DESIGN OF A MINIATURIZED X-BAND CHEBYSHEV
BAND-PASS FILTER BASED ON BST THIN FILM
Thesis
Submitted to
The School of Engineering of the
UNIVERSITY OF DAYTON
In Partial Fulfillment of the Requirements for
The Degree of
Master of Science in Electrical Engineering
By
Chenhao Zhang
Dayton, Ohio
August, 2012
DESIGN OF A MINIATURIZED X-BAND CHEBYSHEV
BAND-PASS FILTER BASED ON BST THIN FILM
Name: Zhang, Chenhao
APPROVED BY:
Guru Subramanyam, Ph.D.
Chairperson, Advisory Committee
Professor
Department of Electrical and
Computer Engineering
Monish Chatterjee, Ph.D.
Committee Member
Professor
Department of Electrical and
Computer Engineering
_______________________________
Robert Penno, Ph.D.
Committee Member
Associate Professor
Department of Electrical and
Computer Engineering
John G. Weber, Ph.D.
Associate Dean
School of Engineering
Tony E. Saliba, Ph.D.
Dean, School of Engineering
& Wilke Distinguished Professor
© Copyright by
Chenhao Zhang
All rights reserved
2012
ABSTRACT
DESIGN OF A MINIATURIZED X-BAND CHEBYSHEV
BAND-PASS FILTER BASED ON BST THIN FILM
Name: Zhang, Chenhao
University of Dayton
Advisor: Dr. Guru Subramanyam
This thesis reports the design procedures of X-band (8-10GHz) Chebyshev bandpass filter based on high dielectric constant Barium Strontium Titanate (BST) thin film.
Design procedures will be illustrated from fundamental formulas and lumped element
circuits to real electromagnetic (EM) geometry. The Chebyshev band-pass filter is
achieved by two coupled hairpin resonators formed by a coplanar waveguide feed-line
structure. The designed Chebyshev band-pass prototype has 3 ripples (3rd order) and 1dB
insertion loss in pass-band. The miniaturized dimension is 2400µm by 2420µm. The
center frequency is 10GHz. The bandwidth is 1GHz. The Q factor is 19.5. Three samples
were fabricated. Two of them were based on sapphire substrate without BST layer, the
other is based on the high resistivity silicon substrate with 0.25µm thick BST thin film.
Measured non-BST band-pass filter has 5dB insertion loss in pass-band and 1.3GHz
bandwidth. The center frequency of sample having BST thin film is shifted 1GHz to
lower frequency while maintaining the same frequency characteristic in pass-band.
iii
ACKNOWLEDGEMENTS
I would like to thank University of Dayton for giving me the opportunity to study
abroad and pursue my master’s degree in electrical engineering. I thank all my professors
and faculty of Electrical and Computer engineering department who taught me and
contributed to my learning through these years.
I would like to thank all of the friends who helped and supported me through this
research and my years of study at University of Dayton. Specially, I want to express my
deep respect and gratitude to Dr. Guru, my advisor who sponsored my study and research
these years and offered me this opportunity to practice the knowledge obtained from
classes, as well as spending time in revising my writing. During the time in Dr. Guru’s
RF research lab, I touched the new technology I have never known before including new
material applications in RF components and semiconductor device fabrication processes.
This amazing research experience will give me great help in my future careers.
I would like to express my most sincere thanks to my group members, doctoral
candidates Mark Patterson, Dustin Brown, Hailing Yue and Dr. Hai Jiang. They gave me
great help in my study and research. Mark was my teacher when I was an undergraduate
student. He introduced me to Dr. Guru and guided me to the RF engineering field. My
iv
research and study cannot be successful without his achievement in device fabrication
and teaching.
At last I would like to thank my parents and Di Li who always support and
encourage me to overcome the tasks during my study and life in Dayton.
v
TABLE OF CONTENTS
ABSTRACT.................................................................................................................................... iii
ACKNOWLEDGEMENTS ............................................................................................................ iv
TABLE OF CONTENTS................................................................................................................ vi
LIST OF FIGURES ...................................................................................................................... viii
LIST OF TABLES .......................................................................................................................... xi
CHAPTER I INTRODUCTION ...................................................................................................... 1
1.1 Background ............................................................................................................................ 1
1.2 Motivation .............................................................................................................................. 4
CHAPTER II LITERATURE REVIEW.......................................................................................... 6
2.1 Microstrip band-pass filter ..................................................................................................... 6
2.2 Hairpin band-pass filter.......................................................................................................... 7
2.3 Coplanar Waveguide with BST ............................................................................................. 9
CHAPTER III FERROELECTRIC MATERIAL BST ................................................................. 10
3.1 Dielectrics ............................................................................................................................ 10
3.1.1 Polarization ................................................................................................................... 11
3.1.2 Static permittivity and dielectric constant of material .................................................. 12
3.1.3 Loss tangent .................................................................................................................. 13
3.2 Barium Strontium Titanate .................................................................................................. 16
3.2.1 BST dielectric properties .............................................................................................. 17
3.2.2 BST deposition.............................................................................................................. 24
3.3 Conclusion of BST electric properties ................................................................................. 26
CHAPTER IV FILTER DESIGN .................................................................................................. 27
4.1 Filter theory.......................................................................................................................... 27
4.2 Chebyshev band-pass filter design....................................................................................... 29
4.2.1 Step 1 ............................................................................................................................ 30
vi
4.2.2 Step 2 ............................................................................................................................ 31
4.2.3 Step 3 ............................................................................................................................ 31
4.2.4 Step 4 ............................................................................................................................ 32
4.2.5 Step 5 ............................................................................................................................ 34
4.2.6 Step 6 ............................................................................................................................ 35
4.2.7 Step 7 ............................................................................................................................ 39
4.3 Conclusion ........................................................................................................................... 46
CHAPTER V MEASUREMENT AND DATA ANALYSIS ........................................................ 48
5.1 Fabricated devices................................................................................................................ 48
5.2 Matching network and system calibration ........................................................................... 49
5.2.1 Matching network ......................................................................................................... 49
5.2.2 System calibration procedure ........................................................................................ 50
5.3 Measurement results and analysis ........................................................................................ 52
5.3.1 Measurement results ..................................................................................................... 53
5.4 Conclusion ........................................................................................................................... 58
CHAPTER VI SUMMARY .......................................................................................................... 61
REFERENCES .............................................................................................................................. 66
vii
LIST OF FIGURES
Figure 1-1 Filter prototypes ............................................................................................................. 3
Figure 1-2 Microstrip hairpin-comb line resonators ........................................................................ 4
Figure 2-1 Side-coupled line band –pass filter ................................................................................ 7
Figure 2-2 Hairpin band-pass filter and S-parameter....................................................................... 8
Figure 2-3 complex hairpin-comb band-pass filter .......................................................................... 8
Figure 3-1 Dipole of atom.............................................................................................................. 11
Figure 3-2 BST layer nano structure ........................................................................................... 16
Figure 3-3 (a) Top view of 5by5 varactor ...................................................................................... 18
Figure 3-3 (b) 3D view of varactor structure ................................................................................. 18
Figure 3-4 Schematic of varactor ................................................................................................... 19
Figure 3-5 (a) Short varactor S11 vs DC bias ................................................................................ 20
Figure 3-5 (b) Short varactor S21 vs DC bias ................................................................................ 20
Figure 3-6 BST dielectric vs voltage ............................................................................................. 22
Figure 3-7 Varactor quality factor vs DC bias ............................................................................... 22
Figure 3-8 BST loss tangent vs voltage bias at 1 GHz .................................................................. 23
Figure 3-9 Leakage current vs the DC bias.................................................................................... 24
Figure 3-10 PLD system diagram .................................................................................................. 25
Figure 4-1 Type two 3rd order 1dB ripple Chebyshev low-pass filter prototype ......................... 29
Figure 4-2 Band-pass filter prototype ............................................................................................ 31
Figure 4-3 Final lumped element circuit for simulation ................................................................ 32
Figure 4-4 Lumped element values. Capacitor units (pF), inductor units (nH) ............................. 33
viii
Figure 4-5 Simulation result of lumped elements .......................................................................... 33
Figure 4-6 EM structure of microstrip band-pass filter (top view), dimension is in µm ............... 35
Figure 4-7 3D view of microstrip hairpin filter ............................................................................. 36
Figure 4-8 EM simulation of microstrip band-pass filter............................................................... 37
Figure 4-9 Top view of electric field intensity of band-pass filter at 10.2GHz ............................. 38
Figure 4-10 Top view of CPW band-pass filter, dimension is in µm ............................................ 39
Figure 4-11 3D view of CPW band-pass filter .............................................................................. 41
Figure 4-12 EM simulation of CPW band-pass filter .................................................................... 41
Figure 4-13 Top view of electric field intensity of band-pass filter at 10GHz .............................. 42
Figure 4-14 CPW hairpin band-pass filter phase S21 .................................................................... 43
Figure 4-15 comparison of CPW band-pass filter has BST vs no BST ......................................... 44
Figure 4-16 S11 comparison of lumped element, microstrip and CPW band-pass filter............... 45
Figure 4-17 S21 comparison of lumped element, microstrip and CPW band-pass filter............... 46
Figure 4-18 Hairpin resonator ........................................................................................................ 47
Figure 5-1 Fabricated devices ........................................................................................................ 48
Figure 5-2 Testing bench and fabricated device ............................................................................ 49
Figure 5-3 Network of probe testing bench ................................................................................... 49
Figure 5-4 Calibration left short, mid load, right transmission ...................................................... 51
Figure 5-5 Network analyzer before and after calibration S21 ...................................................... 52
Figure 5-6 Comparison of band pass filter on BST and no BST ................................................... 54
Figure 5-7 Comparison of backside metalized and none metallized ............................................. 56
Figure 5-8 Comparison between real and simulation result on BST ............................................. 57
Figure 5-9 S11 Smith chart of BST vs no BST band-pass filter (5-12 GHz) ................................ 58
Figure 6-1 3D view of ADS band-pass filter simulation structure ................................................ 63
Figure 6-2 Microstrip structure simulation S-parameter................................................................ 64
Figure 6-3 3D view of CPW structure ADS .................................................................................. 64
ix
Figure 6-4 S-parameter plots of CPW band-pass filter (ADS) ...................................................... 65
x
LIST OF TABLES
Table 3-1 List of BST properties vs DC bias .................................................................... 21
Table 4-1 Low-pass to band-pass transformation ............................................................. 31
Table 4-2 Kuroda’s Identities impedance to admittance .................................................. 32
xi
CHAPTER I
INTRODUCTION
1.1 Background
Filter
An RF Filter is a device which uses energy storage elements such as capacitors,
inductors, and transmission lines to allow certain frequency spectrum and eliminate other
frequency band. Filters are classified in general as digital filters and analog filters. A
digital filter has applications in digital signal processing, and can be defined and
programmed by a computer. An analog filter is achieved by real energy storage
components or transmission lines, which normally plays an important role at the first
stage of a communication system.
An RF Band-pass filter is one of the basic components in RF/Microwave wireless
communication systems. It covers the frequency range from AM/FM (MHz) radio station
system to hundreds of GHz extremely high frequency system. As antenna, it can pick any
frequency from the free space. Normally, the valuable information is only in a narrow
band frequency while the other signals are the noise and unexpected for next signal
processing stage. If the filter has low quality factor and low frequency selectivity, too
much noise will consume much power to bring down the system efficiency and cost. In
1
an ideal mathematical model, filters have vertical edges at the corner frequencies without
any slope in frequency domain. But in real case, this perfect edge frequency response
cannot be achieved. The only way to achieve this model is to expand the ideal math
equation as polynomial equations to approximate it. For that reason, engineers pursue to
design filters with the maximum frequency selectivity and minimum insertion loss in pass
band.
The most widely used filter is a band-pass filter. Many types of band pass filter
have been developed [1] such as comb-line filter, interdigital filter [1], parallel-coupled,
hairpin-line [2], path, ring filters and cavity filter. The advantage of a comb-line filter is
its narrow band and simple structure. The drawback is asymmetric insertion loss at low
frequency band. Parallel-coupled, hairpin, ring filters are kind of resonant filters. They
are realized in mainly microstrip and coplanar waveguide structure at microwave
frequency. Cavity filter has very good frequency response [3] [4], because it is fully
covered at the boundaries. Its insertion loss is very low in pass band and it has very sharp
edge. The drawback is the large dimension and heavy mass. It doesn’t fit modern highly
integrated and small communication systems. For the reasons above, parallel-coupled,
hairpin, ring filters are more attractive for research in band-pass filters because of the
small dimension, lower power consumption and convenient fabrication process.
2
Chebyshev band-pass filter
An RF filter has two prototype approximations. One is a Butterworth filter, and
the other is a Chebyshev filter. A Butterworth filter has maximum transmission in passband, but poor performance at cut off edge (figure 1-1). The slope below 3dB down is
gradual, which means the frequency selectivity is not high enough. Chebyshev filter has
very rapid slope at corner frequency, and the frequency selectivity is very remarkable.
The drawback is that Chebyshev filter has nth ripples in the pass-band, which decrease
the gain of filter (figure 1-2). Generally, filters focus more on the frequency selectivity
than pass-band gain, since higher signal gain can be obtained from low noise amplifier.
Chebyshev band-pass filters have more application in communication system due to the
high frequency selectivity.
(b)
(a)
Figure 1-1 Filter prototypes (a) Butterworth filter response (b) Chebyshev filter response
Hairpin band-pass filter
Hairpin band-pass filter is a type of a resonant filter. It has small compact
microstrip resonators and weak coupling between adjacent resonators which is required
for narrow-band filter [1]. If the filter is tunable, the shifted frequency can maintain same
bandwidth in sizeable range. Hairpin filter behaves like Chebyshev filter with high
3
frequency selectivity and narrow bandwidth. Figure 1-2 shows a microstrip hairpin-comb
line resonator.
Figure 1-2 Microstrip hairpin-comb line resonators
1.2 Motivation
Normally, frequency response of RF stripline devices depends on material
properties, length and shape. The working frequency is fixed. In recent years, a promising
ferroelectric material BST has been researched and reported many times due to the
development of advanced deposition technology [5] [6]. BST has large dielectric constant
in normal situation [5] [7]. High dielectric material can shrink the dimension of
traditional RF components which is satisfied for MMIC/RFIC circuit board [8][9]. The
most attractive property is that the dielectric constant can be tuned under external DC
bias. This property makes traditional RF devices have capability of working at different
frequencies and achieve multiple functions. If a narrow band high selectivity band-pass
filter is combined with this material, it can select different frequency under DC control
[10] [11]. If the DC control signal is coded digital 1/0 stream, filters can work at wider
spectrum to obtain more information. Hairpin filter has narrow bandwidth and high
frequency selectivity. It is an appropriate candidate to be utilized to expanding its
functionality.
4
Our research lab at the University of Dayton has a large area Pulsed Laser
Deposition (PLD) system for BST thin film deposition. PLD is the most advanced BST
deposition system for upto 4 inch diameter wafer. Our group has published papers for this
deposition technology and the application of BST in RF device design [5] such as CPW
tunable shunt varactor [12], microstrip band-pass filter, miniaturized CPW patch antennas
[13] and CPW interdigital capacitor [14]. For that reason, plenty of research resources,
design experience and database are available to support this filter design.
The main RF components researched and designed by our group is based on
Coplanar Waveguide (CPW) devices. A CPW device has the ground plane in the same
layer as the signal transmission line. For CPW transmission line, it has lower loss than
microstrip line [15]. The wave propagation mode is not TEM mode such as microstrip
line. It has TM or TE mode similar to a waveguide device. If combined with the bottom
ground, grounded CPW transmission line has much lower insertion loss. The other
advantage is, there is no air-bridge or via hole needed due to the coplanar ground plane.
This property reduces the fabrication process and cost and attractive for packaged RF
components.
5
CHAPTER II
LITERATURE REVIEW
Microstrip and coplanar waveguide RF filters have been studied and reported in
literature. They are one of the most commonly researched RF components. Many types of
band-pass filter have been developed [1] include comb-line, coupled-line [16] [17], dual
resonator [18] [19], hairpin [20][21], interdigital,[22] and cavity. In recent years, because
of the development of advanced deposition technology, ferroelectric materials such as
Barium Strontium Titanate have been widely applied for the design of band-pass filters.
With the combination of the high permittivity ferroelectric materials, traditional bandpass filters achieve many new attractive characteristics such as tunable working
frequency, and miniaturized dimensions [23].
2.1 Microstrip band-pass filter
Microstrip structure is the most widely used RF structure and the foundation of
coplanar waveguide structure. The most common microstrip band-pass filter is the sidecoupled filter, which is based on the transmission line theory [15]. The advantage of sidecoupled filter is the simple geometry, convenient of fabrication and high DC isolation.
The drawback is the large dimension. In most cases, coupled-line filters are thin and long.
6
They are not convenient for package and mounting on circuit board. As a result, many
research groups find different methods of geometry transformation to shrink the
dimension such as stripline folding [24], ring or loop resonators [25] [16] and slot line
resonators.
Figure 2-1 is a typical side-coupled band-pass filter developed by a different
research group [17]. The coupled lines are quarter-wave resonators. Its center frequency
is at 3GHz. The total length of the filter is around 2cm. This band-pass filter has very low
insertion loss in pass-band and good frequency response at the cutoff edges.
(a)
(b)
Figure 2-1 [17] Side-coupled line band –pass filter (a) fabricated devices (b) S-parameter
2.2 Hairpin band-pass filter
Folded side-coupled line can reduce the dimension of band-pass filter. Figure 2-2
shows a design of miniaturized hairpin stripline band-pass filter developed by another
group [2]. Hairpin band-pass filter is a narrow band filter. The bandwidth of this design is
around 30MHz. The total length of filter is no more than 1cm even it works at low
frequency. To achieve lower insertion loss, filters required are often quite complex with
more hairpin resonators [21]. Figure 2-3 is the example of a narrow band complex
7
hairpin-comb band-pass filter, which uses 3 pairs of resonators, each including 16
hairpins to achieve 2MHz bandwidth [21].
(b)
(a)
Figure 2-2 [2] Hairpin band-pass filter and S-parameter
(b)
(a)
Figure 2-3 [21] Complex hairpin-comb band-pass filter
8
2.3 Coplanar Waveguide with BST
Coplanar waveguide structure is first developed by Dr. Cheng P. Weng in 1969
because of the tremendous growth of microwave integrated circuits (MICs). It has
advantages of simple fabrication, low radiation (low insertion loss) lossless. CPW
structure is ideally suited for MICs as well as MMIC applications [24].
Multiple CPW structure RF components have been developed by our research
group such as CPW shunt varactor [12], high voltage interdigital capacitor (HVIDCs) and
HV shunt IDCs [14]. CPW shunt varactor is as two layer structure. The overlap area of
two layers is a strong coupling capacitor which is due to the high dielectric material BST.
The capacitor’s value can be tuned with the changing of external DC bias. This capacitor
has high tunability [5], high Q factor, low DC power consumption and small dimension.
HVIDC is a single layer series capacitor. The same as varactor, it is a tunable device with
BST material. It can support hundreds of volts with low leakage current.
Some remarkable miniaturized CPW band-pass filters with high dielectric
material have been reported [19] [23]. The most commonly used technique for
miniaturized CPW band-pass filter is to use λ/4 transmission line resonators. The
electromagnetic-field distributions for even and odd mode were calculated by threedimensional finite-elements method [26].
9
CHAPTER III
FERROELECTRIC MATERIAL BST
As mentioned in the introduction, the achievement of miniaturization and
tunability of the band-pass filter is due to the Barium Strontium Titanate thin film
material (BST). BST is a kind of high dielectric constant ferroelectric material which
reveals a spontaneous electrical polarization and can be reversed by external electric
field (hysteresis polarization loops). The most common utilization of this material
property is to make varactors with capacitance tunability and other RF components
such as RFID or memory device. In this chapter, the basic parameters used to
describe the material electric properties will be introduced first, and then the electric
properties of BST thin film such as permittivity, loss tangent will be elaborated.
Finally the process of BST thin film deposition will be illustrated.
3.1 Dielectrics
Dielectrics (insulators) are used to describe a material’s capability to bind the
inner positive or negative charges by atomic or molecular force. The ideal dielectric
material contains no free charges, and the atoms or molecules are neutralized. Under
external field, there are no positive and negative charges can move to the surface of
material because of the bound force, which is opposite to the conductive material.
10
For these reasons, the ideal dielectric material blocks the DC voltage and current. In
real situation, there are always a few charges that can escape from the bound force to
be free charges and move in the same direction under external field. This charge
flow is called leakage current. Leakage current is an important parameter to indicate
material dielectric property, which affect a varactor’s quality factor. Most
RF/Microwave integrated circuits are fabricated on dielectric layer which isolate the
conductor layer and bottom ground layer. Dielectric layer is one of the crucial
materials, which determines the characteristic of RF/Microwave devices.
3.1.1 Polarization
Positive charges are concentrated in the core of atoms or molecules, and they
are surrounded by negative charges. Under external field, the charges of dielectric
material cannot be free, but the centroid of atoms and molecules can be shifted along
with the direction of external field (figure 3.1). This phenomenon creates electric
dipoles and the formation of electric dipoles is referred as polarization.
Figure 3-1 Dipole of atom (a) in normal situation (b) in external field
For an individual atom or molecular, the single dipole can be represented by
dipole moment which is given by
dp  Qdl
11
eq 3.1
Where Q is the magnitude of each negative or positive charge in Coulombs, and
dl is the displacement distance between positive and negative charges in meters. The
total dipole moment of a material is the sum of each dipole moment given in equation
3.1, and the dipole moment per unit volume is defined as electric polarization vector P,
which is given by
 1 Nev 
P  lim   dpn   N eQl eq 3.2
v0 v
n 1


Where v is the unit volume, Ne is the number of electric dipoles per unit
volume. The unit of electric polarization vector is Coulombs per square meter.
3.1.2 Static permittivity and dielectric constant of material
Assuming a short slab dielectric material is set under an external field, electric
dipole exists for each atom or molecule. Because of the realignment and cancellation of
adjacent opposite charges, the material’s inner total charge density becomes zero, but
bound surface charge density exists on the upper and lower surface. The electric
polarization vector P of this short slab is the result of the bound surface charge density,
which can be rewritten as
P  qs
eq 3.3
The electric flux density inside a dielectric material can be represented by the sum
of electric flux density of free space and medium. According to Gauss’s Law, the electric
polarization vector P is equal to the medium electric flux density. Then dielectric
material’s electric flux density is given by
D  D0  P eq 3.4
12
where
D0   0 E is the electric flux density in free space.  0 is the permittivity in
free space, E is the external electric field. Since polarization vector P is related to the
displacement distance between positive and negative charges, and this distance also
depends on the external electric field E. Equation 2.4 can be rewritten as
D   0 E   0  e E eq 3.5
where
 e is electric susceptibility. Reform equation 2.5 to get
D   0 (1   e ) E eq 3.6
Where
 s   0 (1   e )
is called static permittivity, and
 r  1  e
is called
relative permittivity or dielectric constant. It is frequency dependent for ferroelectric
material. Material dielectric constant is a very important parameter for RF/Microwave
components design. Choosing a material with high dielectric constant can significantly
shrink the dimension of device or increase the loss of energy. High dielectric constant
variability makes device impedance change and frequency shifting.
3.1.3 Loss tangent
Resistivity causes the electrical energy consumption in a conducting material.
Similarly, loss tangent is the parameter used to identify the attenuation of electromagnetic
energy in a dielectric material. In static electric field, electrons are dispersed at certain
distance from atoms or molecules by electric force. When the external field is alternative,
it forces the dispersion direction (polarization) to change. Since the mass of atoms or
molecules are much larger than electrons, their positions are assumed as fixed in the
electric field. Otherwise, the electrons are forming a dynamic electric dipole. If an
13
external field with angular frequency ω is applied to the system, the atoms/moleculeselectrons system is similar to the mass-spring-damping system, and both of them can be
represented by second-order ordinary differential equation by classic Newton’s laws [27].
m
d 2l
dl
 b  ls  QE(t )  QE0e jt eq 3.7
dt
dt
d 2l
d 2l
Where m
is the force associated with acceleration times mass, m is mass,
dt
dt
is the negative charges acceleration. Since the moving direction of charges is impossible
to be synchronized with the changing of external field except at the damping frequency, a
damping force is created. In the equation above, b
dl
is defined as damping force and b
dt
is the damping coefficient. ls is inner displacement force caused by electric field
between positive and negative charges. Q is the dipole charges and E (t ) is alternative
external field in time domain. The particular solution of equation 3.7 [27] is
l (t )  l0e jt eq 3.7
Q
E0
m
Where l0 
is solution of l (t ) when t=0. Submitting eq 3.7
 s  2

d
2
      j  
m
 m 

in to eq 3.2 led to
Q2
E0e jt
m
P
eq 3.8
 s  2

d
2
      j  
m
 m 

Ne
Combine equation 2.8 and 2.4
14
Q2
Q2
E0e jt
Ne
D
m
m
D   0 E0e jt 
  '  j ''
 
 0 
jt
2
E
e



 s  2
0
d
s
d
2
2
      j  
      j  
m
m
m
m










Ne
eq 3.9
Equation 3.9 is the derivation of the material complex permittivity. Then the complex
relative permittivity can be defined as
r 

  r'  j r'' eq 3.10
0
According to the Maxwell’s equation [27], the effective loss tangent can be defined
as
   ''   ''
tan  
 '  ' eq 3.11
 '
 
Where

is the static electric loss tangent which expresses the dielectric loss of a
 '
 ''
material under static field. ' is the alternating electric loss tangent which expresses the

dielectric loss of material in an alternative field.
Material dielectric properties determine the performance of RF components.
Dielectric constant determines the reactance (Capacitance and inductance), loss tangent
determine the device RF energy dissipation (quality factor). In RF design, dielectric
constant and loss tangent are two most important parameters to deal with. If the filled
dielectric material has large dielectric constant, huge coupled capacitors and high quality
inductors can be achieved. That means the devices dimension can be significantly
miniaturized [21]. If the dielectric constant can be tuned electrically, a tunable RF device
can be developed to achieve multi-function. These promising applications contribute to
the RF circuit fabrication and RF elements integration.
15
3.2 Barium Strontium Titanate
Barium
Strontium
Titanate
(Ba0.6Sr0.4TiO3)
material
has
been
studied
systematically in tunable microwave/RF components. Normally, this dielectric material is
utilized as a thin film layer in micro-strip and optical devices (figure 3-2) [28]. BST is a
kind of ferroelectric Material with crystalline structure [28], with the C-V plot showing a
hysteresis loop. This is the reason that it can be utilized to develop memory devices. The
most significant properties of this material are its high dielectric constant, large tunability
and low dielectric loss (loss tangent) [5]. According to the reported testing results, the
dielectric constant of BST thin film with 0.25 micron meters thickness is approximate
1000 under zero external DC bias and tunability is up to 80% from 0 volt to +/-10v [5].
BST thin film loss tangent is approximately 0 at 0V.
Figure 3-2 BST layer nano structure
16
3.2.1 BST dielectric properties
The dielectric properties of BST in RF/microwave field can be studied under
basic RF components such as transmission line or RF varactor. Double layers CPW RF
varactor has been developed and reported [28]. Figure 3-3 shows a basic 5µm by 5µm
varactor structure. It is a double layers structure filled by 0.25µm thickness BST thin film
between them. The first layer metal is a CPW transmission line with a length of 500µm.
The center line is signal line, and two ground lines are located symmetrical beside the
signal line. The width of input signal line is 50µm and the gaps between signal and
ground are 50µm. This distribution of 50µm G-S-G structure is in order to make the 50
ohm input impedance transmission line and will be discussed in chapter four. The bottom
metal layer has two ground lines which are shunted by 5µm width metal line. Overlap
area of top metal layer signal line and bottom layer metal shunt line is 5µm by 5µm. This
overlap area with inside filled BST material creates a RF capacitor whose value can be
defined as
C
 0 r A
eq 3.12
d
Where, A is the overlap area of two metal layers, d is the thickness of BST thin
film layer,  0 is the permittivity in free space and  r is the dielectric constant of BST. Both
of the metal layers are 1µm thick conductor layer. Between this two layers are 0.25µm
thickness BST film. The substrate of the varactor is 400µm thickness sapphire or silicon.
17
Ground
-1
-2
Overlap area
Signal line
1
2
Shunt line
Ground
-1
-2
Figure 3-3 (a) Top view of 5by5 varactor
capacitor
BST 0.25µm
Cg
C1
Cg
Sapphire 400um
Figure 3-3 (b) 3D view of varactor structure
Capacitances between two ground planes (Cg) are much larger than the coupling
capacitor between signal and shunt line (C1), because of the large overlap area. For high
frequency, signal pass via capacitor C1, then flow to Cg through bottom shunt line. For
that reason, two Cgs are parallel and series to C1. The relative capacitor is approximate to
the value of C1. Figure 3-4 is varactor schematic with lumped elements. The lumped
18
elements diagram is utilized to analysis the BST properties according to the varactor
behavior.
PORT
P=1
Z=50 Ohm
CPW1LINE
ID=CP1
W=50 um
S=50 um
L=250 um
Acc=1
CPW1LINE
ID=CP2
W=50 um
S=50 um
L=250 um
Acc=1
PORT
P=2
Z=50 Ohm
Relative Capacitor
CPW transmission line
PRC
ID=RC1
R=1000 Ohm
C=0.5 pF
& shunt resistance
Shunt line inductor
SRL
ID=RL1
R=2 Ohm
L=0.01 nH
& series resistance
Figure 3-4 Schematic of varactor
The shunt resistance which is parallel with the capacitor is caused by the BST thin
film leakage current. The common shunt resistance of 0.25µm thickness BST is from
1000-3000. The series inductor and resistance are caused by shunt line.
The RF measurement results of varactor 5by5 with 0.6µm thickness BST thin film
are showed in figure 3-5
19
Figure 3-5 (a) Short varactor S11 vs DC bias
Figure 3-5 (b) Short varactor S21 vs DC bias
S11 parameter plotting graph indicates that the reflection of RF energy getting
lower with frequency rising up. S21 parameter plotting graph is opposite to S11
parameter. When the DC bias is applied, the dielectric constant of BST is changing and
inversely proportional to the voltage. According to eq 3.12, lower dielectric constant
20
causes smaller shunt capacitor, hence more RF energy will be delivered to port 2 and less
be shunted to ground.
CAD software can optimize the value of lumped RLC components (figure 3-4) to
match the simulation output with measured results. Therefore, the information of BST
properties can be obtained from the RLC value. Table 3-1 lists the electric properties of
BST under DC bias. A measured varactor device is fabricated on UDBST-10 based on
Sapphire substrate and 0.6µm thick BST. DC bias is applied from 0V-20V with a step
size of 2V.
Voltage (V)
0
2
4
6
8
10
12
14
16
18
20
UDBST-10 Varactor short 5by5
Rs(0.6um)
Q(0.6um)@1G Er
Shunt Resistance loss tangent
2.45 96.95701681 1261.20021
2500 0.01031385
2.45 120.2985209 1016.48972
2500 0.00831265
2.2
200.953211 677.659815
2500 0.00497628
2 289.3726238 517.656803
2500 0.00345575
2 361.7157798 414.125442
2500
0.0027646
2 430.1484948 348.241849
2500 0.00232478
2 488.2053469 306.829305
2500 0.00204832
2 548.8101486 272.946314
2500 0.00182212
2 589.4627522 254.122431
2500 0.00169646
2 602.8596329 248.475265
2500 0.00165876
2 612.1343965 244.710489
2500 0.00163363
Table 3-1 List of BST properties vs DC bias
BST dielectric constant has significant tuning under DC bias. At 0 Volts, the
relative dielectric constant is around 1260. The tunability can be calculated as (1261.2244.71)/1261.2=80.6%. Shunt resistance is stable in this voltage range at 2500Ω. Series
resistance Rs is around 2Ω which depends primarily on the dimensions of the shunt line.
21
Figure 3-6 BST dielectric vs voltage
Figure 3-6 shows the dielectric constant versus DC bias is non-linear. Changing
slope is increasing from 0 to 4 Volts. After 10 Volts, the slope becomes flat.
Figure 3-7 Varactor quality factor vs DC bias
Figure 3-7 indicates that varactor quality factor at 10GHz is much lower than
at 1GHz, and the quality factor changes with voltage are more significant. There is
almost 10 times difference. Quality factor is affected by the dielectric loss of BST.
22
Since, static dielectric constant is decreasing when the DC voltage is increasing,
dielectric loss (loss tangent) of the BST become lower, which enhances the varactor
quality factor. The loss tangent of BST at 1GHz decreases from 0.01 to 0.002 with
applied DC bias (figure-3.8).
Figure-3.8 BST loss tangent vs voltage bias at 1 GHz
Figure-3.9 is plotting graph of leakage current versus DC bias. The
breakpoint is around 10V. Before 8 volts, leakage current cross the BST is stable and
below 10nA, which means that there is low DC power consumption. After 10 volts,
current increases abruptly. The breakpoint of BST leakage current depends on the
thickness of thin film and the deposition parameters.
23
Figure-3.9 Leakage current vs the DC bias
3.2.2 BST deposition
BST deposition is achieved by the Pulsed Laser Deposition System with real
time control (figure-3.10). PLD system uses KrF laser with 248nm wavelength and
25ns pulse [28]. Deposition is completed in the chamber with Oxygen background
gas. The wafer is held upside by the heater, and the target (BST) is put on the bottom
of chamber. When the pulsed laser shot the target, because of the high energy, BST
particles are sputtered from the target, and recombined with background oxygen on
the path to the wafer. The wafer is spun in this process to ensure the uniform
deposition. BST thickness is controlled by the number of laser shots. Larger number
of shots means thicker BST layer.
24
Figure 3-10 PLD system diagram
Generally, BST deposition quality relies on the following factors
1. Background gas pressure
Higher oxygen gas pressure means more free particles on the path from target to
wafer, which increase the probability of particles collision and reduce the mobility of
sputtered BST molecules. This situation led to thinner BST film. Inversely, lower
pressure led to thicker film layer and lower oxygen percentage in BST.
2. Laser beam energy density
If the laser power is too high, too many BST particles are sputtered from target,
which affect the composition, surface roughness and density uniformity of BST.
3. Wafer coverage area
Sputtered BST particles spread as a spherical shape in the chamber, more particles
land on the center of wafer that is perpendicular to the target sputtered spot. For
large area wafer deposition, BST density is higher and it is thicker near the center of
25
wafer. This thickness and density distribution on the wafer is similar to the normal
distribution.
3.3 Conclusion of BST electric properties
BST has very high dielectric constant and low loss tangent in normal
situation. The dielectric constant is tunable and inversely proportional to DC bias.
The tuning range of dielectric constant is from 1200 at 0V to 200 at 10V which
depends on the BST deposition quality and film thickness. The dielectric loss (loss
tangent) of BST is decreasing with the increasing of voltage. For varactor, the
quality factor ascends with the DC voltage. The break down voltage point of BST
depends on the thickness and capacitor overlap area. Under the same overlap area,
thinner film means lower break down volts. For 0.6um thickness BST, leakage
current amplitude goes up significantly after 20V. BST properties of higher
dielectric tunability and lower dielectric loss makes traditional RF components such
as varactor work at wider frequency range and behavior as a switch capacitor.
26
CHAPTER IV
FILTER DESIGN
This chapter discusses the design and computer simulation methodology of the
3dB Chebyshev band pass filter. First part of this chapter is the overall view of filter
design which explains the mathematical theory of filter including prototype. Based on the
Chebyshev low-pass approximation, second part demonstrates the whole design
procedure of X-band Chebyshev band-pass design from lumped elements to real CPW
structure. The simulation results of each step will be plotted and discussed.
4.1 Filter theory
Filter is one of the most fundamental components in modern electronic systems.
Its main function is to filtering the signal frequency band which is not expected. For RF
analog band-pass filter, there are two commonly used filter models, one is Butterworth
approximation, and the other is Chebyshev approximation. Butterworth filter has
maximum flat response in pass-band, but high insertion loss at cut off edge. Chebyshev
filter improves the frequency response at the edge of band, but has ripples in the passband which increase the insertion loss. Generally, filters are two-port networks that
transform power from source to loads. The reflection coefficient can be presented as
27
 ( s) 
Z in, f s   Rs
Z in,b s   Rs
eq 4.1
Where, s  j is Laplace variable. The filter transducer power ratio [29]
(insertion loss) is defined as
2
P
1 RL VS
eq 4.2
TPR  m 
PL 2 RS VL
Where
Pm
is the maximum power generated by source,
PL is the power absorbed by load.
RL is resistance of load, RS is the resistance of source.
The network transmission coefficient is defined as
T ( s) 
1
RS VL
2
RL VS
TPR( s)
eq 4.3
Combine eq 4.3 and 4.2 filter characteristic function is defined as
K ( s) 
1 ( s)
T ( s) eq 4.4
For any propagation wave, transmission and reflection coefficient has unity relation that
2
2
T ( s )  ( s )  1
eq 4.5
Combine eq 4.5 and 4.6 the transmission coefficient [29] can be written as
2
T ( s) 
1
1  K ( s)
2
eq 4.6
For lumped element (RLC) filter design, transfer function must be expanded to
the polynomials in frequency domain to obtain the capacitor or inductor network.
28
T ( s) 
am s m  am 1s m 1    a1s  a0
s n  bn 1s n 1    b1s  b0 eq 4.7
4.2 Chebyshev band-pass filter design
To obtain the maximum frequency response at the edge of filter, Chebyshev filter is
chosen for the design prototype. Commonly, most of the filters design is based on the prototype
of low-pass filter. Chebyshev low-pass filter transfer function approximation [29] can be derived
from eq 4.6 as
1
2
T ( s) 
1   K ( s)
2
2
eq4.8
Where  is design parameter define the pass-band ripple as
 1 
PBR dB  10 log10 
2  eq 4.9
1  
Which define the dB value of ripples in pass-band. The characteristic function of Chebyshev filter
for nth-order can be expressed as
Kn ()  2Kn1 ()  kn2 ()
eq4.10
3rd 1dB Chebyshev
low pass prototype
g1
RF
g3
g5
g4
g2
Figure 4-1 Type two 3rd order 1dB ripple Chebyshev low-pass filter prototype
When the Laplace variable of filter transfer function is extracted by the lumped
LC elements by ladder synthesis, the lumped element circuit of filter can be constructed.
29
Commonly, filter design is based on the low pass prototype. The first step is to build a
low-pass filter, then convert the low-pass to band-pass.
The design of band-pass filter begins from the Chebyshev low-pass prototype.
The lumped elements value of Chebyshev low-pass prototype can be found from the
recursive formula [29] where
g1 
gk 
2a1

4ak 1ak
, k  2,3,n
bk 1 g k 1
 2k  1 
ak  sin 
, k  1,2 n
 2n 
 
  sinh 
 2n 
 k 
bk   2  sin 2   k  1,2 n
 n 

RdB


  Lncoth

 17.3717793 



RdB  10 log  2  1
g k is the value of kth capacitor or inductor. The value of lumped elements can be found
from the design table [29]
4.2.1 Step 1
The designed prototype is a 3rd order (three ripples) 1dB down lowpass filter
(figure 4-1), and normalized to a radian corner frequency 1 radian/s and 1 ohm system.
According to the design table, the coefficient of g2 =2.063, g3=0.9941 and g4=2.0236
30
4.2.2 Step 2
Next step is to transform the low-pass prototype to band-pass. This transform is
completed by the impedance transformations. This transform can be completed by the
formula below (table 4-1)
Table 4-1 Low-pass to band-pass transformation
Where
 is the transformation constant and equals to

0
2  1
 2 is the high cutoff frequency in radian/s and 1 is low cutoff frequency in radian/s. The
expected center frequency is 10GHz, and the bandwidth is 1GHz, then   10 . Diagram
of figure 4-1 low-pass prototype is converter to the figure 4-2
3rd 1dB Chebyshev
g1
g5
L3
C3
band pass prototype
RF
L1
C2
C1
L2
Figure 4-2 Band-pass filter prototype
4.2.3 Step 3
Lumped element circuit is a physical model for filter design. It has to be
converted to the RF stubs and real microstrip structure. Some lumped components are
difficult to implement in fabricated structure. For this design, the final EM structure of
the filter is a two coupled hairpin resonator band-pass filter. In order to achieve the real
31
structure, band-pass filter prototype (figure 4-2) needs impedance and admittance inverter
such as conversion between inductor and capacitor using Kuroda’s Identities. It is
showed in table 4-2.
Table 4-2 Kuroda’s Identities impedance to admittance
4.2.4 Step 4
After Kuroda’s identities transformation the final lumped element schematic is
showed in figure 4-3.
CPW module
Matching network
PORT
P=1
Z=50 Ohm
CPW1LINE
ID=CP1
W=50 um
S=50 um
L=240 um
Acc=1
IND
ID=L3
L=0.133 nH
CAP
ID=C3
C=0.0188 pF
IND
ID=L5
L=0.823 nH
IND
ID=L6
L=0.833 nH
IND
ID=L4
L=0.1 nH
CPW1LINE
ID=CP2
W=50 um
S=50 um
L=240 um
Acc=1
PORT
P=2
Z=50 Ohm
CPW_SUB
Er=12.9
H=400 um
T=1 um
Rho=1
Tand=0.005
Hcover=1000 um
Hab=2 um
Cover=0
Gnd=0
Er_Nom=12.9
H_Nom=H@ um
Hcov_Nom=Hcover@ um
Hab_Nom=Hab@ um
T_Nom=T@ um
Name=CPW_SUB1
CAP
ID=C4
C=0.11 pF
IND
ID=L1
L=0.164 nH
CAP
ID=C2
C=0.27 pF
CAP
ID=C1
C=0.26 pF
IND
ID=L2
L=0.164 nH
CAP
ID=C5
C=0.11 pF
3rd 1dB Chebyshev
band pass module
Figure 4-3 Final lumped element circuit for simulation
The red box indicates the main structure of the Chebyshev band-pass filter.
Orange part indicates the matching network between band-pass the CPW transmission
32
line. The substrate module is setting as a sapphire wafer with dielectric constant 9.7, loss
tangent 0.005 and thickness 400µm.
The real lumped elements value for band pass filter is computed by AWR
simulation software and showed in figure 4-4.
Figure 4-4 Lumped element values. Capacitor units (pF), inductor units (nH)
The simulation results of the band-pass filter from 1 to 18GHz is in figure 4-5.
Figure 4-5 Simulation result of lumped elements
33
The S21 shape shows a very good Chebyshev band-pass response. There are three
ripples in the pass band, and two ripples are at the edge of pass-band. The maximum
insertion loss in pass-band is 1.89dB, and the minimum insertion loss in pass-band is
2.627dB. The pass-band ripples are close to the design expectation. The center frequency
is at 9.5GHz, which shifted 0.5GHz lower compared to the design expectation. The band
width counted 3dB down from the maximum insertion loss is 0.951GHz, which is close
to 1GHz.
4.2.5 Step 5
The lumped elements should be converted to RF stubs, which can be achieved by
Richard’s transformation. Richard’s transformation is remarkable scheme that takes into
account the actual properties of transmission lines. Applying Richard’s transformation to
a capacitor, the admittance of the element is transformed as follow
Y  ja1C tan( )
And the impedance of the inductor element is transformed as
Z  ja 2 L tan( )
Where,
a1 is the characteristic admittance of the transmission line for capacitor
element, a2 is characteristic impedance of the transmission line for inductor element.
  l is the electrical length of transmission line. Richard’s transform converts the
capacitor to open-circuited stub, and inductor to short circuit stub. The open-circuited
stub in real transmission line is coupled line, and the short -circuited stub in transmission
line is a strip line or via conductor.
34
4.2.6 Step 6
Generally, design of RF components are based the structure of microstrip
transmission lines. Coplanar waveguide devices can follow this design methodology. In
lumped element circuit, inductor L5 and L6 are the short stub and determined by the
electrical length of hairpin transmission line. L1 and L2 is the short stubs of via
conductor between top and bottom metal. C1 and C2 are the relative capacitors, which
are parallel capacitors from hairpin transmission line to bottom ground and coupling
capacitor of hairpin structure. C3 is the coupling capacitor between two hairpin
resonators (figure 4-6).
L6
L6
Via conductor to the
L6
bottom ground plane
C3
Hairpin resonator
Input impedance
L5
L5
L5
Figure 4-6 EM structure of microstrip band-pass filter (top view), dimension is in µm
The simulated microstrip hairpin band-pass filter has 1860µm total length and
160µm width transmission linea. In simulation the conductor is assumed to be perfect
35
conductor with 0 thicknesses. The substrate is sapphire with 9.7 dielectric constant, 0.005
loss tangent and 400µm thickness. Between the metal layer and substrate is the 0.25um
thickness BST with dielectric constant 500 and loss tangent 0.02. The hairpin resonator is
connected to the bottom ground plane by via conductor. The characteristic impedance of
microstrip transmission line can be calculated by the formula when W<H [24]
Z0 
60
 eff
W
 H
Ln 8
 0.25 
H
 W
And when W>H
Z0 
 eff
120
W
2 W

 H  1.393  3 Ln H  1.444 



Where H is the thickness of substrate, W the width of transmission line
 eff
is the
effective dielectric constant
BST 0.25um
L2
C2
C1
L1
Bottom ground
Sapphire
Via conductor
Figure 4-7 3D view of microstrip hairpin filter
Figure 4-7 is the 3D view of the microstrip band-pass filter. L2, L3 are the short
conductors and C2, C1 are relative coupling capacitors. EM simulation is completed by
36
the AWR software. AWR software use method of moment to simulate the EM structure.
The simulation results are showed in figure 4-8
Figure 4-8 EM simulation of microstrip band-pass filter
The EM simulation result shows the S21 curve is a good band-pass filter
response. The Center frequency is at 9.8 GHz, the insertion loss is 2.132dB which is 1dB
higher than the lumped elements circuit and design expectation. The 3dB down
bandwidth is 0.5GHz. It is narrower than lumped circuit and design requirement. The
Quality factor is 19.4. The higher insertion loss is reasonable and acceptable. Because the
lumped element is an ideal lossless system without the effect of conductor resistance and
dielectric loss tangent, EM simulation contains these effects. In real situation, resistors
should be parallel with capacitors, and series with inductors. S11 parameter shows the 3
order ripples, which prove this filter has a Chebyshev band-pass filter response. The
reason that S21 doesn’t show these ripples in band-pass is because of the simulation
37
sampling point doesn’t pick this frequency. If changing the simulation frequency scale,
the ripples will appear.
Sidewall coupling
E - Field
Excitation port
Figure 4-9 Top view of electric field intensity of band-pass filter at 10.2GHz
Figure 4-9 shows the E-field intensity at 10.2GHz. Bright color means the strong
coupling electric field at fringing area.
Since the simulated conductor is a perfect
conductor, all electrons are at the conductor surface. There is no electric field inside the
conductor. For that reason microstrip line color is dark blue inside. 10.2 GHz is in the
pass-band, there are strong RF fields coupled between resonators. In AWR default
setting, the sidewall of the bulk is a perfect conductor. Because of that, there is E-field
coupled to the sidewall.
38
4.2.7 Step 7
Based on the previous design of microstrip band pass filter structure, the CPW
structure can be developed. The difference between microstrip and CPW transmission is
that mirostrip has ground plane (boundary condition) on the back side of substrate; CPW
has symmetric coplanar ground plane bounding the transmission line, which means
everything is on the same plane. For this filter design, if ground planes are on the same
layer with transmission, via conductor is unnecessary, and hairpin transmission line can
be shorted to the ground through a single strip line. (figure 4-10)
L2
L1
Short line instead
Ground
of via conductor
CPW port
L1
L1
Figure 4-10 Top view of CPW band-pass filter, dimension is in µm
Figure 4-10 shows the top view of CPW band-pass filter, the major dimension of
hairpin resonator is similar to the microstrip structure. The distance between two
39
resonators is 560µm the total dimension is 2400µm by 2420µm. In this structure, the
short line from resonator to ground is the inductor L1, L2 in lumped circuit. The signal
line of CPW transmission line is 50µm and the gaps between signal and ground is 50µm.
The characteristic impedance of CPW transmission line can be calculated by formula
[15]
Z0 
60
1
 eff K (k )  K (kl)
K (k ' )
K (kl' )
Where
k
W
2*S
k'  1 k 2
kl'  1  kl 2
 W
tanh
 4H
kl 
 b
tanh
 4H






H is the thickness of substrate, W is the width of signal line, and S is the gape space
between the signal and ground of each side. According to the CPW characteristic
calculator, 50µm gap and width make the characteristic impedance of CPW line around
50Ω.
40
BST 0.25um
Sapphire
Bottom ground
Short line instead
of via conductor
Figure 4-11 3D view of CPW band-pass filter
3D view of Band-pass filter shows via conductor is converted to the short line.
Figure 4-12 EM simulation of CPW band-pass filter
Figure 4-12 shows the electric filed intensity obtained from EM simulation of
CPW band-pass filter. The simulation condition is the same as microstrip structure. S21
parameter shows the frequency response is a good band-pass. The center frequency is
41
9.8GHz, which is close to design requirement. The insertion loss at pass-band is 1.8dB.
The 3 dB down bandwidth is 0.6GHz. Quality factor of CPW band-pass filter is 16.315.
S11 curve shows two ripples in the pass band, one at -20dB, and the other is not
significant. S21 doesn’t show any ripple in pass band. If increasing the simulation
sampling point, the ripples will occur.
Sidewall coupling
E - Field
Excitation port
Figure 4-13 Top view of electric field intensity of band-pass filter at 10GHz
Electric field intensity shows there is strong E-field coupling between two
resonators in pass band. Electric field also coupled between the sidewall and resonator.
To avoid this coupling effect, the space between sidewall and resonator should be
enlarged.
42
Phase delay
at 9.78GHz
Figure 4-14 CPW hairpin band-pass filter phase S21
Figure 4-14 shows the S21 phase of CPW hairpin band-pass filter. In pass-band,
because of the ripples, Chebyshev band-pass filter has non-linear phase. Magnitude S21
curve doesn’t show the Chebyshev behaviors due to the small sampling scale, but the
phase indicated the non-linear change and delay, which confirm the Chebyshev band-pass
behaviors.
43
Figure 4-15 Comparison of CPW band-pass filter has BST vs no BST
Figure 4-15 shows that due to the high dielectric constant of BST, band-pass filter
center frequency is shifted 0.7GHz to the left side. The insertion loss is almost the same
as the band-pass filter without BST. BST thin film can change the center frequency of
band-pass filter. The shift range from Er 500 to 0 is 0.7GHz. If the BST quality is higher,
the filter can work at lower frequency.
44
Figure 4-16 S11 comparison of lumped element, microstrip and CPW band-pass filter
Figure 4-16 shows lumped elements circuit has largest space between two peaks
of ripples. CPW structure has smallest space. CPW structure has the lowest return loss in
pass band. They all show the Chebyshev filter behavior in pass band.
45
Figure 4-17 S21 comparison of lumped element, microstrip and CPW band-pass filter
S21 plotting shows the lumped element band-pass filter has lowest center
frequency, lowest insertion loss in pass band and most significant Chebyshev band-pass
filter behavior. Microstrip structure has the narrowest bandwidth and highest insertion
loss in pass-band. For microstrip and CPW structure, Chebyshev filter behavior is not
quite significant. That is the reason that, two peaks of ripples are closer to each other than
lumped circuit, and the simulation scale is not small enough to capture the peak point.
The higher insertion loss in pass-band for microstrip and CPW structure is caused by the
resistance of dielectric, since lumped element circuit is an ideal model without resistance.
4.3 Conclusion
The design procedure is following the requirements of band-pass filter. Whatever
the lumped elements circuit, microstrip or CPW structure meets the design requirements.
46
After tuning the lumped components value, the design conclusion can be obtained as
follows
1) Center frequency is primarily affected by the coupling capacitors inside the hairpin
resonator.
2) Filter gain mainly depends on the quality of inductors and coupling capacitor between
two resonators.
3) The changing of BST dielectric constant can significantly shift the center frequency of
pass band.
4) The length ratio of l1,l2, l3 determines the performance of the hairpin resonators and
the filter (figure 4-18). This affect can be studied in the future to improve the filter.
1
L2
L1
L3
Figure 4-18 Hairpin resonator
47
CHAPTER V
MEASUREMENT AND DATA ANALYSIS
This chapter demonstrates the real fabricated band-pass filter. Real devices are
fabricated under three different conditions. RF vector network analyzer calibration and
testing procedures will be introduced. Measured data will be plotted and analyzed in this
chapter.
5.1 Fabricated devices
Figure 5-1 shows the fabricated devices. BST deposition is completed by Pulsed
Laser Deposition (PLD) system which is introduced in chapter 3. The metallization is
accomplished by E-beam evaporation method.
(a)
(b)
(c)
Figure 5-1 Fabricated devices (a) Sapphire without BST, no backside metallization (b) sapphire
without BST backside metalized (c) high resistivity silicon with BST, no backside metallization
48
(a)
(b)
Figure 5-2 Testing bench and fabricated device (a) RF testing bench (b) fabricated band-pass filter
5.2 Matching network and system calibration
5.2.1 Matching network
RF testing bench includes HP8720B (0.3GHz-20GHz) vector network analyzer,
DC power supplier, microscope testing station, and 150μm width GSG RF probe (Figure
5-2). Before the measurement, vector network analyzer must be calibrated to match the
impedance of cable and probe (Figure 5-3). In initial state, testing bench is an open
circuit network without load. VNA, cable and probe are cascaded together.
Probe
&
cable
Matching
network
VNA
Zn=50Ω
Zp
Zm
Zin
Figure 5-3 Network of probe testing bench
49
Zout
VNA has initial 50Ω output impedance, the cables and probes network has
complex input impedance Zin  X1  jY1 . In order to eliminate the complex part, an extra
matching network is added between the VNA and probes & cables. Assuming the
matching network has impedance Zm  X 2  jY2 , it should have relation with VNA and
probe & cable as
Zn  (Zm  Zp)*  ( X1  X 2 )  j (Y1  Y2 )  50
eq 5.1
Then the matching network complex value is
Zm  50  X1  jY1 when X 1  50
Zm  X1  50  jY1 when X 1  50
The total output impedance of testing bench equals to 50Ω. The function of system
calibration is to eliminate the complex part of cable and probe by computer calculation to
achieve 50Ω output system.
5.2.2 System calibration procedure
For two port calibration, HP8720B Vector network analyzer has three main steps:
reflection, transmission and isolation. The calibration substrate is CS-5 picoprobe. The
calibration contact substrate see figure 5-4.
A. Reflection steps:
1) Open: lift off the probe in free space without any contact. This step measures the cable
and probe impedance without load
2) Short: contact the probe to short trace on calibration substrate. Ground and signal line
is shorted together. This step measures the short circuit response of the total network
50
3) Load: contact the probe to load trace on substrate. A 50Ω load is loaded between
signal and ground. This step to measures the response with load impedance of 50Ω
B. Transmission steps:
For one port calibration, this step can be ignored. Reflection calibration computes
the impedance matching of each port separately. For two ports, they should be connected
together to balance the input and output ports. Transmission steps include forward
matching through and reverse matching through from port 1 to port 2.
Figure 5-4 Calibration left short, mid load, right transmission
51
Figure 5-5 Network analyzer before and after calibration S21
Figure 5-5 shows the effect of system calibration. Two ports are shorted with each
other. In ideal situation and lossless system, all RF power flow from port1 to port2
without dissipation. The S21 log magnitude should be 0dB means no power loss. Before
calibration, S21 is above 0dB and has higher loss after 15 GHz. Since the transmission
line is passive system, S21 cannot be higher than 0dB. There must be unexpected energy
flow into the passive system. This noise signal will distort the measurement accuracy.
After calibration, S21 curve has flat and smooth response and approximates to 0dB,
which expresses energy flow to port 2 with low loss.
5.3 Measurement results and analysis
Band pass filters are fabricated under three different conditions. There are two
wafers being processed and three samples tested. One is fabricated on 400μm sapphire
substrate without BST and backside gold coating, the other is fabricated on the same
52
substrate with 560nm thickness backside gold coating, and the third sample is fabricated
on high resistivity silicon wafer deposited by 0.25μm thickness BST thin film without
backside coating. The three samples are tested at room temperature and without DC bias.
5.3.1 Measurement results
Figure 5-6 shows the comparison results of band pass filter based on sapphire and
high resistivity silicon wafer. High resistivity silicon wafer is deposited by 0.25μm
thickness BST film. Sapphire substrate has no BST deposited.
(a) S11parameter
53
(b) S21 parameter
Figure 5-6 Comparison of band pass filter on BST and no BST.(a) S11 comparison (b) S21
comparison
Fabricated device shows the center frequency of band-pass filter on BST wafer is
8GHz. The 3dB down cutoff frequency is at 7.4GHz and 8.6GHz. The bandwidth is
around 1.2GHz. The Quality Factor can be calculated as
Q
f 0 8GHz

 6.7
f 1.2GHz
eq5.2
The insertion loss in the pass band is -5dB. S11 parameter shows the minimum return
loss is -9dB at 8.1GHz.
Device fabricated on sapphire wafer without BST shows the center frequency at
9GHz. The 3dB down cutoff frequency is at 8.3GHz and 9.8GHz. The bandwidth is
around 1.5GHz. The quality factor is 6. The insertion loss in pass-band is -5.379dB and
the minimum return loss (S11) is -8.7dB at 9.2GHz. Center frequency of filter with BST
54
is 1GHz lower than filter without BST. The quality factor worsened to 5.3 and the
bandwidth is higher by 0.3GHz.
Metalized filter has extra boundary condition on the backside. Figure 5-7 shows
comparison of filter with backside ground and without backside ground. Both of these
samples are diced from same sapphire wafer without BST thin film
(a) S11 parameter
55
(b) S21 parameter
Figure 5-7 Comparison of backside metalized and non-metallized (a) S11 parameter (b)
S21parameter
Filter with backside metallization has lower return loss than filter without
metallization before 9.7GHz. The minimum return loss of metalized sample is -10.57dB
at 9.05GHz. The minimum return loss of non-metalized sample is -8.735dB at 9.2GHz.
The center frequency of metalized sample is at 8.76GHz, the bandwidth is 1.4GHz and
the quality factor is 6.25. The center frequency of non-metalized sample is at 9.124GHz,
the bandwidth is 1.4GHz and the quality factor is 6.1.
Figure 5-8 is the comparison between measured results on high resistivity silicon
with BST deposition and EM simulation with BST εr of 500.0
56
(a)
(b)
Figure 5-8 Comparison between real and simulation result on BST
Center frequency between simulation and measured result has 1.8GHz difference.
Bandwidth has 0.8GHz difference and quality factor has 10 differences. Real
measurement data shows the fabricated devices have higher insertion loss in pass band
and lower quality factor. The center frequency is 1.8GHz lower than design expectation.
57
Figure 5-9 S11 Smith chart of BST vs no BST band-pass filter (5-12 GHz)
S11 Smith Chart shows the strongest coupling of the filter happens at each center
frequency, and filter with BST thin film has higher impedance than filter without BST at
that frequency. It is caused by more capacitance due to the presence of BST thin film.
5.4 Conclusion
Although measured and plotted S21 curves show the devices has band pass filter
behaviors, the fabricated filter doesn’t achieve the design expectation. The center
frequency of pass band is 1.8GHz lower than design. And the quality factor is low. The
58
bandwidth is 0.8GHz wider than design and the insertion loss is almost 4dB higher than
design. The reasons cause these can be concluded below
1). Low coupling capacitor
Since the insertion loss in pass band is 4dB higher than design, which means the coupling
between two resonators is low. To improve it, the third hairpin resonator can be added
between these two resonators to increase the coupling capacitance [15]. The other method
is to increase the space between coupled line and ground to avoid power coupled to the
ground during the transmission.
2). Low quality inductor
The lumped element circuit shows inductance has significant effect on the Q factor of
band pass filter. Inductance is determined by the electrical length of hairpin strip line.
Adjusting the ratio of inductance will improve the frequency response in pass band.
3). Difference between simulation and real measurement condition
In simulation, all conditions are assumed to be ideal. The conductor is perfect conductor
with zero thickness. The real fabricated device has 1μm thickness metal.
If the
metallization is not uniform or the conductor surface is rough, it will increase the signal
attenuation during the transmission.
Filter with BST has lower center frequency than filter without BST. It proves that
BST thin film can significantly change the center frequency of filter. If DC bias is applied
to the filter, the center frequency will shift to high frequency with the decreasing of
dielectric constant.
59
There is no significant difference of frequency response between metalized filter
and non-metalized filter. The thickness of sapphire is 400μm which is much thicker than
the BST, and it has low dielectric constant (9.7) and low loss tangent (0.005). For that
reason, substrate backside RF energy is very low.
60
CHAPTER VI
SUMMARY
The design procedures of an X-band CPW Chebyshev band-pass filter from
lumped elements to real Coplanar Waveguide structure are presented in this thesis. The
simulation results of each step illustrate the design achieves the requirements. There are
three different samples of Chebyshev hairpin band-pass filter being fabricated and
measured. Dimension of the CPW Chebyshev hairpin band-pass filters are 2400µm by
2420µm. The miniaturization goal is accomplished. Two of the samples are based on
400µm thick sapphire substrate without BST. The third sample is fabricated on high
resistivity silicon substrate with 0.25µm thick BST.
The center frequency of band-pass filter based on sapphire substrate without BST
is 9GHz. It is 1GHz lower than design requirement. Center frequency of band-pass filter
on high resistivity silicon with BST thin film is 8GHz. For all of the samples, the
bandwidth is fixed at 1.2GHz and the shape of S21 curve is almost the same. The
insertion loss in pass-band is 5dB, which is much higher than 1dB. The Quality factor of
filter is around 6.
61
The real fabricated filters don’t achieve design requirements. The center
frequency shifts 2GHz to lower spectrum. The insertion loss in pass-band is 4dB higher
than designed parameter. Quality factor of 10 is lower than simulation result. In passband, Chebyshev’s ripples characteristic doesn’t exist. According to the simulation, the
concept of improvement can be listed as follows

Building more accurate lumped and strip line models of the hairpin resonator to
find the best ratio between L1, L2 and L3 (figure-4-20). This ratio determines the
center frequency of pass-band and the edge frequency response.

Decreasing the gap of hairpin coupled line to increase the coupling capacitors. It
can shrink the bandwidth and improve the high frequency edge.

Decreasing the gap between two resonators to reduce the insertion loss in passband.

Redesign the shunt line between hairpin resonator and ground.
BST thin film shifts the center frequency of band-pass filter about 1GHz,
however, S21 curve maintains the same insertion loss and bandwidth. This phenomenon
proves that BST can expand the working frequency of the band-pass filter without
distortion. If the external DC bias is applied, the center frequency would shift to the
higher frequency (figure 4-17).
Because of simulation environment and parameter settings, measurement results
have huge difference with simulation results. For example, in simulation, the conductor is
62
set as perfect conductor and the transmission line is a lossless system. In real case,
because of the metallization quality and conductor roughness surface, parasitic capacitors
or inductors enhance the pass band insertion loss and distort the edge frequency response.
For single layer microstrip structure, AWR simulation results are reliable. This can be
proved by the Agilent Advance Design System (ADS) (figure 6-1, 6-2). For CPW
structure, AWR and ADS has different results because ADS uses slot structure to
simulate CPW. The comparison of two software simulation results illustrates that
Chebyshev band-pass filter design is following the characteristic till step 6 (microstrip
structure). The distortion happens in step 7 (converting the microstrip to CPW). ADS
simulation results of CPW band-pass filter are closer to the real measurement results. A
more accurate simulation method of AWR for CPW structure should be found.
Otherwise, CPW structure simulation results cannot be trusted in AWR. The further
research can be focused on how to convert microstrip structure to CPW structure without
distortion.
Figure 6-1 3D view of ADS band-pass filter simulation structure
63
Figure 6-2 Microstrip structure simulation S-parameter
Figure 6-3 3D view of CPW structure ADS
64
Figure 6-4 S-parameter plots of CPW band-pass filter (ADS)
Although the measurement results are not ideal and expected, this research helps
me to review and practice the knowledge of RF design which is obtained from classes.
An analog band-pass filter design procedure is developed in this research
65
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