each
resonator at different frequencies. To design triplet filter with extra
transmission zero, non-adjacent resonators were coupled directly with
interdigital capacitor, which is equivalent to transmission line of electrical
length 90o with the impedance of 200Ω. The bandwidth obtained by
simulation was 3.3% and central frequency 1.505 GHz. The experimental
results are presented in chapter 7.
Trisection filters very important and advantageous as these filter topology is
based on three resonators which make it compact. If double side selectivity is
required then two Trisection filters can be cascaded. In practice single side
selectivity is used in diplexer design.
CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz
140
REFERENCES
[1] Jia-Sheng Hong and M.J.Lancaster, “Microstrip Filters for
RF/Microwave Applications”, © 2001 by Wiley Series in Microwave and
Optical engineering.
[2] Microwave office” Advancing the wireless revolution (AWR)” software
[3] Brain C.Wadell, “Transmission Line Design handbook”, © 1991 Artech
house, Inc.
[4] “Sonnet 7.0b”, ©1989, 1991, 1993, 1995-2001 Sonnet Software, Inc.
CHAPTER 6: FABRICATION PROCESS
141
INTRODUCTION
The main objective of this chapter is to describe the fabrication process for
the resonator and filter on high resistivity silicon (HR-Si) substrate at 10 GHz.
In first section, we depict about the mask to define the structure for resonator
and Chebyshev filter. In second section, we illustrate micromaching
techniques to etch the silicon (HR-Si). In last section; we give details of the
fabrication process.
6.1 MASK The design of photolithography mask for micromachining is generally
straightforward. Normally, designs incorporate relative large structures
(1-10 μm +) compared to the sub-micron structures that are now incorporated
into advanced Very Large Scale Integrated (VLSI) technologies. All that is
required is some suitable CAD (computer aided design) software, and a
platform to run it on. The basic CAD software required to design mask is a
"layout editor" (L-Edit). This enables to place different polygons onto different
layers, each layer being a mask design for a particular step in the fabrication
CHAPTER 6: FABRICATION PROCESS
142
process, assemble these into "structures" (or "cells") which can be placed
adjacent to one another on the final design, and export the design file in a
suitable format [1].
Two masks where made using L-Edit [1]. The first one is of patch resonator at
10 GHz shown in Figure 6.1 and the second one is of 3-pole Chebyshev filter
at 10GHz illustrated in Figure 6.2. The Figure 6.1 (a) represent mask of metal
layer for resonator structure and coplanar waveguide (CPW) and 6.1(b)
corresponds to bottom layer of cavities designed for CPW. Figure 6.2 (a)
correspond to metallic layer for Chebyshev filter and CPW and Figure 6.2(b)
corresponds to bottom layer of cavities designed for CPW.
CHAPTER 6: FABRICATION PROCESS
143
(a) Top layer mask for metal
(b) Bottom layer cavity mask
Figure 6.1: Mask of single Resonator on Silicon substrate at 10 GHz, (a) top metal layer mask, (b) bottom layer cavity mask. (Scale corresponds to 1λ = 1 μm).
CHAPTER 6: FABRICATION PROCESS
144
(a) Top layer mask for metal
(b) Bottom cavity layer mask
Figure 6.2: Mask of Chebyshev band stop filter on Silicon substrate at 10 GHz (a) top metal layer mask, (b) bottom cavity layer mask. (Scale corresponds to 1λ = 1 μm).
CHAPTER 6: FABRICATION PROCESS
145
6.2 TYPES OF ETCHING TECHNIQUES
In this section we describe about types of etching technique to obtain cavity.
There are two types of etching process:
1) WET ETCHING 2) DRY ETCHING
Wet etching was the technique we used in our work to fabricate filter
coupled with CPW.
Wet etching is the removal of material by immersing the wafer in a
liquid bath of the chemical etchant. Wet etchants fall into two broad
categories; isotropic etchants and anisotropic etchants.
♦ Isotropic etchants: These etchants attacks the material being etched
at the same rate in all directions. Figure 6.3 presents isotropic etching.
These etchant are available for oxide, nitride, aluminum, polysilicon,
gold, and silicon. Since isotropic etchants attack the material at the
same rate in all directions, they remove material horizontally under the
etch mask (undercutting) at the same rate as they etch through the
material.
Figure 6.3: Isotropic Etching
CHAPTER 6: FABRICATION PROCESS
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♦ Anisotropic etchants: These etchants attack the silicon wafer at
different rates in different directions, and so there is more control of the
shapes produced.
Some etchants attack silicon at different rates depending on the
concentration of the impurities in the silicon (concentration dependent
etching). Anisotropic etchants are available which etch different crystal planes
in silicon at different rates. The most popular anisotropic etchant is
potassium hydroxide (KOH) [2].
The simplest structures that can be formed using KOH to etch a silicon wafer
with the most common crystal orientation <100> are shown in figure 6.4.
These are V shaped groves, or pits with right angled corners and sloping side
walls. Using wafers with different crystal orientations can produce grooves or
pits with vertical walls.
Both oxide and nitride etch slowly in KOH. Oxide can be used as an etch
mask for short periods in the KOH etch bath (i.e. for shallow grooves), for
long periods, nitride is a better etch mask as it etches more slowly in the
KOH.
Figure 6.4: Grooving by KOH etchant.
CHAPTER 6: FABRICATION PROCESS
147
Dry etching is also known as ion etching .The most common
micromachining applications is reactive ion etching (RIE). Ions are
accelerated towards the material to be etched, and the etching
reaction is enhanced in the direction of travel of the ion. RIE is an
anisotropic etching technique. Deep trenches and pits (up to ten or a
few tens of microns) of arbitrary shape and with vertical walls can be
etched in a variety of materials including silicon, oxide and nitride. The
etching rate is lower than wet etching rate. Dry etching is recognized
as practical alternative to wet etching.
For the proper flow of aluminum through cavities, it is necessary to have
smooth slope at the edges. Hence, wet etching process was selected for this
work.
The following section (6.3) presents the mathematical calculation that was
used to obtain the base of pyramidal cavity structure with respect to the upper
dimension of cavity and thickness of substrate [2] (Figure 6.5).
6.2.1 CAVITY DIMENSION
Figure 6.5 shows the shape of a cavity etched in Silicon using wet etching
process to obtain the base dimension (X) of pyramidal cavity with respect to
the dimension of top layer cavity and thickness of substrate, equation (6-1) is
used [2].
yhx +×⎟⎠⎞
⎜⎝⎛
×= 2
7.54tan (6-1)
Where, h = Thickness of substrate (μm)
x = Length of the edge.
CHAPTER 6: FABRICATION PROCESS
148
y = Upper dimension of pyramid
Values used to obtain via hole was, y = 500 μm, from equation (6-1) the
dimension obtained for the base (x) of pyramidal cavity was 1066 x 1066 μm
(a) top view of via (b) Cross- section view of wafer to calculation of dimensions for via
Figure 6.5: Dimensions obtained for base of pyramidal via.
6.3 FABRICATION PROCESS
In this section, we describe the complete lithographic process using
micromaching technique with the help of two experiments done to machine
via holes to ground of our CPW (Figure 6.5). Figure 6.6 shows the structure
used for Experiment-I and Figure 6.7 structure was used for Experiment-II.
CHAPTER 6: FABRICATION PROCESS
149
Figure 6.6: Experiment-I SiO2 as protective layer on silicon.
Figure 6.7: Experiment-II SiO2 and Silicon Nitride (Si3N4) as protective layer on silicon.
N-type high resistivity silicon (HR-Si) as substrate reduces the DC leakage
current between the signal and ground conductors of CPWs, and for
minimizing the attenuation loss [3].
The characteristics of the substrate used to fabricate our device are:
Substrate type = N type Silicon (HR-Si)
Resistivity = greater than 2000 Ω-cm
CHAPTER 6: FABRICATION PROCESS
150
Thickness = µm 15400 ±
Orientation = <100>
The thickness for conductors (aluminum) proposed for our work is 2 µm.
6.3.1 EXPERIMENT- I: LITHOGRAPHIC PROCESS USING SiO2 LAYER
ON SILICON AS SUPPORTIVE LAYER.
In this section, the experimental steps of fabrication process to via through a
substrate of thickness 400 µm are described.
STEP 1 : CLEANING PROCESS OF WAFER
Contaminants present on the surface of silicon wafers at the start of
processing, or accumulated during processing, have to be removed at
specific processing steps in order to obtain high performance and high
reliability semiconductor devices, and to prevent contamination of process
equipment, especially the high temperature oxidation, diffusion, and
deposition tubes. The RCA (Radio Corporation of America) is the industry
standard cleaning process for removing contaminants from wafers.
The RCA cleaning procedure has three major steps used sequentially:
I. RCA-I (Organic Clean): Removal of insoluble organic
contaminants with a ration of 5:1:1 (H2O: H2O2: NH4OH)
solution.
II. RCA-II (Oxide Strip): Removal of a thin silicon dioxide layer
where metallic contaminants may accumulated as a result of
RCA-I, using a (diluted H2 O: HF) solution.
CHAPTER 6: FABRICATION PROCESS
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III. RCA-III (Ionic Clean): Removal of ionic and heavy metal
atomic contaminants using a solution of ratio 6:1:1 ( H2O: H2O2:
HCl).
In this step of cleaning of wafer we followed only two steps of RCA (I and
II).
STEP 2 : OXIDATION PROCESS
SiO2 on wafer was used as a protective layer on both sides of wafer as shown
in Figure (6.8a). The deposition of silicon oxide was done under following
conditions:
Technique = Thermal oxidation
Thickness of SiO2 = 1.5 µm (measured)
Temperature = 1200oC
Total time = 4 ½ hrs.
Thermal oxidation is a way to produce a thin layer of oxide (usually silicon
dioxide) on the surface of a wafer (semiconductor). The technique forces an
oxidizing agent to diffuse into the wafer at high temperature and react with it.
Thermal oxidation of silicon is usually performed at a temperature between
800 and 1200 oC. It may use either water vapor (steam) or molecular oxygen
as the oxidant. The reaction is:
22 SiOOSi →+
The expected thickness of SiO2 was 1.5 μm and the measured thickness was
1.5 μm, measured by the use of an alpha-stepper.
CHAPTER 6: FABRICATION PROCESS
152
STEP 3 : PHOTOLITHOGRAPHY PROCESS
Photolithography is a process used in microfabrication to selectively remove
parts of a thin film (or the bulk of substrate). It uses light to transfer a
geometric pattern from a photomask to a light-sensitive chemical (photoresist)
on the substrate. A series of chemical treatments then engraves the exposure
pattern into the material underneath the photoresist. This process is used
because it affords exact control over the shape and size of the objects it
creates, and because it can create patterns over an entire surface
simultaneously. Its disadvantages are that it requires a flat substrate to start
with, it is not very effective at creating shapes that are not flat, and it can
require extremely clean operating conditions
In this step, the wafer was coated on both sides with a photoresistive polymer
which is sensitive to ultra-violet (UV) light called as photoresist.
The wafer is covered with photoresist (“PR”) by spin coating. A viscous, liquid
solution of photoresist is dispensed onto the wafer, and the wafer is spun
rapidly to produce a uniformly thick layer. The spin coating typically runs at 20
to 80 Hz for 30 to 60 seconds, and produces a layer between 2.5 and 0.5 μm
thick. The photoresist- coated wafer is then “soft baked” or “prebaked” to drive
off excess solvent, typically at 60 to 100 oC for 5 to 30 minutes.
This process shown in Figure (6.8b) was done under following specific
conditions:
Type of photoresist = photoresist (+)
Spinning Rotation = 3000 rpm for 30 sec.
Temperature = 85 oC for 17 mints.
CHAPTER 6: FABRICATION PROCESS
153
Positive Photoresist, the most common type, becomes less chemically robust
when exposed; negative photoresist becomes more robust. This chemical
change allows some of the photoresist to be removed by a special solution,
called "developer" by analogy with photographic developer. A post-exposure
bake is performed before developing, typically to help reduce standing wave
phenomena caused by the destructive and constructive interference patterns
of the incident light [5].
STEP 4: EXPOSURE AND DEVELOPING
After prebaking, the photoresist is exposed to a pattern of intense light (UV)
shown in Figure 6.8 (c). Ultraviolet light was then passed through the mask
onto the photoresist for 9 seconds.
The resulting wafer is then “hard baked”, typically at 120 to 180 oC for 20 to
30 minutes. The hard bake solidifies the remaining photoresist, to make a
more durable protecting layer in future ion implantation, wet chemical etching.
STEP 5 : PHOTORESIST DEVELOPING PROCESS
In the etching step, a liquid ("wet") chemical agent removes the uppermost
layer of the wafer in areas that are not protected by photoresist shown in
Figure 6.8(d).
Semiconductor fabrication prefers dry etchants, because they do not undercut
the photoresist as much. However, this same property makes wet etchants
indispensable for microelectromechanical systems; where suspended
structures must be "released" from the underlying layer by a strongly
undercutting etch.
CHAPTER 6: FABRICATION PROCESS
154
STEP 6: PHOTORESIST REMOVAL
After a photoresist is no longer needed, it must be removed from the
substrate. This usually requires a liquid “resist stripper”, which chemically
alters the resist so that it no longer adheres to the substrate.
STEP 7 : SiO2 ETCHING PROCESS
In this process Silicon oxide was etched with respect to the pattern on the
photoresist positive layer. An etching solution was used to remove the oxide
where it was exposed through the openings in the photoresist and obtain
structure as shown in Figure 6.8 (e1), Figure 6.8(e2). Specifications of this
step are:
Etching Solution= H2O + NH4F + HF (7:1)
Chemical etching duration =3mint
Boiler Temperature =32 oC
After this step, the wafer was ready for complete etching of silicon completely
to obtain via holes to ground.
STEP 8 : Si ETCHING PROCESS
In this step the silicon was completely etched to obtain the via holes of CPW
using wet etching technique under following specific conditions:
Wet Etching Solution= KOH
Etching duration =10 -30 mints.
Boiler Temperature =80 oC
CHAPTER 6: FABRICATION PROCESS
155
The wet etching process was done from bottom side toward the top side; this
step was repeated until the silicon gets completely etched. This process goes
for 24 hours as a resulting in the structure as shown in Figures 6.8(f1), Figure
6.8(f2).
STEP 9 : METALLIZATION PROCESS
Deposition of aluminum metal was done by evaporation technique in which
the vapor source is heated; the vapor pressure of the evaporant (metal to be
evaporated) becomes substantial. Hence, atoms are sent out into the vacuum
chamber, some of which reach the substrate to form a metal film. This step
was done under following conditions:
Technique= Evaporation Technique
Thickness = 2µm both sides of wafer
Time taken for deposition of Al = 2 hrs
The ideal case of this process is shown in figure 6.8(g); the flow of metal was
done from bottom side of wafer toward the top side to make proper flow of
aluminum. The thickness of aluminum was measured to be 2 µm with the
help of alpha stepper which is similar to the expected thickness.
STEP 10 : LITHOGRAPHY, MASKING, PHOTORESIST
DEVELOPING AND REMOVAL OF PHOTORESIST PROCESS
These processes and condition are exactly similar from step 3 till step 6. The
photoresist process under metallization is shown in Figure 6.8(h). The
masking process is shown in Figure (6.8i) and photoresist developing process
is shown in Figure 6.8(j).
CHAPTER 6: FABRICATION PROCESS
156
STEP 11 : METAL ETCHING OF ALUMINUM
The aluminum metal was etched by the use of Al etch (phosphoric acid,
acetic acid, nitric acid) solution. Figure (6.8k) shows the metal etching
process and Figure (6.8l) corresponds to the finally fabricated device.
Table-6.1 shows the dimensions of cavity proposed and measured after
fabrication. As it can be seen, the final dimension is very close to the desired
ones.
Structure Thickness of metal (µm)
Base of pyramidal cavity (µm)
Top of pyramidal cavity (µm)
CAVITY IN CPW 2 1066 x 1066 500 x 500 Proposed Dimensions
2 1050 x 1050 550 x 550 Dimensions measured after
fabrication
Table- 6.1: Results of measurement of dimension of cavity in CPW on HR-Si using experiment – I
(a) OXIDATION PROCESS
(b) PHOTORESIST (+) PROCESS
CHAPTER 6: FABRICATION PROCESS
157
(c) MASKING PROCESS
(d) DEVELOPING PROCESS
(e1) SiO2 ETCHING PROCESS
(f1) SILICON ETCHING PROCESS
(e2) : SiO2 ETCHING
( f2) : SILICON ETCHED WAFER
CHAPTER 6: FABRICATION PROCESS
158
(g) METALLIZATION PROCESS
(h) PHOTORESIS (+) PROCESS
(i) MASKING PROCESS
(j) DEVELOPING PROCESS
CHAPTER 6: FABRICATION PROCESS
159
(k) METAL ETCHING PROCESS
(l) FINAL DEVICE
Figure 6.8: STEPS OF FABRICATION PROCESS FOR EXPERIMENT- I
6.3.2 EXPERIMENT-II: LITHOGRAPHIC PROCESS USING SiO2,
SILICON NITRIDE (SiH4+NH3) ON SILICON AS SUPPORTIVE
SUBSTRATE.
In this experiment we followed similar lithographic process steps as
mentioned in experiment-I. To protect the silicon surface, silicon nitride over
SiO2 layer was used which results in reducing silicon etching time. In the
pervious experiment we obtained irregular, rough surface and the flow of
aluminum was not fine through the whole cavity due to lengthy Silicon etching
process of. To improve these effects experiments-II was performed.
STEP 1 : OXIDATION PROCESS
The procedure of this step is exactly similar to the step2 of experiment-1
under following conditions [refer Figure 6.9(a)].
Deposition technique = Thermal oxidation
CHAPTER 6: FABRICATION PROCESS
160
Thickness of SiO2 = 0.2 μm
Temperature = 1200oC
Time = 20 mints.
STEP 2 : DEPOSITION OF SILICON NITRIDE
Deposition of silicon nitride over silicon oxide was done to act as extra
protective layer for silicon surface under following conditions [refer Figure
6.9(b)]:
Technique = Low Pressure Chemical Vapor Deposition (LPCVD)
Thickness of Si3N4 = 0.66 μm
Temperature = 755 oC
Pressure applied = 2.332 torrs
Time = 27 mints.
STEP 3 : PHOTOLITHOGRAPHY AND MASKING PROCESS
The lithographic process is similar to step 3 till step 4 of experiment-I with
similar conditions [refer Figures 6.9 (c), Figures 6.9 (d)].
STEP 4 : DEVELOPING AND PHOTORESIS REMOVAL
PROCESS
This process is similar to step 5 and step 6mentioned in experiment-I with
similar conditions of temperature and time [refer Figure (6.9e)].
CHAPTER 6: FABRICATION PROCESS
161
STEP 5 : SILICON NITRIDE ETCHING PROCESS
In this step removal of silicon nitride was done using Reactive ion etching
(RIE) etching technique. In RIE, Ions are accelerated towards the material to
be etched, and the etching reaction is enhanced in the direction of travel of
the ion. RIE is an anisotropic etching technique. Deep trenches and pits (up
to ten or a few tens of microns) of arbitrary shape and with vertical walls can
be etched in a variety of materials including silicon, oxide and nitride. The
etching rate is lower than the wet etching rate.
Specific conditions for RIE process [refer Figure 6.9(f)] are:
Etching technique = RIE
Power applied = 200 Watts
Pressure applied = 300 m torrs
Gases passed = CF4 & Freon
Time = 5 mints.
STEP 6 : SILICON OXIDE ETCHING PROCESS
This process is exactly similar to step 7 of experiment-I [refer Figure 6.9(g)]
under following conditions:
Etching solution = HF+H2O+NH4F
Temperature = 32 oC
Time = 3 mints.
CHAPTER 6: FABRICATION PROCESS
162
STEP 7 : WET ETCHING FOR SILICON ETCHING PROCESS
In this process, similar etching technique was used as mentioned in step 8 of
experiment-I with following etchant and conditions:
Etching agent = KOH
Temperature = 80 oC
Total time for process = 4 hrs
This step was repeated until silicon was completely etched [refer Figure
6.8(f)].
STEP 8: METELLIZATION AND METAL ETCHING PROCESS
Metallization process and metal etching was done in experiment-II following
similar steps and condition from (step 9) till (step 11) of experiment-I, [see
Figures 6.9 (g) till 6.9(l)].
Table-6.2, present the measurement of the dimensions of proposed cavity
and measured dimensions after fabrication. As it can be seen, the final
dimensions are very similar to the theoretical ones.
Structure Thickness of metal (µm)
Base of pyramidal cavity (µm)
Top of pyramidal cavity (µm)
Cavity in CPW 2 1066 x 1066 500 x 500 Proposed
dimensions
2 1050 x 1050 550 x 550
Dimensions
after
measured
fabrication
Table-6.2: Measured and proposed dimensions of cavity using experiment-II
CHAPTER 6: FABRICATION PROCESS
163
CHAPTER 6: FABRICATION PROCESS
164
Figure 6.9: FABRICATION PROCESS OF EXPERIMENT- II
Figure 6.10, shows photos obtained from Scanning electronic microscope
(SEM) viewing the edges and slope obtained after wet etching of silicon and
the flow of aluminum through cavity and on the surface.
Figure 6.10 :(a) SEM microscope and display
Figure 6.10 :(b) View of Coplanar waveguide with cavity in SEM
CHAPTER 6: FABRICATION PROCESS
165
Figure 6.10: ( c) View of cavity edge
Figure 6.10 : (d) View of flow of Aluminum at the edges and on surface
Figure 6.10 Photos from SEM (a) SEM and display of device , (b) View of Coplanar waveguide with cavity in SEM, ( c) View of cavity edge, (d) View of flow of Aluminum at the edges and on surface.
CONCLUSION
Two different experiments to fabricate resonator and Chebyshev filter at
10 GHz using bulk micromachining technique to obtain cavities for CPW have
been described in this chapter. Very rough and irregular surface of Silicon
was obtained with first experiments due to longer process of etching SiO2 and
Silicon which result in imperfect flow of Aluminum through cavities which lead
to poor continuity between upper and bottom layer of Aluminum, which
effected experimental results.
To improve surface of silicon after etching process we introduced Silicon
nitride layer over SiO2 as protective layer in experiment-II. In this experiment
all the fabrication procedures were similar to the ones as followed in
experiment-I. Etching of Silicon Nitride was performed with a RIE process.
CHAPTER 6: FABRICATION PROCESS
166
Here it was observed that, a smoother surface of Si was obtained as compare
to experiment –I. Also the process of etching of silicon oxide, silicon nitride
and silicon takes less time as compare to the experiments -I process.
REFERENCES
[1] “L-Edit version 12.2 user guide”.
[2] Danny Banks “Introduction to Microengineering MEMS Micromachines
MST”, © D Banks 1999. All rights reserved.ueng@dbanks.demon.co.uk
5 June 1999.
[3] J.A.Reynoso-Hernández, Raúl Rancel-Rojo, M.Aceves, I. Zaldivar,
L.E. Sánchez, and M.Herrera “ Influence of the SRO as passivation
Layer on the Microwave attenuation Losses of the CPWs Fabricated
on HR-Si”, IEEE microwave and wireless components letter
,Vol.13,No.12,Dec.2003.
[4] http://en.wikipedia.org/wiki/Thermal_oxidation.
[5] http://en.wikipedia.org/wiki/Photolithography
CHAPTER 7: EXPERIMENTAL RESULTS
167
INTRODUCTION
In this chapter the experimental results are presented. The comparisons of
experimental and simulated results are done to know the performance of
proposed filters.
This chapter is divided into three subsections; first section 7.1 describes the
experimental results of Chebyshev bandstop filters at 1.5 GHz, second
section 7.2, presents the experimental results of Triple bandstop filter with an
extra transmission zero, and the last section 7.3, and shows the experimental
results obtained for patch resonator on silicon substrate at 10 GHz.
7.1 EXPERIMENTAL RESULTS OF CHEBYSHEV BANDSTOP
FILTERS AT 1.5 GHz
In this thesis work two different structure of Chebyshev bandstop filter have
been proposed at 1.5GHz. In this section the experimental results obtain by
Chebyshev bandstop filters are presented. Experimental and simulated
results have been compared throughout to know the actual performance and
effect of the proposed device.
CHAPTER 7: EXPERIMENTAL RESULTS
168
7.1.1 3 POLE CHEBYSHEV BANDSTOP FILTER AT 1.5GHZ
USING T-SHAPE STRAIGHT RESONATORS ON
DUROID SUBSTRATE
3-pole Chebyshev bandstop filter using T-shape straight resonators response
was tested using a Vector Network Analyzer Antrisu (model 360B Network
Analyzer), with VF 1M-KM S/N 3113 cables (coaxial). The measurement set
up for testing is shown in Figure 7.1(a). The testing device, 3-pole Chebyshev
bandstop filter using T-shape interdigital resonators is shown in Figure 7.1(b).
Figure 7.1 (a) VNA (model 360B Network Analyzer) and cables are VF 1M-KM S/N 3113
CHAPTER 7: EXPERIMENTAL RESULTS
169
(b)
Figure 7.1: (a) shows the set up to measure this filter with the help of VNA, (b) the device for test. Figure 7.2, shows the experimental results of the filter. Figure 7.2(a), presents
the experimental S11 and S12 response of filter before tuning. The center
frequency was measured was 1.414 GHz. The insertion loss was about
-53dB and the return losses was -2.3dB throughout the band. The bandwidth
measured was 10%. Figure 7.2(b), shows the S11 experimental and simulated
response of the filter after tuning and Figure 7.2(c), illustrate S12 experimental
and simulated response after tuning. With simulation the central frequency
was 1.496GHz and bandwidth obtained was 9.9%.The insertion losses
obtained with simulation was -30.3dB. The return losses of simulated result
were -2.4dB. The tuning was performed to the filter by inserting small
substrate bits of duroid on the filter. After tuning, the central frequency was
1.38GHz and bandwidth was 11%. The insertion loss was improved by -22dB
and the return loss lower than 1dB. The over all frequency shift obtained was
CHAPTER 7: EXPERIMENTAL RESULTS
170
0.1GHz. The simulated and experimental results show overall good
agreement.
1.0 1.1 1.2 1.3 1.4 1.5 1.6-60
-55
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
Mag
nitu
de (d
B)
Frequency (GHz)
S11_m easured S12_m easured
EXPERIMENTAL RESULT BEFORE TUNING
BW = 0.16GHzfo=1.41 GHz
Figure 7.2 (a) The response of filter without tuning obtained bandwidth 10%
CHAPTER 7: EXPERIMENTAL RESULTS
171
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7-35
-30
-25
-20
-15
-10
-5
0
Mag
nitu
de(d
B)
Frequency(GHz)
S11_experimental S11_simulated
Figure 7.2 (b) S11 simulated and experimental results after tuning.
CHAPTER 7: EXPERIMENTAL RESULTS
172
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
-35
-30
-25
-20
-15
-10
-5
0
Mag
nitu
de(d
B)
Frequency(GHz)
S12_experimental S12_simulated
Δf
(c) S12 simulated and experimental results after tuning
Figure 7.2: Results of 3 pole Chebyshev bandstop filter using T-shape straight resonators, (a) The response of filter without tuning, (b) S11 simulation and electrical response after tuning, (c) S12 simulation and electrical response after tuning.
CHAPTER 7: EXPERIMENTAL RESULTS
173
7.1.2 3 POLE CHEBYSHEV BANDSTOP FILTER USING
ULTRA COMPACT MEANDERED RESONATORS AT
1.5GHz
Figure 7.3(a), shows the photo of Chebyshev bandstop filter using ultra
compact meandered resonators. Figure 7.3 (b), presents the response of filter
before tuning. The center frequency was measured to 1.424GHz. The
insertion losses were about -15.7dB and the return loss was -2.4dB
throughout the band. The bandwidth measured experimentally was 10%.
Figure 7.3 (c), shows the S11 experimental and simulated response of the
filter after tuning and Figure 7.3 (d), illustrate S12 experimental and simulated
response after tuning. With simulation the central frequency was 1.506GHz
and bandwidth obtained was 8.6%.The insertion loss obtained with simulated
response was -23.5dB. The return loss of simulated result was -2.7dB. The
tuning was performed to the filter response by inserting small substrate bits of
duroid on the filter. After tuning, the central frequency was 1.417GHz and
bandwidth was 9.8%.The insertion loss was improved by -25.2dB and the
return loss was -3dB. The overall frequency shift obtained was 0.09GHz. The
simulated and experimental results show overall good agreement.
CHAPTER 7: EXPERIMENTAL RESULTS
174
Figure 7.3 (a) The 3 pole Chebyshev bandstop filter using ultra compact T-shape
meandered resonator
CHAPTER 7: EXPERIMENTAL RESULTS
175
1.0 1.1 1.2 1.3 1.4 1.5 1.6-30
-25
-20
-15
-10
-5
0
EXPERIMENTAL RESULT WITHOUT TUNING
Mag
nitu
de (d
B)
Frequency (GHz)
S11_measured S12_measured
fo =1.428 GHz
BW=10%
Figure 7.3 (b) Experimental response of filter without tuning
CHAPTER 7: EXPERIMENTAL RESULTS
176
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7-30
-25
-20
-15
-10
-5
0
Mag
nitu
de (d
B)
Frequency (GHz)
S11_experimental S11_simulated
S11 SIMULATION AND EXPERIMENTAL RESULTS AFTER TUNING
Return loss_experimental=-2.7dBReturn loss_simulated ==2.7dB
Figure 7.3 (c) S11 simulation and experimental results of filter after tuning.
CHAPTER 7: EXPERIMENTAL RESULTS
177
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
-25
-20
-15
-10
-5
0
Mag
nitu
de (d
B)
Frequency (GHz)
S12_experimental S12_simulation
fo_experimental =1.417GHzfo_simulation=1.506GhzBW 3db_experimental=9.8%Bw3db_simulation=8.6%
S12 SIMULATION AND EXPERIMENTAL RESULTS AFTER TUNING
(d) S12 simulation and experimental results of filter after tuning
Figure 7.3: Results of 3 pole Chebyshev bandstop filter using interdigital T-shape
meandered resonators, (a) The response of filter without tuning, (b) S11 simulation and electrical response after tuning, (c) S12 simulation and electrical response after tuning.
CHAPTER 7: EXPERIMENTAL RESULTS
178
7.2 TRIPSECTION BANDSTOP FILTER WITH AN EXTRA
TRANSMISSION ZERO USING ULTRA COMPACT
INTERDIGITAL MEANDERED RESONATORS AT 1.5GHz
The set up to test this filter is similar to the one presented in Figure 7.1.
Figure 7.4, shows the experimental results of the filter. Figure 7.4(a), presents
the photo of Triplet bandstop filter using ultra compact interdigital meandered
resonators. Figure 7.4(b), presents the response of filter before tuning. The
center frequency measured was 1.406 GHz. The insertion losses at the
center frequency were about -18.1dB and the return loss was –2.6dB
throughout the band. The bandwidth obtained was 4%. Figure 7.4(c), shows
the S11 experimental and simulated response of the filter after tuning and
Figure 7.4(d), illustrate S12 experimental and simulated response after tuning.
With simulation the central frequency was 1.505 GHz and bandwidth obtained
was 3.3%.The insertion loss obtained with simulated response was -15.7dB.
The return loss of simulated result was -0.95dB. The tuning was performed to
the filter response by inserting small substrate bits of duroid on the filter. After
tuning, the central frequency was 1.403GHz and bandwidth was 4.5%. The
insertion loss was improved by –16.4dB and the return loss was -2.7dB.
Successfully obtained transmission zero towards lower frequency with
experimental response. Overall, simulation and experimental results was a
good agreement.
CHAPTER 7: EXPERIMENTAL RESULTS
179
Figure 7.4: (a) Trisection bandstop filter with an extra transmission zero using ultra compact interdigital meandered resonators to test.
CHAPTER 7: EXPERIMENTAL RESULTS
180
1.3 1.4 1.5 1.6
-25
-20
-15
-10
-5
0
f0=1.46GHzBW =4%
EXPERIMENTAL RESULTS OF TRIPLE BANDSTOP FILTER WITHOUT TUNING
Mag
nitu
de (d
B)
Frequency (GHz)
S11_measured S12_measured
fo
Figure 7.4: (b) The experimental response of Trisection bandstop filter without tuning.
CHAPTER 7: EXPERIMENTAL RESULTS
181
1.35 1.40 1.45 1.50 1.55 1.60-35
-30
-25
-20
-15
-10
-5
0
Mag
nitu
de (d
B)
Frequency (GHz)
S11_simulated S11_experimental
Figure 7.4: (c) S11 simulation and experimental results of filter after tuning
CHAPTER 7: EXPERIMENTAL RESULTS
182
1.35 1.40 1.45 1.50 1.55 1.60
-30
-25
-20
-15
-10
-5
0
Mag
nitu
de (d
B)
Frequency(GHz)
S12_simulated S12_experimental
Δf = 0.1GHz
(d): S12 simulation and experimental results of filter after tuning
Figure 7.4: Results of Trisection bandstop filter using ultra compact T-shape
meandered resonators, (a) photograph of device to be test ,(b) The response of filter without tuning, (c) S11 simulation and electrical response after tuning, (d) S12 simulation and electrical response after tuning.
CHAPTER 7: EXPERIMENTAL RESULTS
183
7.3 INTERDIGITAL T- SHAPE PATCH RESONATOR ON SILICON SUBSTRATE AT 10GHZ
The set up to test this resonator at 10GHz is shown in Figure 7.5, where input
and output ports of the device is coplanar waveguide. One end of the probe is
connected to the coplanar and other to the VNA.
Figure 7.6, shows the experimental and simulated result for the weakly
coupled resonator. The experimental Q value was 26 whereas the simulated
Q value was 40.
For the simulation the following parameters were used:
Metal: Aluminum
Thickness: 2 μm
Tan δ: 0.01
Conductivity of HR-Si: 0.05 (S/cm)
Metal Conductivity: 0.13440(Ω/sq)
Figure 7.5: The set up to test resonator at 10GHz.on silicon substrate.
CHAPTER 7: EXPERIMENTAL RESULTS
184
The difference in Q value from the experimental (26) to the simulation (40) is
small. This small difference is thought to be due to surface roughness,
manufacturing tolerance and em radiation not considered in the simulation.
Factors which affects the experimental results:
Some of them are:
1) Rough surface of substrate due to not proper fabrication process due
to long process of etching for larger size via holes in CPW connected
to resonator at both ends.
2) The resistivity of the substrate was not according to the simulation
values used.
3) There are radiation losses due to higher frequency.
4) Non uniform distribution of metal on the surface of silicon.
The central frequency obtained from experimental result was 9.9GHz and
with simulation it was 10.2GHz. There was a frequency shift of 0.3GHz. For
comparison purposes both the experimental and simulated graphs were
shifted to same frequency (Figure 7.6).
CHAPTER 7: EXPERIMENTAL RESULTS
185
9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4
-32
-30
-28
-26
-24
-22
-20
Δ f
Mag
nitu
de (d
B)
Frequency (GHz)
S12_simulated S12_experimental
Δ f = 0.3GHzfo_simulated=10.2GHzfo_experimental =9.9GHz
EXPERIMENTAL AND SIMULATION RESPONSE OF PATCH RESONATOR AT 10GHz
Figure 7.6: S12 experimental and simulation results of patch resonator on HR-Si
substrate using Aluminum at 10GHz.
CHAPTER 8: CONCLUSION AND FURURE WORK
186
8.1 CONCLUSION
In this thesis work novel compact bandstop filters topologies at L and X band
have been presented. Full design procedure along with simulation and
experimental results with fabrication methods were described. All the filters
find applications in satellite communications, mobile communications and
radioastronomy.
At 1.5GHz two novel resonators have been proposed on duroid substrate of
relative permittivity (10.8) and thickness 0.64mm using copper as conductor
of thickness 0.017mm (chapter 4). The first one is conventional λ/2 resonator;
with simulated Q-value were 108. The length of this resonator was 37mm and
0.6mm width. Second resonator is T-shape straight resonator, which is
27.6mm in length. This reduction of size by the addition of extra capacitance
to ground. The simulated Q-value obtained from this resonator was 107. The
third resonator proposed at 1.5 GHz is an ultra compact meandered
resonator. This resonator is three times smaller that conventional
CHAPTER 8: CONCLUSION AND FURURE WORK
187
λ/2 resonator; its length is 12.4mm. The Q value of this resonator is 100,
which is very close to the Q value of the conventional resonator.
Using these latter two resonators at 1.5GHz, a Chebyshev bandstop filter with
3 poles has been designed (chapter 4). The total length of this filter is 41mm
x 38.6mm (4.1cm x 2.9cm). The bandwidth obtained by simulation was 9.9%
with central frequency 1.495GHz. The experimental response after tuning
filter gives a bandwidth of 11% with central frequency 1.38GHz. The
frequency shift between simulations and experiment was only 0.1GHz which
is thought to be due to manufacturing tolerances. Overall, the simulation and
experimental results were very similar.
A second Chebyshev bandstop filter with 3 pole has been designed using
meandered resonators of length 12.4mm x 10.6mm (chapter 4). The total
length of this filter is 39.2mm x 13mm. The bandwidth obtained by simulation
was 8.6% with central frequency 1.506GHz and return loss -2.6dB at the
centre frequency. The bandwidth obtained with experimental result was 9.8%
with central frequency 1.417GHz with return loss -3dB at the centre
frequency. The frequency shift was 0.09GHz. With these results it can be said
that there is good agreement between simulated and experimental results.
At 1.5 GHz, a Novel Trisection bandstop filter with 4.5% bandwidth has been
shown using T-shape meandered resonator of (12.4mm x 10.6mm)
(chapter 5). The total size of Trisection bandstop filter is 72mm x 34mm
(7.2cm x 3.4cm). For this Trisection bandstop filter, as extra cross coupling
between the first and the third resonator is included, this gives the needed
transmission zero of the response. In the experimental results, the
transmission zero of the characteristic triplet response is clearly seen. The
CHAPTER 8: CONCLUSION AND FURURE WORK
188
bandwidth obtained by simulation was 3.3% and central frequency 1.505
GHz. The experimental results gave bandwidth of 4.5% with central frequency
of 1.403GHz and the return loss was -2.7 at central frequency. The frequency
shift obtained between simulation and experiment was 0.1 GHz. Also, good
agreement was found between simulation and experimental results.
Finally, at 10GHz three compact resonators on HR-Si substrate have been
proposed (chapter 4). The thickness of the substrate is 400µm with resistivity
2000 Ωcm. A 2 µm aluminum layer was taken as conductor. The first
resonator at 10GHz adds a capacitive patch (1.8mm x 1.7mm) to a
conventional λ/2 resonator, achieving size miniaturization. The length of the
strip is 2.6mm and its width is 0.4mm. With simulation the obtained unloaded
Q-value was 40 at a central frequency of 10.2 GHz. The experimental results
of this resonator gave a Q value of 26 with central frequency of 9.9 GHz. The
small difference between the measured and simulated values is thought to be
due to conductor roughness plus the radiation losses not taken into account
in simulator.
At 10GHz, two patch resonators with selective removal of substrate to
increase Q value have been proposed and it has been proven that by
removing selective parts of the silicon using micromaching techniques higher
Q values are achieved. The Q value obtained with patch resonator having air
window beneath the patch is 114 (using Aluminum as conductor). The Q
value, obtained with second proposed micromachined patch resonator with
air window beneath the strip was 171 when Aluminum was used as
conductor. The Q value increased from 40 (patch resonator on silicon
substrate) to 114 and 171 with resonator with selective removal of substrate.
It was also proven that if silver was used as conductor, the Q values would
CHAPTER 8: CONCLUSION AND FURURE WORK
189
improve to 117 (Si removed underneath the patch) and 229 (Si removal
underneath the strip).
At 10GHz, Chebyshev band stop filter using patch resonators on silicon
substrate was designed (chapter 4). With simulation response the bandwidth
obtained was 9% and insertion losses -15dB dB and return losses through
out band was -1.5 dB.
8.2 FUTURE WORK Firstly, the fabrication of Chebyshev bandstop filter using patch resonator at
10GHz on HR-Si is proposed.
Secondly, the fabrication of patch resonators at 10GHz with improved Q by
removal of selective part of the substrate using micromaching is left as future
work. The fabrication procedure is described in Appendix-I.
Thirdly, the fabrication of Chebyshev bandstop filter (chapter 4) on Silicon
substrate at 10GHz using fabrication steps presented in chapter 6 is
proposed.
Fourthly, the designing and fabrication of Chebyshev bandstop and Triplet
filters with improved Q by selective removal of substrate is proposed for future
work.
APPENDIX-I
190
PROPOSED FABRICATION PROCESS TO OBTAIN AIR WINDOW
BENEATH PATCH AND STRIP OF THE RESONATOR AT 10GHZ FOR
FUTURE WORK
Fabrication of pact resonator on HR-Si with selective removal of substrate
follows similar lithographic process till masking step as mentioned in
chapter 6.
For the step to obtain via holes and completely removal of selective part of
silicon substrate, use SiO2 and Nitro as a protective layer on silicon and KOH
as the etching agent to achieve smooth surface and less time of etching
silicon. For this follow similar steps of the fabrication till Silicon etching as
presented in chapter 6. Subsequently, a mask is placed on the air window
section before metallization and then Aluminum metal layers is deposited
from top to bottom, allowing the connection between top metal layer and
bottom metal layer through via shown in Figure-I (a). The mask prevents the
Al to be deposited over the air window. Afterward the resonator / filter
structures are patterned using UV photolithography as shown in Figures-I (b)
and (c). Finally the mask is removed by Lift Off process and additional wafer
with 2 µm aluminum layer could be bonded to the ground plane as shown in
Figure-I(e).
APPENDIX-I
191
(a) Metallization
(c) Developing process
(b) Photoresist (+) and masking
(d) Metal etching process
(e) LIFT OFF process and adding additional wafer with metal both side
Figure-I: Fabrication process for future work.
APPENDIX-II
192
A.1 PHYSICAL CONSTANTS
Speed of light in vacuum
Permittivity of vacuum
Permeability of vacuum
Impedance of free space
Bolzmann´s constant
Charge of electron
Electron rest mass
C = 2.99792458 x 108m/s
εo = 8.85418782 x 10-12 ≈ (1/36π ) x 10-9 F/m
μo = 4π x 10-7 H/m
ηo = 376.7303 ≈ 120 π Ω
k =1.3806 x 10-23 J/K
e = 1.602177 x 10-19 C
m = 9.10938 x 10-31 kg
A.2 CONDUCTIVITY OF METALS AT 25o C (298 K)
MATERIAL
CONDUCTIVITY
σ (S/m)
MATERIAL
CONDUCTIVITY
σ (S/m)
Silver
Copper
Gold
Aluminum
6.18 x 107
5.84 x 107
4.43 x 107
3.69 x 107
Zinc
Nickel
Platinum
Chromium
1.66 x 107
1.40 x 107
0.97 x 107
0.79 x 107
APPENDIX-II
193
A.3 ELECTRICAL RESISTIVITY ρ IN 10-8 Ω m OF METALS*
T/K
ALUMINUM
COPPER
GOLD
SILVER
40
60
100
200
273
300
400
0.0181
0.0959
0.442
1.587
2.417
2.733
3.87
0.0239
0.0971
0.348
1.046
1.543
1.725
2.402
0.141
0.308
0.650
1.462
2.051
2.271
3.107
0.0539
0.162
0.418
1.029
1.467
1.629
2.241
* Conductivity σ= 1/ ρ
A.4 PROPERTIES OF DIELECTRIC SUBSTRATES
MATERIAL
RELATIVE
DIELECTRIC
CONSTANT AT
10GHz
LOSS
TANGENT
AT 10GHz
THERMAL
CONDUCTIVITY
(W/m K)
Aluminum
Fused quartz
Polystyrene
Beryllium oxide
GaAs
Si
RT/duroid 5880
RT/duroid 6002
RT/duroid 6006
RT/duroid 6010
9.7
3.8
2.53
6.6
12.9
11.7
2.20 ± 0.015
2.94 ± 0.04
6.15 ± 0.15
10.8 ± 0.25
0.0002
0.0001
0.00047
0.0001
0.0016
0.005
0.0009
0.0012
0.0019
0.0023
30
1
0.15
250
30
90
0.26
0.44
0.48
0.41
194
Figure 1.1: Electromagnetic Spectrum (Taken from © 2005 SURA www.sura.org
Copyrighted images used with permission. Rev2C
6-June-2005)……………………….…………………………………..………2
Figure 1.2: Voltage and current definition and Equivalent circuit of an element of a
transmission line with a length of Δ z (a) Voltage and current definition,
(b)Lumped element equivalent circuit……………………………….…….5
Figure 1.3: Diagram of transmission line with load showing incident, reflected-
transmitted wave……………...……………………………………..…………8
Figure 1-4: Types of Transmission Lines-……………………….……………………….9
Figure 1-5: (a) the general geometry of a Microstrip line, (b) Electric and magnetic
field lines………………………………………………………............………10
Figure 1-6: (a) Schematic diagram of coplanar waveguide, (b) Field patterns in
coplanar waveguide ……………………………………………...…………..14
Figure 1.7 Signal flow graph in two port network…………………………………….15
Figure 1.8: Vector Network Analyzer Antrisu (model 360B Network Analyzer)……..20
Figure 2.1: LC circuit diagram………………………………………..………………….23
Figure 2.2: Series RLC resonator and its response, (a) Series RLC circuit, (b) the
input impedance magnitude versus frequency………………………….....24
195
Figure 2.3: Parallel RLC resonators and its response, (a) Parallel RLC circuit,
(b) the input impedance magnitude versus frequency…………………….26
Figure 2.4: Transfer characteristic of resonant circuit………………………………….29
Figure 2.5: Butterworth (maximally flat) lowpass response……………………………33
Figure 2.6: Chebyshev lowpass response…………………...………………………….34
Figure 2.7: Elliptic function lowpass response…………………………...……………..35
Figure 2.8: Lowpass prototype filters for all- pole filters with ladder (a) A ladder
network structure, (b) its dual……………………..…………………………37
Figure 2.9: Lowpass prototype to 3 pole bandstop transformation (a) basic element
transformation, (b) a practical bandstop filter based on the
transformation……………………………………………………………..….42
Figure 2.10: (a) Immittance inverter used to convert a shunt capacitance into as
equivalent circuit with series inductance. (b) Immittance inverter used to
convert a series inductance into as equivalent circuit with shunt
capacitance……………………………………………………………………44
Figure 2.11: Immittance inverts comprised of lumped and transmission line
element………………………………………………………………………...45
Figure 3.1: Layout of the 4 pole membrane quasi elliptic filter L1=820, L2=2180,
L3=645, L4=300, L5=675, w=500, G1=15, G2=200, G3=175, G4=625
(Dimensions in microns), taken from [10]……………………………...…..51
196
Figure 3.2: Measured response of the 4 pole membrane quasi elliptic filter,
taken from [9]……………...…………..……………………………………..52
Figure 3.3: Layout of the K-band diplexer, taken from [10]………..…..………………53
Figure 3.4: Response of the K band diplexer, taken from [10]……….……….………54
Figure 3.5: Bandstop filter with shunt-connected L resonators, taken from [11].…..55
Figure 3.6: Bandstop filter with shunt-connected L resonators, taken from [11]…...56
Figure 3.7: Theoretical loss and return loss of degree 5 elliptic-function
L-resonator bandstop filter, taken from [11]……………………………….56
Figure 3.8: Transverse section of the microstrip structure, taken from [12]……....…58
Figure 3.9: Circuit wafer of 29 GHz microstrip resonator in bandstop configuration
(a) Bottom view, (b) Top view, taken from [12]……………………. ….……58
Figure 3.10: Measured S11 of bandstop resonator including effects of transition,
taken from [12]…….…………………………………………………………..59
Figure 3.11: The bandstop filter specification taken from [13]………….……...……..60 Figure 3.12: Measurement of the bandstop filter, taken from [13]………...…………61
Figure 3.13: (a) Coupling structure between the resonator and 50Ω microstrip line
on a 0.508 mm-thick LaAlO3 substrate, (b) Layout of the 7-pole microstrip
HTS bandstop filter on 0.508mm-thick LaAlO3 (44mm×26mm),
taken from[16]……………………..………………………….……………….62
Figure 3.14: Measured (thick solid line S21 (dB); thick dash line S11 (dB)) and
simulated (thin solid line S21 (dB); thin dash line S11 (dB) performance of
the seven-pole HTS microstrip bandstop filter, taken from [16]......……..63
197
Figure 3.15: Complete Band-stop Filter Assembly, taken from [17]….………………64
Figure 3.16: S-parameter plot of B band-stop filter (includes 12 dB LNA gain), taken
from [17]……………………………………..………….……………….…….65
Figure 3.17: S-parameter plot of AMPS-B micro enclosure, take from [17]….…..….65
Figure 4.1: Microstrip resonator λ/2 on Duroid substrate at 1.5GHz…………………72
Figure 4.2: S12 Response of microstrip resonator (λ/2) at 1.5 GHz………………….73
Figure 4.3: Interdigital T-shape straight resonator on Duroid using Copper at
1.5GH………………………………………………………………………......74
Figure 4.4: S12 Response of Interdigital T-shape straight resonator (λ/2) on Duroid
using Copper at 1.5GHz………………….…………………………………..75
Figure 4.5: Proposed novel ultra compact interdigital meandered resonator on Duroid
using Copper at 1.5 GHz……………………………………………………..76
Figure 4.6: S12 response of novel ultra compact interdigital meandered resonator on
Duroid using Copper at 1.5GHz……………………………..………………77
Figure 4.7: Comparison of proposed resonators with respect to size…...……..….…80
Figure 4.8: Three pole Chebyshev bandstop filter T-shape straight resonator on
Duroid at 1.5 GHz using copper………………………………………..……81
Figure 4.9: (a) Structure to obtain x1/ Zo and x3 / Zo value of Normalized reactance
slope parameter in EM simulator by varying Li, (b) Structure to obtain
x2 / Zo value of Normalized reactance slope parameter in EM simulator
by varying Li……………………………………………………………….82
198
Figure 4.10: Illustrate the extracted normalized reactance slope parameter against
variable lengths (Li) of capacitor (a) Normalized reactance slope
parameters obtained by varying (Li) capacitor by for 1st and 3rd
resonators, (b) Normalized reactance slope parameters obtained by
varying (Li) capacitance by for 2nd resonators……………….…………83-84
Figure 4.11: Detail dimension of 3 pole Chebyshev bandstop filter using T-shape
straight resonators at 1.5 GHz……………...…………….…..85
Figure 4.12: Simulation response of 3 pole Chebyshev bandstop filter using
interdigital T-shape straight resonators using copper at 1.5Hz…...…..86
Figure 4.13: The 3 pole compact Chebyshev bandstop filter using ultra compact
interdigital meandered resonators at 1.5 GHz…………………………..87
Figure 4.14: Structure to calculate reactance slope parameter by varying length of
interdigital capacitor (Li)…………....…...……..…………………………..88
Figure 4.15: (a) Photograph of the fabricated microstrip 3 pole Chebyshev bandstop
filter using compact interdigital meandered line resonator, (b) The
simulation response of microstrip 3 pole Chebyshev bandstop filter
using compact interdigital meandered line resonator at
1.5GHz………………………...………………………………..……..89-90
Figure 4.16: Cross section view of microstrip ………………………….………………92
Figure 4.17: conventional resonator at 10GHz on HR-Si substrate using
Aluminum…………………………………………………………………….93
Figure 4.18: S12 Response of microstrip resonator (λ/2) at 10 GHz…………………94
Figure 4.19: (a) Layout of patch resonator on HR-Si substrate, (b) S12 Simulation
results of patch resonator representing at 10 GHz………..………………95
199
Figure 4.20: (a): (i) Cross section view of Patch resonator having Air window
underneath the Patch, (ii) 3-D view of Patch resonator on Silicon having
Air window underneath the Patch (using Coventor), (b): S12 simulation
result of patch resonator with high Q on air window beneath the patch on
HR-silicon substrate at 10GHZ using Aluminum………….………...…96-97
Figure 4.21: (a)(i): cross section view of patch resonator with selective removal of
substrate beneath the strip of resonator, (ii): 3-D view of Patch
resonator on Silicon having Air window beneath the strip (using
Coventor), (b): S12 simulation result of patch resonator with high Q on
air window beneath the patch on HR-silicon substrate using Aluminum
metal………………………………………………….……….……..…..98-99
Figure 4.22: Three pole Chebyshev bandstop filter using patch resonator at 10 GHz
using Aluminum as metal…………….…………………………………..101
Figure 4.23: Structure to calculate normalized reactance slope parameter by varying
length of capacitor (Li)…………… ……………….………..……………103
Figure 4.24:Extracted normalized reactance slope parameter against variable
lengths (Li) of extra capacitance coupled to the patch resonator, (a):
The reactance slope parameter by the extra capacitance introduced to
patch of the resonator, (b): The reactance slope parameters obtained
by varying extra capacitance length introduced towards strip of patch
resonator…………………………………………………………………..104
Figure 4.25: Simulation response of microstrip Chebyshev bandstop filter on silicon
substrate at 10GHz using Aluminum……………….………………….105
Figure 4.26: Proposed CPW to microstrip transition (a) Proposed CPW structure,
(b) Transition frequency response……………………………..106-107
200
Figure 5.1: Comparison of frequency of the Chebyshev filter and the design filters
with single pair of attenuation poles at finite frequency (n=6)……….113
Figure 5.2: Standard Chebyshev filter the approximate synthesis method based on a
lowpass prototype filter…………………………………………………….115
Figure 5.3: (a) Equivalent circuit of a trisection bandpass filter, (b) Associated
lowpass prototype filter, (c) the comparison between ideal Chebyshev
filter and Trisection filter response…………………….…………...116-117
Figure 5.4: Photograph of proposed novel Trisection Bandstop filter at
1.5GHz……………………………………………….………….……………120
Figure 5.5: The steps follow to design Trisection filter……………………….………120
Figure 5.6: Chebyshev bandstop filter using lump elements………………….…….122
Figure 5.7: (a) Cross-coupling of non-adjacent resonators of Chebyshev bandstop
filter with 50Ω transmission line of 90 degrees electrical length, (b)
Response of initial trisection filter, (c) Optimization goals to obtain
required response.………………………………………………...123-125
Figure 5.8: (a) Cross-coupling of non-adjacent resonators of Trisection bandstop
filter with 200Ω transmission line of 90 degrees electrical length, (b)
Response of Trisection filter with lump elements………………......126-127
Figure 5.9: (a) the reactance slope parameter by varying the length (Li) of interdigital
capacitance at 1.5GHz, (b) The reactance slope parameters obtained by
varying interdigital capacitance length (Li) at 1.49
GHz…………………………………………………………………..….128-129
201
Figure 5.10: (a) The initial circuit with transmission line inverter, (b) Response of filter
with interdigital capacitor equivalent to transmission
line of 200 Ω……………………………………………………………130-131
Figure 5.11: (a) Steps and formulas used to convert transmission line of 200 Ω to 50
Ω transmission line using Admittance, (b) The final circuit with
transmission line inverter, (c) the circuit with interdigital capacitor, which is
equivalent to the transmission line 200 Ω, (d) Response of filter with
interdigital capacitor equivalent to transmission
line of 200 Ω……………………………………………………..…..…132-135
Figure 5.12: (a): The interdigital capacitor which is connected to the transmission line,
(b): The practical structure of Triplet bandstop filter at 1.5GHz,
(c):Simulation results of Triplet bandstop filter with extra transmission
zero………………………………………………………………….….136-138
Figure 6.1: Mask of single Resonator on Silicon substrate at 10 GHz, top metal layer
mask, (b) bottom layer cavity mask.
(Scale corresponds to 1λ =1 µm)………………………….………………143
Figure 6.2: Mask of Chebyshev band stop filter on Silicon substrate at 10 GHz (a)
top metal layer mask, (b) bottom cavity layer mask.
(Scale corresponds to 1λ =1 µm)……………………………………..…...144
Figure 6.3: Isotropic Etching………………………………………………………..…..145
Figure 6.4: Grooving by KOH etchant…………………………,……………….……..146
Figure 6.5: Dimensions obtained for base of pyramidal via………………………..148
Figure 6.6: Experiment-I SiO2 as protective layer on silicon……..…………………149
Figure 6.7: Experiment-II SiO2 and Silicon Nitride (Si3N4) as protective layer on
silicon…………………………………………………………………………149
202
Figure 6.8: Steps of fabrication process for experiment- I…………….………156-159
Figure 6.9: Fabrication process of experiment- II…………..…………………..163-164
Figure 6.10 Photos from SEM (a) SEM and display of device, View of Coplanar
waveguide with cavity in SEM, ( c) View of cavity edge, (d) View of flow
of Aluminum at the edges and on surface………………………..164-165
Figure 7.1: (a) shows the set up to measure this filter with the help of VNA,
(b) the device for test…………………………………….………….168-169
Figure 7.2: Results of 3 pole Chebyshev bandstop filter using interdigital
T-shape straight resonators, (a) The response of filter without tuning,
(b) S11 simulation and electrical response after tuning,
(c) S12 simulation and electrical response after tuning………….170-172
Figure 7.3: Results of 3 pole Chebyshev bandstop filter using interdigital T-shape
meandered resonators, (a) The response of filter without tuning, (b) S11
simulation and electrical response after tuning, (c) S12 simulation and
electrical response after tuning…………………………………….…174-177
Figure 7.4: Results of Trisection bandstop filter using ultra compact interdigital
meandered resonators, (a) photograph of device to be test ,(b) The
response of filter without tuning, (c) S11 simulation and electrical
response after tuning, (d) S12 simulation and electrical response after
tuning………………………………………...……………………...…..179-183
Figure 7.5: The set up to test resonator at 10GHz.on silicon substrat……………..183
Figure 7.6: S12 experimental and simulation results of patch resonator
on HR-Si substrate using Aluminum at 10GHz. ………..………………185
Figure 9.1: Fabrication process for future work………………………………………191
203
Table I: (a) Standard Radar Frequency Letter-Band Nomenclature (IEEE Standard
521-1984), (b) Typical Frequencies………………………………………………3
Table 2.1: Formulas of Series RLC resonant circuit……………….....………….……25
Table 2.2: Formulas of Parallel RLC resonant circuit…………………....……..……..27
Table 2.3: Elements values for Chebyshev lowpass filters (g0=1, Ωc = 1) for
passband ripples LAr = 0.04321 dB (taken from [3])……………..……..…38
Table 4.1: Specifications of substrate to design resonators at 1.5GHz [5]………..71
Table 4.2: Specifications of Copper to design resonators at 1.5GHz [7]……….…71
Table 4.3: Summary of Q-value obtained with Copper and lossless metals on
Duroid (εr= 10.8, thickness (t) = 0.64mm and tan δ = 0.0023) for all
types of resonators proposed at 1.5 GHz. ……….………………..……79
Table 4.4: Specifications of substrate to design microstrip resonators at
10GHz [6, 7]…………………………………………………….………….92
Table 4.5: Specifications of Copper and Silver metals to design microstrip
resonators at 10GHz [7]………………………………………….………..93
Table-4.6: Comparison of Q-value of resonators proposed obtained with Aluminum
and Silver metal at 10GHz………………..…………….…………..……100
204
Table 5.1: Specifications of substrate to design microstrip resonators at
1.5GHz [5]………………………… …………………….…………..……119
Table-5.2: Specifications of copper to design microstrip resonators at
1.5GHz [7]………………. …………………………………….……..……119
Table- 6.1: Results of measurement of dimension of cavity in CPW on HR-Si using
experiment – I……………..…………………………………..…………..156
Table-6.2: Measured and proposed dimensions of cavity using experiment-II…162
205
Kataria Tejinder Kaur, Corona Chávez Alonso, Llamas-Garro Ignacio, “Novel Trisection bandstop filter ”, IEE Electronics Letter (under preparation).
Kataria Tejinder Kaur, Alonso Corona-Chavez , Ignacio Zaldivar-Huerta,
Ignacio Llamas-Garro, “Micromachined Compact High-Q Microstrip Resonators Using Selective Substrate Removal for Wireless Communication Systems at 10 GHz”, accepted in IEEE XVII International
Conference on Electronics Communication and Computers, Conielecomp
2007 , Mexico.
Kataria Tejinder Kaur, Corona-Chávez Alonso, Zaldivar-Huerta Ignacio,
Llamas-Garro Ignacio, “Compact High-Q Microstrip Resonator for
Wireless Communication Systems Using Micromachined Technology at 10 GHz”, Séptimo Encuentro de Investigación INAOE, 8-9 November 2006,
México.
Kataria Tejinder Kaur, Corona Chávez Alonso, Zaldivar-Huerta Ignacio,
Llamas-Garro Ignacio, “Compact High-Q Resonators For Wireless
Communication Systems Using Micromachining Technology at 10 GHz”, XXVI Congreso Nacional de la Sociedad Mexicana de Ciencia y
Tecnología de Superficies y Materiales, 25-29 de Septiembre 2006, Puebla,
México, pp 203.
INVITED TALK
Invited talk on “HIGH SPEED FUTURE RF-MEMS FILTERS” Congreso de
Electronica I Telecommunicacion I Sistema, IEEE, at Veracruz, Mexico.
14th Nov.2006.
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