10-SECTION, 6 TRANSMISSION-ZERO DIELECTRIC RESONATOR BAND-PASS
FILTER AT 1.9 GHZ WITH INNOVATIVE CROSS-COUPLING TECHNIQUES FOR
CO-CHANNEL INTERFERENCE REJECTION
Syed Junaid Hossain
B.S., California State University, Sacramento, 2006
THESIS
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
ELECTRICAL AND ELECTRONIC ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
SPRING
2010
© 2010
Syed Junaid Hossain
ALL RIGHTS RESERVED
ii
10-SECTION, 6 TRANSMISSION-ZERO DIELECTRIC RESONATOR BAND-PASS
FILTER AT 1.9 GHZ WITH INNOVATIVE CROSS-COUPLING TECHNIQUES FOR
CO-CHANNEL INTERFERENCE REJECTION
A Thesis
by
Syed Junaid Hossain
Approved by:
__________________________________, Committee Chair
Milica Markovic, Ph.D
__________________________________, Second Reader
Preetham Kumar, Ph.D
__________________________________, Third Reader
Mr. Jerry Roberds
____________________________
Date
iii
Student: Syed Junaid Hossain
I certify that this student has met the requirements for the format contained in the
University format manual, and that this thesis is suitable for shelving in the Library and
credit is to be awarded for the thesis.
__________________________, Graduate Coordinator
Preetham Kumar, Ph.D
Department of Electrical and Electronic Engineering
iv
___________________
Date
Abstract
of
10-SECTION, 6 TRANSMISSION-ZERO DIELECTRIC RESONATOR BAND-PASS
FILTER AT 1.9 GHZ WITH INNOVATIVE CROSS-COUPLING TECHNIQUES FOR
CO-CHANNEL INTERFERENCE REJECTION
by
Syed Junaid Hossain
The objective of this thesis is to design, simulate and fabricate a dielectric resonator
band-pass filter to operate at a center frequency of 1.905 GHz with a narrow bandwidth
of 8.0 MHz and 60 dB rejection ± 1 MHz from the pass-band edge. In this thesis, I will
be designing this band-pass filter with the aid of innovative cross coupling techniques
between non-adjacent resonators to produce finite transmission zeros at the desired
rejection frequencies. This filter will be utilized in the wireless industry where colocation interference between neighboring cell sites is causing an issue. The aim is to
achieve the 60 dB rejection whilst maintaining the 1.5 dB insertion loss and 15 dB return
loss over the pass-band frequencies. Various simulation programs and machines will be
used to design, develop and fabricate the band-pass filter. The emphasis will be to
maintain the insertion loss, return loss and rejection over the temperature range 0 to 70°C
by use of a high Q dielectric resonator and temperature compensated cross couplings.
_______________________, Committee Chair
Milica Markovic, Ph.D
_______________________
Date
v
ACKNOWLEDGMENTS
I wish to take this opportunity to give my sincere thanks to everyone that has contributed
and inspired me to complete this thesis. I would like to thank the Department of Electrical
and Electronic Engineering for giving me the chance to work on this thesis. I would like
to thank Dr. Preetham Kumar, Graduate Co-ordinator at California State University,
Sacramento and my Committee Chair, Dr. Milica Markovic, professor at California State
University, Sacramento, in taking the time, patience and interest in guiding me through
the thesis. I would also like to thank my parents and wife in supporting and inspiring me
during my thesis.
I would like to give special thanks to my mentor, Mr. Jerry Roberds, of whom I dedicate
this thesis to, for his knowledge, guidance and belief in me as a Microwave Engineer.
vi
TABLE OF CONTENTS
Page
Acknowledgments....................................................................................................... vi
List of Tables .............................................................................................................. ix
List of Figures ............................................................................................................... x
Chapter
1. INTRODUCTION .................................................................................................. 1
2. BACKGROUND .................................................................................................... 5
2.0 Unloaded Dielectric Resonator … ................................................................... 5
2.1 Loaded Dielectric Resonator in Unit Cavity ................................................... 7
2.2 Electromagnetic Fields Supported by Dielectric Resonators ........................ 10
2.3 Temperature Stability of Dielectric Resonator Filters ................................... 12
3. GOALS ................................................................................................................. 14
3.0 General Design Goals .................................................................................... 14
3.1 Electrical Specifications ................................................................................ 16
3.2 Mechanical Specifications ............................................................................. 17
4. ELECTRICAL DESIGN OF DIELECTRIC RESONATOR FILTER ................ 18
4.0 All-pole Filter Synthesis ................................................................................ 18
4.1 Geometric Filter Synthesis with Finite Transmission Zeros ......................... 20
4.2 Dielectric Resonator Filter Synthesis with Finite Transmission Zeros ......... 26
4.3 Electrical Implementation of Finite Transmission Zeros .............................. 29
4.4 Determination of Coupling Matrix ................................................................ 35
5. MECHANICAL DESIGN OF DIELECTRIC RESONATOR FILTER .............. 38
5.0 Unit Cavity Design ........................................................................................ 38
5.1 Complete Filter Cavity Design ...................................................................... 40
5.2 Dimensional Tolerance Analysis ....................................................................44
5.3 Design of Input and Output Coupling Structures ...........................................46
5.4 Design of Cross Coupling Structures .............................................................48
vii
6. DEVELOPMENT PROCESS............................................................................... 53
6.0 Measurement Setup ........................................................................................53
6.1 Unit Cavity Q Measurement .......................................................................... 54
6.2 Iris Development ........................................................................................... 63
6.3 Tuning Methods ............................................................................................. 65
6.4 Temperature Testing .......................................................................................67
7. CONCLUSIONS................................................................................................... 70
References ................................................................................................................... 72
viii
LIST OF TABLES
Page
1.
Table 1 Electrical specifications for band-pass filter given by Provider A…….. 16
2.
Table 2 Mechanical specifications of filter.………………………………...….. 17
3.
Table 3 Phase relationships for lumped-element prototype elements [1] ……… 32
4.
Table 4 Total phase shifts for non-adjacent transmission-zeros ……………….. 33
ix
LIST OF FIGURES
Page
1.
Figure 1 10-section, 6-Transmission-Zero Dielectric Resonator Band-pass Filter
………………………………………………………………………………........ 3
2.
Figure 2 Unloaded Cylindrical Dielectric Resonator ………………………….... 6
3.
Figure 3 Dielectric Resonator in Unit Cavity ………………………….………... 7
4.
Figure 4 Electric and Magnetic Fields in a cylindrical dielectric resonator ….... 11
5.
Figure 5 Infinite Q, all-pole band-pass filter equivalent circuit ….………...….. 18
6.
Figure 6 Infinite Q, all-pole band-pass filter ….………………….......................19
7.
Figure 7 Metallic resonator quality factor Vs. coaxial line impedance [11] …... 23
8.
Figure 8 Method 1: Increasing bandwidth of the filter ……………………....… 24
9.
Figure 9 Band-pass filter transmission and return loss simulation …....……..… 26
10.
Figure 10 Band-pass filter passband insertion loss …………………………….. 27
11.
Figure 11 Band-pass filter Smith Chart simulation of return loss ………….….. 27
12.
Figure 12 Band-pass filter group delay simulation …………………………..… 28
13.
Figure 13 Dielectric resonator band-pass filter layout …………………..…...… 30
14.
Figure 14 Chebyshev lumped-element equivalent circuit …………………..…. 30
15.
Figure 15 Coupling tuning of dielectric resonators with field orientations ….… 31
16.
Figure 16 Coupling and routing diagram of dielectric resonator band-pass
filter..……………………………………………………………………………. 35
17.
Figure 17 Generalized coupling matrix of 10-th order band-pass filter …....….. 36
18.
Figure 18 Synthesized coupling matrix of the dielectric resonator band-pass filter
………………………………………...…………………………………....….... 37
x
19.
Figure 19 Dielectric resonator unit cavity measurement [5] ……………........... 39
20.
Figure 20 Inefficient Cavity Layout for band-pass filter …………………......... 42
21.
Figure 21 Open Space Cavity Layout for band-pass filter ……………..…….... 42
22.
Figure 22 Optimum complete cavity layout for band-pass filter ……………..... 43
23.
Figure 23 (a) Largest coupling (b) Lesser coupling than (a), (c) Least coupling..47
24.
Figure 24 Example of low-side zero produced in dielectric resonator filters ...... 50
25.
Figure 25 Example of high-side zero produced in dielectric resonator filters …. 50
26.
Figure 26 Measurement setup of dielectric resonator band-pass filter …...……. 53
27.
Figure 27 Initial wire placement for critical coupling …...…………………….. 55
28.
Figure 28 Using tuning screw to short resonator ……………………..………... 56
29.
Figure 29 Polar chart with calibrated frequency and span [11]……………........ 56
30.
Figure 30 Normalized response with marker at desired center frequency ……... 57
31.
Figure 31 Over-coupled: Probe too long/too close to resonator …….................. 58
32.
Figure 32 Under-coupled: Probe too short/too far from resonator .……………. 58
33.
Figure 33 Shortening of wire for critical coupling adjustment ………………… 59
34.
Figure 34 Optimum critical coupling in polar format ……………….................. 59
35.
Figure 35 Optimal critical coupling in log-mag format ………………………... 60
36.
Figure 36 Q-measurement searching for notch frequency ………………….….. 61
37.
Figure 37 Developed and tuned dielectric resonator filter measured response ... 65
38.
Figure 38 Downward temperature swing measured filter response (0ºC) ……... 69
39.
Figure 39 Upward temperature swing measured filter response (70ºC) ……….. 69
xi
1
Chapter 1
INTRODUCTION
As the Federal Communications Commission (FCC) tightens the frequency allocation
bands for cell phone providers, the need for “brick wall” filters becomes increasingly
large. Neighboring cell sites cause co-location interference where Provider A’s frequency
band is almost contiguous to Provider B’s frequency band. In other words, the usability
of Provider A’s passband is degraded if the power in Provider B’s pass-band is not
sufficiently attenuated. Typically the passband frequency separations are less than a few
MHz.
To sufficiently attenuate Provider B’s passband frequencies while aiming to
preserve Provider A’s passband frequencies with minimum loss, a high quality factor
filter is needed. Over the years, microwave band-pass filters have been designed in
various topologies such as waveguide, combline or cavity structure. In cases where a very
sharp rolloff is required, transmission zeros are introduced with the use of non-adjacent
resonator couplings (cross-couplings). In modern day filter design, for narrow bandwidth
band-pass filters, this is often implemented with a dielectric resonator filter with crosscouplings. Dielectric resonators offer compact size, temperature stability and the high
quality factor necessary for this type of design. The filter is synthesized with finite
transmission zeros placed at Provider B’s passband frequencies to attenuate unwanted
emissions. A microwave dielectric resonator band-pass filter described in this thesis deals
with the situations mentioned above.
2
In 1968, S.B. Cohn implemented the first high-Q dielectric resonator band-pass
filter and his exploratory studies paved the way for “brick-wall” filters [3]. In the recent
past, dielectric resonator filters have been used widely in mobile communication systems,
radar and satellite [15] due to their high Q, compact size and temperature stability. They
offer high selectivity in narrow bandwidth applications with low insertion loss. Dielectric
resonator filters have been developed in multi-mode [4], mixed-mode [8] and singlemode cavity [9] applications. Despite multi-mode and mixed-mode dielectric resonator
cavity filters providing low loss and smaller volume, their inferior spurious transmissions
and high-cost manufacturing keeps them a design rarity [7].
This thesis deals with the innovative cross couplings used to design and develop
the dielectric resonator band-pass filter as shown in Figure 1. The cross-couplings that
will be used are both temperature compensated and tunable, facets that many designs in
the past have failed to achieve. This will be discussed in detail in Chapter 5.4 which
entails how the cross coupling structures produce low side and high side finite
transmission zeros by changing their orientations.
3
Figure 1 10-section, 6-Transmission-Zero Dielectric Resonator Band-pass Filter
Chapter 1 focuses on an introduction of the report and the purpose of the filter in
the thesis. Chapter 2 reviews current state of the art and gives a background into loaded
and unloaded temperature compensated dielectric resonators. Chapter 3 deals with the
goals of the thesis and what is set out to achieve by giving the electrical and mechanical
specifications of the band-pass filter. Chapter 4 focuses on the electrical design and
simulation of ideal filters and the process involved in reaching the conclusion to use a
dielectric resonator filter, detailing the coupling matrix used for development. Chapter 5
describes the mechanical design of the filter, including the unit cavity design, the
complete cavity design of the filter and the design of the input/output and innovative
cross coupling structures. Chapter 6 deals with the development of the band-pass filter
including the measurement setup, the iris development using the coupling matrix derived
in Chapter 4, the temperature drift measurements of the filter and the final electrical
performance of the filter after being optimally tuned for return loss and transmission.
4
Chapter 7 of the thesis concludes the project and the directions of future work,
summarizing the major hurdles overcome by the design.
5
Chapter 2
BACKGROUND
2.0 Unloaded Dielectric Resonator
In 1939, R.D. Richtmeyer discovered dielectric resonators and his first exploratory
studies on the resonant frequency of various modes began two decades later.
A dielectric resonator filter uses ceramic dielectric “pucks” as resonators to form
a multi-section filter. Dielectric resonators have a high dielectric constant and a low
dissipation factor, which produces a high quality factor and in-turn gives a low insertion
loss measurement over the filter’s passband. Usually, dielectric resonators are inductively
coupled (magnetic field) and can be mounted on a microstrip network or inside a metallic
cavity. The physical dimensions of the dielectric resonator (puck), the cavity dimensions
of the puck’s housing and the dielectric constant of the puck’s material determine the
resonant frequency, which can be approximated by
fGHz 

34 D
  3.45

I r H
where I is the inner diameter of the resonator, D is the outer diameter of the

resonator and H is the height of the resonator as shown in Figure 2. The resonant
frequency formula is accurate within 2% when 0.5 < I/H < 2 and 30 < er < 50 [7].
(1)
6
Figure 2 Unloaded Cylindrical Dielectric Resonator
Dielectric resonators trap most of their energy inside the ceramic and approximate
a circular waveguide. There is little radiation loss in the dielectric puck as there is a large
difference in permittivity at the boundary of the resonator to the surrounding air. This
allows for the electromagnetic fields to be confined within the resonator and significantly
reduces radiation loss, in-turn increasing the Q factor, improving the insertion loss,
selectivity and interference from spurious modes. The puck is seated on a ceramic or
plastic support, which determines its position in the cavity of the housing.
7
2.1 Loaded Dielectric Resonator in Unit Cavity
The common materials used for dielectric resonators contain titanium dioxide (Ti02),
titanates and zirconates, glass-ceramic systems, ferrites and ferroelectrics. Due to these
complex mixtures, the Q factor typically varies with frequency. When measuring the Q of
the resonator, the cavity, as seen in Figure 3, should be at least 1.5 times larger than the
outer diameter of the dielectric resonator. To minimize the spurious mode interference,
the H/D ratio should be 0.3 to 0.5, where H is the height and D is the outer diameter of
the resonator, which can also be calculated by
D
12.873
f o  r
(2)
where fo is the center frequency of the resonator in GHz and εr is the resonator

material’s dielectric constant [7].
Metallic Housing
A
B
C
G
D
F
E
A – Ultem Tuning Screw
B – Metallic Tuning Nut
C – Ceramic Tuning Disk
D – Ceramic Dielectric Puck
E – Ceramic Dielectric Standoff
F – Metallic Coupling Wire
G – SMA Connector
Figure 3 Dielectric Resonator in Unit Cavity
8
The use of a low loss support and a bent coaxial probe to critically couple to the
puck also helps in keeping the center frequency of the resonator “true”. When these
conditions are met, the resonant frequency of the dielectric resonator approximates to
fo 
8766
1


1
 3


2
r     D H 3 



3




(3)
where fo is the resonant frequency in MHz, D is the outer diameter of the resonator in

inches and H is the height of the resonator in inches. For minimum loss and maximum Q
factor the resonators are placed in the center of the cavity [7]. The Q factor is inversely
proportional to the loss tangent and also to the resonator’s bandwidth. This is the reason
for narrow band applications possessing high Q factors. The Q factor is a measure of the
energy lost compared to the energy stored in the magnetic fields of the resonator. The
unloaded Q factor, Qu, is the Q factor that accounts only for internal losses in the filter. It
is due to the losses in the cavity and the resonator and is defined as
Qu 
 uW
Pu
(4)
where  u is the resonant angular frequency in radians, W is the stored energy in

Joules and Pu is the internal power dissipation in Watts.
 The external Q factor, Qe, is the Q factor that accounts only for the external losses
inthe filter.
The loaded Q factor, QL, is the overall Q factor, which is the sum of the internal
and external Q factors.
9
The dielectric resonator Q factor, Qd, is inversely proportional to the loss tangent
and is defined by
Qd 
1
tan
(5)
where tan  is the dielectric resonator’s loss tangent given by


tan  
0r 

(6)
where r is the dielectric constant of the resonator,  0 is the dielectric constant of

the medium,  is the conductivity of the resonator and  is the angular velocity of the
 in radians/sec [7].
resonator



10
2.2 Electromagnetic Fields Supported by Dielectric Resonators
There are three categories of modes in a dielectric resonator: Transverse Electric (TE),
Transverse Magnetic (TM) and Hybrid Electromagnetic (HEM). Each mode can be used
for a particular application but the TE01δ mode is the most common mode used for filter
designs, since it is the lowest order mode to propagate through the dielectric resonator,
i.e. the fundamental mode. The TE01δ mode offers a planar layout, which is suitable for
mass production and ease of tuning. The index 01 refers to the electric field along the zaxis equal to 0 ( E z  0 ) and the magnetic field along the z-axis not equal to 0 ( Hz  0 ), as
seen in Figure 4. The index δ refers to the z variation of the TE01δ mode and is always
 one [7].
less than

In order to prevent electromagnetic energy from being lost, dielectric resonators
are placed in cavities of a metallic housing that completely surround the resonator as
described in Chapter 2.1. The cavity is often made of aluminum and silver plated for
optimum Q. The closer the cavity walls are to the dielectric resonator, the higher the
resonant frequency of the TE01δ mode becomes. Dielectric resonators come in many
shapes and sizes such as spheres and parallelepipeds. However cylindrical dielectric
resonators at a low frequency are the most common as seen in Figure 4.
11
Z
H
Figure 4 Electric and Magnetic Fields in a cylindrical dielectric resonator
Note how the magnetic field lines are concentric with the z-axis of the resonator
in Figure 4. Most of the electrical field (> 95%) and the magnetic field (> 60%) are stored
within the dielectric resonator when the relative dielectric constant is over 40 [7]. The
further the signal is from the dielectric resonator, the lower the signal energy distributed
in the air becomes, i.e. the weaker the magnetic field becomes.
12
2.3 Temperature Stability of Dielectric Resonator Filters
One of the main advantages of dielectric resonator’s over other resonator topologies is
their high temperature stability. The manufacturing of the ceramic material used for
dielectric resonators must be carefully controlled to maintain very low loss tangent and
temperature stability. The temperature coefficient of the resonant frequency, commonly
known as  f which includes the temperature coefficient of the dielectric constant,  , and
the thermal expansion of the dielectric material is of utmost importance when controlling

 coefficient of
the temperature characteristics of the dielectric resonator. The temperature
the resonant frequency is measured in parts per million, per degree Centigrade (ppm/°C).
This gives us the change in frequency of the resonator for a given temperature range. If
the frequency change is by the same fixed incremental amount as the temperature
changes, the temperature coefficient is a constant. The slope of the line (Hz/°C) is given
by
f 
f Hz 
1

f 0 MHz  T
(7)
where ∆f is the change in frequency of the filter due to temperature drift, fo is the

center frequency of the filter and ∆T is the change in temperature of the filter.
This frequency change includes the dielectric resonator in a cavity so the
measurement is also influenced by the housing. On the other hand, if the frequency vs.
temperature slope is non-linear, then we curve fit the data with an nth order polynomial
13
expression. If we take room temperature (25°C) as the nominal reference point, then the
data can be curve fit by
f
2
  f t  25  f t  25
f0
(8)
where τf is the linear component and τ’f is the non-linear component of the frequency
 [2].
change
Temperature stability of cross couplings to produce transmission zeros has been a
challenge in many filter designs. Typically Teflon has been used to form the dielectric of
the capacitor. Teflon is a soft material and can change its form over temperature by
expansion and contraction. The change of Teflon has a great impact on the conductive
material used to couple to the resonator (probe) and can alter the locations of
transmission zeros over temperature. If the end of the probe is placed close to the
resonator, the subtle change in the probe’s location with respect to the resonator has a
great impact on the coupling needed to produce the transmission zero [11]. For example,
if the probe is placed 0.100” from the resonator and moves a mere 0.010”, that is a 10%
change in the coupling value to produce the transmission zero and may place the filter
response out of specification. In order to deal with this issue, temperature-compensated
cross couplings will be implemented. The coupling probe is placed further away from the
resonator to increase the resonator to probe spacing, decreasing the probe’s percentage
change, in-turn, stabilizing the filter’s response over temperature.
14
Chapter 3
GOALS
3.0 General Design Goals
Due to Q limitations, low-loss requirements and stringent specifications, a dielectric
resonator cavity filter with cross-couplings will be chosen for this design. Transmission
zeros are implemented with cross couplings between non-adjacent resonators to achieve
sharp rejection requirements close to the passband. Depending on the sense, the
dimensions of the inductive or capacitive coupling structures, the material and the
configuration of the cross coupling with respect to the magnetic or electric field
distribution in the cavity, one can achieve low side and/or high side transmission zeros.
This 10-section, 6 Transmission-Zero Dielectric Resonator Band-pass Filter will
pass frequencies from 1901 MHz to 1909 MHz while maintaining a passband insertion
loss of less than 1.5 dB and reject lower and upper frequencies 1 MHz away from the
passband with 60 dB of attenuation. The filter will reject Provider B’s frequencies in the
reject band and pass Provider A’s passband frequencies. Design, synthesis, testing, and
development of the band-pass filter will be addressed in this effort. The development
process will entail determination of iris dimensions for in-line and non-adjacent cross
couplings, design of capacitive and inductive cross coupling structures, input and output
impedance matching lines, design and testing of puck (dielectric resonator) resonant
frequencies and temperature performance testing of filter. The filter will be optimally
15
tuned for best return loss (S11) and transmission loss (S21) to achieve customer
specification.
16
3.1 Electrical Specifications
The performance specifications that were given for the band-pass filter are shown in
Table 1. These specifications were given by Provider A to improve their signal
transmission by sufficiently attenuating Provider B’s frequencies by 60 dB, 1 MHz away
from Provider A’s passband edge frequencies.
Center Frequency (fo)
1905 MHz
Passband
 4.0 MHz (8.0 MHz wide)
Passband Insertion Loss
 1.50 dB
Return Loss

 15 dB (VSWR = 1.43:1)
Rejection

fo  1.0 MHz  60 dB
Group Delay

Over Passband  300 nsec
Operating Temperature Range 
(ºC)
0 to 
+70

Table 1 Electrical specifications for band-pass filter given by Provider A
Provider A provided the above electrical specifications for a band-pass filter that
rejects the co-channel interference they were experiencing from Provider B.
17
3.2 Mechanical Specifications
The customer’s mechanical design specifications for the filter can be seen in Table 2.
Provider A’s setup location for the band-pass filter calls for the following outline to be
achieved for indoor wall mounting.
Connector Type
SMAF
Package (inches)
< 13.00” X 7.00” X 3.00” (L x W x H)
Connector Location
All connectors on same surface
Mounting
Indoor Wall Mounted
Table 2 Mechanical specifications of filter
Provider A presented the above mechanical specifications for the band-pass filter.
The entire package, including all cavities, iris walls and connectors need to fit inside the
13.00” X 7.00” X 3.00” package outline. The package can be smaller than this but not
larger due to Provider A’s size restrictions at their base station. The connectors need to be
located on the same side of the housing as this is Provider A’s fixture methods in their
base station. The filter is an indoor, wall-mounted unit and hence does not need weather
seal or weatherproof paint. The connector type is to be a standard SMAF for the input
and output ports of the band-pass filter.
18
Chapter 4
ELECTRICAL DESIGN OF DIELECTRIC RESONATOR FILTER
4.0 All-pole Filter Synthesis
The first approach that was taken to design the band-pass filter was to use an infinite
quality factor geometric filter without the presence of transmission zeros (all-pole filter).
This approach allows for the determination of the maximum number of sections needed
to meet the electrical specifications given in Table 1. As can be seen in Figures 5 and 6, a
total number of 17 sections were needed via an all-pole filter synthesis using an in-house
synthesis program with no finite transmission zeros to meet the electrical specifications.
The reason this is a preliminary band-pass filter is because it is impossible to achieve an
infinite quality factor. However, 17 sections is now the maximum number of sections that
we can improve our design upon. In order to decrease the numbers of sections in the
band-pass filter all of the following needs to be addressed in the next synthesis phases:
 Introduction of Finite Transmission Zeros
 Introduction of a Realizable Q-Factor
 Adjustment of Design Bandwidth
Figure 5 Infinite Q, all-pole band-pass filter equivalent circuit
19
Figure 6 Infinite Q, all-pole band-pass filter
20
4.1 Geometric Filter Synthesis with Finite Transmission Zeros
A Geometric synthesis of a band-pass filter mirrors the center frequency about the
geometric mean of the filter. The geometric mean is the square root of the products of the
passband edges of the filter (fL and fH). Geometric mean representation is an optimum
method in beginning to design a filter and assumes that all capacitances and inductances
are ideal. (I.e. capacitors have no parasitic inductance and vice versa). The geometric
mean representation has a sharper low skirt due to the infinite frequency being at infinity
but is only visible in broadband applications (percent bandwidths greater than 40%). On
the other hand, a combline filter uses quarter-wave inductively coupled resonators and
has a sharper high skirt due to the infinite frequency being brought down to the quarterwave frequency of the filter.
A geometric center frequency calculation of the filter can be computed by
fC 
fL  f H
(9)
where fc is the centre frequency and fL and fH are the lower and upper -3dB, or
 equiripple cutoff frequencies, respectively [8].
The geometric mean of the dielectric band-pass filter calculated by (9) is 1904.99 
1905 MHz, which is the design and specified center or midband frequency of the band-

pass filter. The reason that synthesis by geometric mean representation was used rather
than a combline cavity representation is due to the following reasons:
 The band-pass filter is symmetric about the centre frequency in both insertion loss
and rejection specifications.
21
 In a combline design, the quarter wave frequency is about the quarter wave of the
center frequency of the filter and hence there are more zeros at this frequency,
which is closer to the upper edge of the passband giving a sharper upper skirt.
 The degree of this filter is 10 and since it has an even number of sections, the lowpass to band-pass transformation is antimetric and therefore there are more
transmission zeros at infinity than at DC.
The second approach to designing this band-pass filter was to minimize the number
of sections and simultaneously add transmission zeros in the upper and lower stopbands
of the filter. This is an iterative process and the intermediate steps will not be discussed.
Only the final outcome will be discussed and analyzed.
In order to get closer to meeting the specifications in Table 1, a coaxial cavity
filter was designed. A coaxial cavity filter uses a metallic rod as a resonator, which is
placed preferably at the center of a circular, square or rectangular cavity achieving
maximum Q and minimum loss characteristics. Air is used for the dielectric medium and
the filter size is usually larger than microstrip and stripline filters. Typically base stations
use air dielectric cavity filters.
The impedance of a coaxial cavity resonator (coaxial line) is calculated by
Z0 
138
r
log10
b
a
(10)
where r is the dielectric constant of the dielectric material, b is the outer diameter

of the coaxial line and a is the inner diameter of the coaxial line [11]. The maximum Q is
 by using a 77Ω resonator, which gives a b/a ratio of approximately 3.61. Hence
achieved
22
the diameter of the cavity must be 3.61 times the outer diameter of the coaxial resonator
[11].
The unloaded Q factor is calculated by two of the following formulae:
Qu 
27.3 td n sec  fGHz
I.LdB
QC  K  Binches 


fGHz
(11)
(12)
where, td (nsecs) is the group delay, fGHz is the frequency and I.L (dB) is the
insertion loss all used to calculate the conductor loss Q. This formula is the overall Q
measured in am actual filter and (12) is an approximation formula, where K is a constant
and dependant on the resonator dimensions. This formula is for a single resonator’s Q
factor. Approximating the coaxial-line attenuation vs. Q curve in Figure 7, the maximum
value of the curve at 77Ω is approximately 3400.
23
Figure 7 Metallic resonator quality factor Vs. coaxial line impedance [11]
If we assume that the capacitor Q is half the total Q of the resonator, with the
other half being the inductor Q, taking half this Q, we have
1700 
QC
Binches  fGHz
Rearranging (13) to get (12) gives us the real world unloaded Q factor of a

coaxial-line resonator, as can be seen from Figure 7. At this stage, there are several
simulations techniques we can perform in order to get closer to our band-pass filter
(13)
24
design; decrease the number of sections and increase the bandwidth to meet insertion
loss, decrease the number of sections and add finite transmission zeros, or combine the
above two ideas. If we perform the first method alone, the increase in bandwidth will
allow for the insertion loss to be met, however the filter will be too broad to meet the
rejection specification even with the addition of finite transmission zeros, as can be seen
in Figure 8.
Figure 8 Method 1: Increasing bandwidth of the filter
25
If we perform the second method alone, the introduction of finite transmission
zeros will allow for the rejection to be met, however the filter will be Q limited and won’t
meet the insertion loss.
26
4.2 Dielectric Resonator Filter Synthesis with Finite Transmission Zeros
Therefore, we attempt Method 3 in our design by adding finite transmission zeros and
increasing the bandwidth and/or unloaded Q factor to that of a dielectric resonator to
achieve the electrical specification in Table 1. In Figures 9-12, we see the band-pass filter
designed to meet insertion loss, rejection, group delay and return loss with design margin.
In order to design this band-pass filter, the unloaded Q factor was driven as high as
23,000. To achieve such a high Q, a metallic resonator band-pass filter cannot be used
and hence we need a dielectric resonator band-pass filter.
Figure 9 Band-pass filter transmission and return loss simulation
27
Figure 10 Band-pass filter passband insertion loss
Figure 11 Band-pass filter Smith Chart simulation of return loss
28
Figure 12 Band-pass filter group delay simulation
29
4.3 Electrical Implementation of Finite Transmission Zeros
Transmission zeros can occur either at DC, infinity or at finite frequencies. Transmission
zeros occur when the signal transmission between the source and the load is blocked.
They are placed outside the passband for improved selectivity and within the passband
for group delay equalization.
A Transmission zero at DC means that the degree of the filter has been increased
by one. We see these transmission zeros occur in high-pass and band-pass filters where a
greater number of zeros at DC gives a sharper lower skirt (higher selectivity) of the filter
in the lower stopband. A Transmission zero at infinity also increases the degree of the
filter by one and is used in low-pass and band-pass filters where a greater number of
zeros at infinity gives a sharper upper skirt. Cross couplings between non-adjacent
resonators produce finite transmission zeros. A Transmission zero at a chosen or arbitrary
finite frequency increases the degree of the filter by two. This is due to the extraction
process that takes place when “taking” a zero from DC or infinity and realizing it as a
parallel tuned circuit in series or a series resonator in shunt [11]. A series resonator stops
the signal transmission, as it becomes a short circuit to ground at the resonant frequency.
The dielectric resonator band-pass filter in this thesis can be seen in Figure 13.
The filter is draw from a top view. The red arrows inside the dielectric resonator
represent the electric field direction. The dots and crosses represent the magnetic field
orientation, where the dot is the magnetic field coming out of the page and the cross is the
magnetic field going into the page. Analysis of the field orientations and associative cross
30
couplings will be discussed in Chapter 5. A Chebyshev lumped-element equivalent
circuit as shown in Figure 14 represents the dielectric resonator band-pass filter in Figure
13.
Figure 13 Dielectric resonator band-pass filter layout
Figure 14 Chebyshev lumped-element equivalent circuit
The shunt inductors and capacitors in Figure 14, L1, C1, L2, C2, …, L10, C10, represent the
dielectric resonators. The inductors, L1-2, L2-3, …, L9-10, represent the irises between two
adjacent dielectric resonators . The capacitors, C2-4, C2-5, C1-5, C7-10 and C8-10, represent
the capacitive cross-couplings between non-adjacent dielectric resonators 2 and 4, 2 and
31
5, 1 and 5, 7 and 10, and 8 and 10, respectively and inductor, L1-6, represents the iris
cross-coupling between non-adjacent resonators 1 and 6. The irises between the two
resonating elements, which are represented by the series inductors, have both magnetic
and electric components, which are out of phase with each other. In other words, the total
coupling is the magnetic field minus the electric field. Hence, to increase the magnetic
field between two dielectric resonators, the magnetic field is toroidal in nature and the
metallic tuning screw used for coupling decreases the magnetic field and hence, the
overall coupling between the dielectric resonators as seen in Figure 15 [7].
Figure 15 Coupling tuning of dielectric resonators with field orientations
The resonance away from the passband (below and above) causes transmission
zeros to occur. In other words, a signal passing through a series or shunt inductor or
capacitor will undergo a phase shift at the opposite port. The phase shift approaches ±90
32
degrees. Table 3 illustrates the phase relationships for series inductors and capacitors and
shunt resonators below and above the passband.
Element Type
S21 (ø) approximation
Series Inductor
-90º
Series Capacitor
+90º
Resonator above passband
-90º
Resonator below passband
+90º
Table 3 Phase relationships for lumped-element prototype elements [1]
For the Chebyshev lumped-element prototype equivalent circuit of the dielectric
resonator filter in this thesis we refer to Figure 13 and Table 4.
Below the
Above the
Transmission
passband
passband
Zero
1-2-5
-90+90-90 = 90
-90-90+90=-90
1-5
+90
+90
Phase
In phase
Out of phase
2-4-5
+90+90-90 = +90
+90-90-90 = -90
2-5
+90
+90
Phase
In phase
Out of phase
High side TZ
Relationship
Relationship
High side TZ
33
2-3-4
-90+90-90 = -90
-90-90-90=-
2-4
+90
270=+90
Phase
Out of phase
+90
Relationship
Low side TZ
In phase
1-5-6
+90+90-90=+90
+90-90-90=-90
1-6
-90
-90
Phase
Out of phase
In phase
7-8-10
-90+90+90=+90
-90-90+90=-90
7-10
+90
+90
Phase
In phase
Out of phase
8-9-10
-90+90-90=-90
-90-90-90=-
8-10
+90
270=+90
Phase
Out of phase
+90
Low side TZ
Relationship
High side TZ
Relationship
Relationship
Low side TZ
In phase
Table 4 Total phase shifts for non-adjacent transmission-zeros
All the resonators that are associated with the cross coupling paths are denoted as
+90º or -90º for below and above passband resonance, respectively. The series inductors
are denoted as -90º and the series capacitors are denoted as +90º, as seen in Table 3 [1].
The summation of the phase shifts in each triplet and quadruplet path is compared with
34
the cross coupling paths for phase shifts to determine the transmission zero locations.
Note in Table 4, the transmission zeros occur when there is a phase mismatch. The phase
mismatch occurs when there are multiple paths from resonator to resonator and the signal
transmitted through is out of phase. There are six finite transmission zeros produced due
to phase mismatch relationships between non-adjacent resonators. There are three lowside transmission zeros and three-high side transmission zeros associated with the filter
orientation in Figure 13. The placement of these finite transmission zeros will depend on
the coupling matrix synthesis in further chapters that will allow for sharp rejection points
to occur close to the pass-band edge frequencies.
35
4.4 Determination of Coupling Matrix
The coupling matrix is a relationship between the polynomial coefficients of the transfer
function and the S21 from the coupling matrix. In general, the filter’s transfer function is
written as
1 P(s)
S21(s)  
 E(s)
(14)
where  epsilon is the ripple factor defined by

1


10
RL
10
(15)
1
where RL = Return Loss (dB), s is a complex frequency, E(s) is the N-th degree

Hurwitz
polynomial and P(s) is the characteristic polynomial containing the transmission
zeros [3]. A Hurwitz polynomial has its transmission zeros and reflection zeros in the left
half of the s-plane where its coefficients are all positive real numbers. For the coupling
and routing diagram of the dielectric resonator band-pass filter, refer to Figure 16.
Figure 16 Coupling and routing diagram of dielectric resonator band-pass filter
Note that in Figure 16, these are all the couplings that are in the 10-section dielectric
resonator band-pass filter. R1, R2, …, R10 represent the dielectric resonators. The
36
coupling matrix that is derived from Figure 16 can be seen in Figure 17. The C matrix is
a (N+2) X (N+2) matrix containing complex frequency variables and frequency
independent couplings. For the 10-section filter in this thesis, the C matrix would be a 12
X 12 matrix.
M 00

M10
M 20

M 30
M 40

M
C   50
M 60
M
 70
M 80
M
 90
M100
M
 110
M 01
M 02
M 03
M 04
M 05
M 06
M 07
M 08
M 09
M 010
M11
M 21
M12
M 22
M13
M 23
M14
M 24
M15
M 25
M16
M 26
M17
M 27
M18
M 28
M19
M 29
M110
M 210
M 31
M 41
M 32
M 42
M 33
M 43
M 34
M 44
M 35
M 45
M 36
M 46
M 37
M 47
M 38
M 48
M 39
M 49
M 310
M 410
M 51
M 61
M 52
M 62
M 53
M 63
M 54
M 64
M 55
M 65
M 56
M 66
M 57
M 67
M 58
M 68
M 59
M 69
M 510
M 610
M 71
M 81
M 72
M 82
M 73
M 83
M 74
M 84
M 75
M 85
M 76
M 86
M 77
M 87
M 78
M 88
M 79
M 89
M 710
M 810
M 91
M101
M 92
M102
M 93
M103
M 94
M104
M 95
M105
M 96
M106
M 97
M107
M 98
M108
M 99
M109
M 910
M1010
M111
M112
M113
M114
M115
M116
M117
M118
M119
M1110
M 011 

M111 
M 211 

M 311 
M 411 

M 511 
M 611 
M 711 

M 811 
M 911 

M1011
M1111

Figure 17 Generalized coupling matrix of 10-th order band-pass filter

The coupling matrix term, M0-0, denotes the coupling between the input connector and
itself. The coupling matrix term, M11-11, denotes the coupling between the output
connector and itself. All the diagonals of the matrix, Ma-a, except for M0-0 and M11-11,
denote the coupling of each resonator to itself. In general, the coupling matrix term, Ma-b,
denotes the coupling between resonator a, and resonator b. If the filter had no
transmission zeros and were an all-pole filter, the coupling matrix would be symmetric.
In Figure 18, using the in-house synthesis program, the coupling matrix for the
filter was created. Comparing Figures 17 and 18 the coupling between adjacent
resonators and non-adjacent resonators can be deduced. These coupling matrix values
will allow for the development of iris dimensions in Chapter 6.
 1
7.865
0
0
0
0
0
0
0
0
0
0 


1
6.858
0
0
0.154 0.582
0
0
0
0
0 
7.865
 0
6.858
1
4.210 0.690 3.121
0
0
0
0
0
0 


0
4.210
1
7.106
0
0
0
0
0
0
0 
 0
 0
0
0.690 7.106
1
3.756
0
0
0
0
0
0 


0
0.154
3.121
0
3.756
1
4.511
0
0
0
0
0 
C  
0.582
0
0
0
4.511
1
4.563
0
0
0
0 
 0
 0
0
0
0
0
0
4.563
1
3.787
0
3.141
0 


0
0
0
0
0
0
3.787
1
6.985 0.984
0 
 0
 0
0
0
0
0
0
0
0
6.985
1
6.045
0 


0
0
0
0
0
0
3.141 0.984 6.045
1
7.865
 0
 0
0
0
0
0
0
0
0
0
0
7.865
1 



37
Figure 18 Synthesized coupling matrix of the dielectric resonator band-pass filter
38
Chapter 5
MECHANICAL DESIGN OF DIELECTRIC RESONATOR FILTER
5.0 Unit Cavity Design
The design of the dielectric resonator (puck) unit cavity used in this filter is significantly
based on the vendor’s stock dielectric puck sizes. The puck size chosen for the design has
an outer diameter of 1.175” and an inner diameter of 0.410”. The puck stands on a
rexolite support that is 0.570” high and the puck thickness is 0.537”. A ceramic puck with
a hole in the center, i.e. a donut shaped puck, was chosen because it increases the
spurious free region of the cavity. This is due to the fundamental mode having a
minimum electric field at the center of the dielectric resonator, whilst the close spurious
modes have their maximum electric fields at the center. The cavity size of the dielectric
resonator housing needs to be less than half a wavelength, otherwise it will support a
waveguide mode. Also, the aspect ratio of the dielectric resonator cavity needs to be
chosen such that the higher order modes are as far away from the fundamental mode as
possible. The spurious mode that causes the greatest interference is the TM01 mode
because it has a stronger coupling through coupling irises and is very sensitive when
tuning the TE01δ mode. Hence, the cavity size was designed to be 2.265” x 2.315”, a
rectangular shape to maximize the Q. The puck frequency was chosen to be 1922 MHz,
17 MHz higher than the center frequency of the filter so tuning the resonator down in
frequency would be possible. The dielectric resonator’s allowed temperature coefficient
was +1.5 ppm/ºC.
39
A dielectric resonator design program [5] was used to confirm the measurements
and the results and can be seen in Figure 19. The Q factor given from the program was
33,175.
Figure 19 Dielectric resonator unit cavity measurement [5]
40
5.1 Complete Filter Cavity Design
Since the filter needs to be fit inside a certain volume, the mechanical design of the filter
is crucial in preserving the resonator Q and ease of assembly. The filter is a mass
production order and hence the assembly process needs to be precise and repeatable to
save time and cost.
The first step in designing the filter is to determine the cavity size. This process
has already been detailed in Chapter 5.0. Hence, the cavity size in this dielectric resonator
filter is 2.265” X 2.315”. The cavity was designed as a rectangular cavity to maximize the
quality factor.
The second step in the filter component design was to determine sufficient wall
spacing between cavities for cover screws. The adjacent cavities that will be coupled
together will have the same wall spacing as the non-adjacent and isolated cavities to keep
a uniform ground throughout the filter. The wall spacing needs to be thin enough to keep
the filter outline as small as possible but also thick enough to prevent RF leakage
between non-adjacent and isolated cavities, in-turn preventing loss of filter Q and in-turn
maintaining the sharpness in the rejection and minimize passband loss. A typical iris wall
thickness that is used throughout designs is 0.150”. This allows for a #4 cover hold-down
screw to be attached with sufficient spacing between the screw’s edge and the iris wall
preventing any breakthroughs from occurring. A #4 screw is readily found in many screw
house companies and is cheap and sturdy for maintaining good contact between the
housing and the cover.
41
The third and most difficult step is to layout the cavities in such a way where they
can be coupled effectively and efficiently to achieve the coupling matrix values found in
Chapter 4.4. The in-line couplings are conventionally placed perpendicularly to each
other so an iris magnetically couples two resonators together. Typically two adjacent
cavities are not coupled diagonally as the coupling is more difficult to achieve and hence
the iris becomes larger. The coupling matrix in Chapter 4.4, Figure 18, shows that there
are cross-couplings located between resonators 1 and 5, 1 and 6, 2 and 4, 2 and 5, 7 and
10, and 8 and 10. Hence the layout needs to consider these cross couplings locations and
the cavities need to be situated so that they are achievable. For example, if cavity 1 and 6
are more than one cavity away from each other diagonally, they will not be able to be
coupled effectively. On the other hand, if the cavities are placed too close each other to
allow for cross couplings, there will be “wasted”, empty space in the filter design and this
will make the design larger than the given outline. In Figures 20 and 21, we see some
examples of inefficient layouts. Figure 20 illustrates the situation where the cavities are
so far from each other that some of the cross couplings cannot be efficiently achieved,
and Figure 21 illustrates the cavities being too close to each other and there is open space.
42
Figure 20 Inefficient Cavity Layout for band-pass filter
Figure 21 Open Space Cavity Layout for band-pass filter
Hence, after some trial and deliberation, the optimum cavity layout that was chosen is
shown be Figure 22. This layout meets the customer outline. It has the adjacent cavities
43
in-line with each other, and it has the non-adjacent cavities directly coupled with the
input and output port connectors on the same side. Note in Figure 22 that the blue lines
represent the in-line resonator couplings, whilst the red lines represent the non-adjacent
cross couplings.
Figure 22 Optimum complete cavity layout for band-pass filter
Now that the preliminary layout has been chosen, the next step is to design the
holes that will hold down the cover to the housing, the design of the input and output
connectors and the tuning mechanism to tune the filter. The cover hold screws are chosen
as 4-40 X 5/16 screws meaning they are #4 diameter screws with 40 threads per inch and
are 5/16ths of an inch long. There are many conversion charts that one can refer to in
order to convert the diameter number to a measurement in inches. Basically the number is
multiplied by 0.013 and added to 0.060, giving 0.112” for a #4 screw.
44
5.2 Dimensional Tolerance Analysis
Dimension Tolerance Analysis can be a project on its own and hence in this thesis only
the basics will be discussed, as it is a very important topic in the design of filters. Since
we are dealing with microwave frequencies, a few thousandths of an inch can make a big
difference in overall performance. Tolerance analysis is a mechanical design issue but it
affects the electrical performance of filters due to issues encountered during assembly
and manufacturing.
Silver plating improves the conductivity of microwave energy and optimized
circuit Q. However, in tolerance design this has to be accounted for. The plating
thickness that is applied to the housings is very thin as the microwave signals only travel
in the uppermost surface of the cavity. Compensating for the plating thickness before and
after the process can go a long way in optimizing the filter design. For instance, if a
resonator and cover gap is a mere 25 thousandths of an inch and a silver-plating thickness
of 3 thousandths is added, the spacing is reduced by more than 10 percent. This may
seem trivial, however, reducing the spacing by 10 percent means increasing the
capacitance of the resonator by 10 percent, in turn making the resonator appear longer
and hence decreasing the resonant frequency. Depending on the design and the initial
depth of the tuning screw, this may be compensated by “backing-out” the tuning screw to
increase the frequency of resonance. However, in good filter design practice it is
optimum to design the resonator’s self-resonance as close as possible to the desired
frequency to maximize the quality factor, and reduce transmission loss. In this case, in
45
many instances, without a tuning screw, the self-resonance of the resonator may be too
low if tolerance design due to silver plating is not accounted for.
Another issue when dealing with tolerance design is in the assembly process of
the filter. In many cases parts may not fit together if they are at the edge of their
dimensional tolerance. This may be due to bad design techniques or mistakes overlooked
when designing, or may be due to the capability of machines and measuring tools used in
the process. When machining with a CNC machine, tolerances of one-tenth of a
thousandth of an inch can be designed. When machining with a manual lathe, the
machine is operated by a human not a computer. Human error has to be accounted for
and the experience of the machine’s operator in holding “tight” tolerances.
Another tolerance design issue may be inexperience. One may not realize the
importance and intricacy of tolerance design when dealing with microwave frequencies.
It is recommended to consult with textbooks and more importantly, with experienced
machinists and engineers as to what is possible when tolerancing parts.
46
5.3 Design of Input and Output Coupling Structures
The input and output coupling structures usually are the same because the input and
output coupling bandwidths are the same. Since we are dealing with dielectric resonators,
the coupling structures vary compared to metallic resonator filters. In metallic resonator
filters the further up the resonator the coupling structure is tapped, the greater the
coupling. This is due to the coupling mechanism being primarily inductive. Inductive
coupling is magnetically induced due to current values producing a magnetic field around
the wire, meaning high current and low voltage. The top of the resonator has a very high
voltage and low current, and hence couples tighter than the bottom of the resonator,
which is higher in current density. However, in dielectric resonator filters we refer to
Figure 4. Since most of the electromagnetic field lines are confined within the ceramic
puck and the field lines are torodial in nature, the center of the puck has the greatest
magnetic field density. If the wire is brought closer to the puck perpendicular to the
center x-y axis, the coupling will increase. However, if the wire is pushed up or down and
also brought closer to the puck, depending on the proximity of the wire to the puck with
respect to the height of the wire, the coupling will either increase or decrease. Figure 23
below is a good visual aid for the explanation above.
47
Figure 23 (a) Largest coupling (b) Lesser coupling than (a), (c) Least coupling
Note that in Figure 23(b), the coupling wire is higher than in Figure 23(a) and due
to being a dielectric resonator, the electromagnetic field lines are ‘weaker’ and the
coupling decreases. It is worth noting that if the wire is pushed down rather than up, as in
Figure 23(b), the coupling decreases even more so due to the resonator standoff. The
resonator standoff’s dielectric constant is much less than the dielectric puck and hence
the signal is weakened. In Figure 23(c), the coupling decreases further because the wire is
further away from the resonator. To achieve the desired input/output coupling the wire is
positioned brought closer to the resonator parallel to the puck’s x-y axis. If the wire gets
too closer to the resonator, the wire can be lengthened so that it can be pushed away from
the resonator to keep the coupling value the same. The goal objective is to achieve an
input/output coupling where the wire is assembled almost parallel to the cavity wall and
needs little adjustment. This helps in the tuning process and allows for the setting of the
input/output coupling.
48
5.4 Design of Cross Coupling Structures
Coupling probes have been used to produce the opposite sense to in-line coupling values
to produce transmission zeros outside the passband, however, these probes are mostly untunable [16]. The coupling probes produce different coupling senses when implemented
on a triplet vs. a quadruplet. In a triplet section, coupling probes have typically been used
to form a negative (inductive) coupling between two non-adjacent dielectric resonators.
In a quadruplet section, coupling probes have typically been used to form a positive
(capacitive) coupling between two non-adjacent dielectric resonators [16]. These
coupling probes are placed close to the dielectric resonator to achieve the coupling
necessary to produce transmission zeros and once again, are mostly un-tunable.
Non-adjacent coupling has been used with many capacitor and inductor
topologies. For inductance cross coupling, drop loop wires grounded to the housing or
cover have been used to form a positive coupling for transmission zero implementation.
For capacitive cross coupling, many forms of Teflon based geometries have been used.
For instance, a solid aluminum cylinder placed inside a Teflon sleeve has been used to
form a capacitive cross coupling to implement a low and high side transmission zero in
both metallic and dielectric resonator topologies, respectively [16]. Triplet and quadruplet
sections are regarded as the basic building blocks to form transmission zeros. According
to the resonator topology used, the varying building blocks are able to produce low side
and high side transmission zeros simultaneously.
49
In a regular metallic resonator configuration, the magnetic field that is induced in
each resonator is opposing the adjacent resonator. This is the “natural” way a magnetic
coupling works in a transcendental resonator format. However, in a dielectric resonator
the magnetic field in a dielectric resonator cavity filter is toroidal and hence we see this
“negative” coupling result.
This is the basis of the innovation in this thesis; the unique cross-coupling
structures were developed in order to produce finite transmission zeros close to the passband. A generic example of the cross coupling structures used are shown below. The
result is that by changing the wavelength and sense of the coupling, a “positive” or
“negative” coupling between non-adjacent resonators is achieved to produce a finite
transmission zero above or below the passband.
Figure 24 has a low-side transmission zero produced by an iris (magnetic) cross
coupling between non-adjacent resonators 1-3. The reason that the dielectric resonator
filter has a low-side zero with a positive cross coupling sense is due to the “negative”
nature of the in-line couplings with resonators 1-2, 2-3 and 3-4. Since the in-line
couplings are “negative”, they are opposite in sense to the cross-coupling and hence
produce a finite transmission zero on the low side of the passband. In Figure 25, we see
the same concept applied. The cross couplings are the same senses and they produce a
high-side transmission zero.
50
Figure 24 Example of low-side zero produced in dielectric resonator filters
Figure 25 Example of high-side zero produced in dielectric resonator filters
51
In general, if the cross coupling capacitor wire is in the shape of a “V” and is coupled
between a triangular section, the wavelength is the determining factor on the sense of the
cross-coupling. If the length of the wire is greater than half the wavelength at the filter’s
center frequency, the coupling is deemed “negative”. If the wire was re-shaped to an inline structure and was still greater than half the wavelength at the filter’s center
frequency, the coupling is deemed “positive”.
For a quad-section, if the cross coupling capacitor wire is in the shape of an “L”
and the wire is greater than half the wavelength at the filter’s center frequency, the
coupling is deemed “negative”. If the wire was re-shaped to an “S” structure and was still
greater than half the wavelength at the filter’s center frequency, the coupling is deemed
“positive”.
The 1-6 iris cross coupling is optimized in the iris dimensioning section and is
tuned with a 10-24 X 1.000” silver-plated tuning screw. However, the 1-6 cross coupling
is a positive cross coupling, yet still produces a low-side transmission zero. This is due to
the “negative” nature of the in-line couplings in a dielectric resonator filter. Since the inline couplings in a dielectric resonator filter are seen as “negative”, a coupling of the
opposing sense produces a low-side transmission zero, compared to a metallic resonator
whose in-line couplings are positive. A negative (opposite sense) cross coupling also
produces a low-side transmission zero.
The 1-5 Teflon and Wire non-adjacent coupling is optimized by an in-line cross
coupling. Since the total wire length of the in-line cross coupling is less than half a
52
wavelength and hence is seen as a “negative” cross coupling. From Chapter 4, it was
deduced that the 1-5 cross coupling produced a high-side transmission zero. Since the
coupling value is the “least” out of all 6 cross-couplings, the 1-5 cross coupling produces
to the furthest away high side transmission zero.
A “V” shaped cross coupling optimized the 2-4 Teflon and Wire non-adjacent
coupling. Since the total wire length of the “V shaped cross coupling is less than half a
wavelength, the non-adjacent coupling is seen as a “positive” cross coupling. The 2-4
cross coupling is a positive (opposite sense) to the in-line coupling of a dielectric
resonator filter and hence produces a low-side transmission zero.
An “S” shaped cross coupling optimizes the 2-5 Teflon and Wire non-adjacent
coupling. Since the total wire length of the “S” shaped cross coupling is less than half a
wavelength, the non-adjacent coupling is seen as a “negative” cross coupling. The 2-5
cross coupling is a negative (same sense) as an in-line coupling of a dielectric resonator
and hence produces a high-side transmission zero.
The same principle applies as the 2-4 and 2-5 non-adjacent cross couplings apply
to the 7-10 and 8-10 cross couplings. The 7-10 is also an “S” shaped cross coupling and
less than half a wavelength, giving a “negative” (same sense) high-side transmission zero.
The 8-10 is also a “V” shaped cross coupling and less than half a wavelength, giving a
“positive” (opposite sense) low-side transmission zero.
53
Chapter 6
DEVELOPMENT PROCESS
6.0 Measurement Setup
Calibrating the network analyzer simply means adjusting the network analyzer for better
accuracy and optimal measurements. Calibration of the Network Analyzer is very
important, especially when the specifications of a filter are “tight” and every tenth of a
dB in loss and rejection is needed; as with this dielectric resonator band-pass filter. The
cleaner the connectors are and the better the contact between the calibration standards
and the cables, the more accurate the calibration will be. The calibration procedure was
performed under the room temperature.
Figure 26 depicts the measurement setup for the dielectric band-pass filter in this
thesis. The filter input is connected via a SMA cable to the reflection port of the network
analyzer and the output is connected to the transmission port of the network analyzer.
The saved calibration is recalled and the tuned filter response is measured and plotted as
seen in later chapters.
Figure 26 Measurement setup of dielectric resonator band-pass filter
54
6.1 Unit Cavity Q Measurement
The Q factor at 1 GHz of the dielectric resonator is highly dependant on the intrinsic
quality of the ceramic material, the method of measurement, the measurement
environment and the frequency at which the sample is measured. The intrinsic Q of the
material also varies over the frequency of measurement and that is why it is common to
state the Q vs. frequency relationship. The test fixtures of measurement also have a
significant affect on Q measurement and it is hard to reproduce electrically identical test
fixtures for different test frequencies.
For high dielectric constant materials, a rectangular resonant cavity is used with
high conductivity metal where the cavity is 3-5 times larger than the dielectric resonator
[11]. Usually a low dielectric constant support for the resonator is used and a coupling
probe is placed near the puck. The transmission coefficient (S21) of the TE01 mode is
measured and the Q factor is calculated as
Q
f0
f

I .L 



 20 


110




(16)
where Δf is the -3dB bandwidth, I.L is the insertion loss (dB) [7].

The Q measurement that is performed in this thesis measures the Q of the filter
cavity and the dielectric resonator. The cavity that is used below to determine the Q of
the dielectric resonator was designed in Chapter 5. In order to measure the Q we
introduce the concept of ‘Critical Coupling’.
55
‘Critical Coupling’ is the degree of coupling which produces a particular state of
energy transfer where there is equal energy dissipated in the signal source and dielectric
resonator. The procedure for measuring Q through critical coupling is as follows.
Procedure
1. Solder a wire that is the same length as the radius of the cavity to the connector
and push the wire midway between the cavity wall and the resonator as shown in
Figure 27.
Figure 27 Initial wire placement for critical coupling
2. After the cover is fastened to the housing, short out the resonator by the driving
the tuning screw in until it touches the bottom of the hold down screw of the
resonator or a metal object as shown in Figure 28.
56
Figure 28 Using tuning screw to short resonator
3. Turn off the Transmission Channel and change the analyzer to Polar Mode as
shown in Figure 29.
Figure 29 Polar chart with calibrated frequency and span [11]
57
4. Turn off all markers except Marker 1 and set it to the desired center frequency of
the filter as shown in Figure 30. The trace should be “balled up” where the 0 point
on the polar chart resides. Normalize the response.
Figure 30 Normalized response with marker at desired center frequency
5. Back out the tuning screw until you see a circular trace with Marker 1 in the
middle of the Smith Chart as shown in Figures 31-33. If the circle is beyond the
centre point of the Smith Chart, the coupling is too great and the wire needs to be
cut, moved further away or pushed down.
58
Figure 31 Over-coupled: Probe too long/too close to resonator
Figure 32 Under-coupled: Probe too short/too far from resonator
59
Figure 33 Shortening of wire for critical coupling adjustment
6. Adjust the coupling until the circle passes through the origin of the polar chart as
seen in Figure 34.
Figure 34 Optimum critical coupling in polar format
60
7. Change the trace to a Log Mag setup and center Marker 1 on the screen as shown
in Figure 35.
Figure 35 Optimal critical coupling in log-mag format
61
8. Turn off all markers and search for Notch as shown in Figure 36.
Figure 36 Q-measurement searching for notch frequency
The Q measurement of the dielectric resonator above is the unloaded Q and hence is
double the loaded Q measured in Figure 36. The actual resonator Q measurement for the
dielectric filter in this thesis was approximately 27783 whilst the design Q based on the
prototype dielectric resonator design was 25,000, 10% less than the Q achieved in the real
design. Usually this occurs because irises are opened up to achieve the design filter
62
bandwidth. Opening the iris apertures involved removal of the cavity walls between the
resonators. Removal of the wall material increases the resonator Q.
63
6.2 Iris Development
Irises are often employed between dielectric resonators in adjacent and non-adjacent unit
cavities for coupling structures and tuning screws have been used to fine-tune these iris
coupling values. Irises that are open at the magnetic field’s maximum strength; in-line
with the center of the dielectric puck have typically been implemented for adjacent
coupling. This method allow for linearity in the filter’s phase response and keeps the
transmission zeros symmetric about the center frequency.
The development of the irises in the dielectric filter is a lengthy process. There is
no short-cut method to achieve optimum iris dimensions. Cutting the iris and measuring
the coupling bandwidth on the network analyzer is required to achieve the desired
resonator couplings. However, interpolating the coupling bandwidth between the points
can speed up the process. In Appendix B one can refer to the coupling vs. iris dimension
excel program created to interpolate the couplings between the resonators. When
developing the irises, it was worth noting that the narrower the coupling irises the further
the unwanted TM01 spurious mode can be tuned away from the TE01δ mode. The TM01
mode has a greater coupling than the TE01δ mode in the direction of the magnetic field.
However, a drawback to this iris development method is that too small an enclosure
degrades the filter Q significantly.
The polynomial that is derived in order to determine the iris dimensions is y = 91.859x4 + 178.52x3 – 112.71x2 + 31.024x – 2.6415, where y denotes the coupling
bandwidth in MHz and x denotes the iris width in inches and cut to the floor.
64
By using this polynomial and solving for x, we get the coupling bandwidths associated
with the in-line and cross coupling irises. Since the dielectric resonators are equally
spaced in the x-y axis, the polynomial can be used to interpolate the iris dimensions for
the cross couplings. However, if the dielectric resonators were not equally spaced in the
x-y axis, i.e. the resonators were closer or further away from each other in the x-axis
compared to the y-axis, the polynomial would not hold true for all couplings.
The irises are all cut and optimized to have three to four threads of tuning screw
penetration for the actual coupling to be achieved, the coupling screws were repositioned
to the center of the iris. This required another process to document new positions of the
tuning screws. A new housing needed to be machined and plated. Since this dielectric
resonator filter is close in its specifications, the iris walls needed to be replaced after
being cut to optimize the electrical performance. Hence, once the iris dimensions are
optimized, a new housing is cut and plated for optimal performance.
65
6.3 Tuning Methods
The tuning process follows the optimization of the irises. The initial tuning processes are
produced with the cut and developed housing and cover and will have a lower Q factor
than the optimized iris version plated for production. However, equal rippled band edge
frequencies, typical insertion loss and rejection values can be deduced for future tuning
goals. In Figure 37, one can find the full tuned dielectric resonator filter performance
after development has taken place. All input wires, coupling wires, irises and cover
modifications are made by the engineer and later repeated by the assembler. In this thesis,
the engineer and the assembler are one because of the unit being a development project.
Figure 37 Developed and tuned dielectric resonator filter measured response
66
Note in Figure 37, the dielectric resonator filter’s rejection is not as sharp and defined as
the simulation. This is due to the limited Q factor available in the developed housing,
where some Q is lost at the un-plated edges and floors of the irises. However, all 10
reflection zeros are visible and in the band of tuning and each transmission zero is
helping achieve the 60 dB rejection.
67
6.4 Temperature Testing
The resonator mounting structure has a big effect on the overall temperature performance
of the resonator. The support material and proximity of the resonator to the cavity walls
has a profound effect on the temperature characteristics of the resonator. In order for the
cavity to have little effect on the temperature stability of the dielectric resonator, the
cavity diameter needs to be approximately three times larger then the dielectric
resonator’s diameter. If a metallic tuner is used, the resonant frequency of the dielectric
resonator will increase; if a dielectric tuner is used, the resonant frequency of the
dielectric resonator will decrease as the tuner is positioned closer to the resonator. The
resonant frequency can be changed, as much as 15% but it is recommended that the
resonant frequency only be changed by a few percent to avoid Q degradation when a
metallic tuner is used [7].
Tuning dielectric resonators also affect the frequency and Q factor significantly,
depending on the method and material of the tuning mechanism. Dielectric resonators can
be tuned with a plug, plate or a tuning disk. At 850 MHz a metallic tuning plate decreases
the Q factor by 50% with 75 MHz of tuning whereas plug and disk tuning provide 45
MHz of tuning at 850MHz with less than 5% reduction in the Q factor, and as high as 70
MHz of tuning at 2 GHz [7].
Temperature testing of the dielectric resonator filter is important as we develop
the filter to characterize its electrical performance with change in temperature. The
specified operating temperature range for this filter is -0°C to +70°C. Immediately, we
68
can see that the upward swing in temperature is greater than the downward swing in
temperature with 25°C room temperature being as a design reference. The upward
temperature swing is almost double the downward temperature swing. The dielectric
resonator filter in this thesis has a temperature coefficient of 1.5 ppm/ºC. In this sense,
parts per million refers to the frequency variation of the dielectric resonator filter over
temperature. Converting ppm to Hz can be determined by one of the following formula:
f Hz 
f o  ppm
106
(17)
where ppm is the peak variation expressed as a positive or negative number, f is the

center frequency of the filter in Hz and ∆f is the peak frequency variation in Hz. Hence
using (19), the dielectric resonator will move ±116 KHz between 1904.88 MHz and
1905.11 MHz over the given temperature range. Figures 38 and 39 show the downward
temperature swing filter response and the upward temperature swing filter response,
respectively. Note how in Figures 37 and 38, the insertion loss remains under 1.5 dB, the
return loss remains under 15 dB and the rejection remains under 60 dB, in-turn meeting
the customer specifications from Chapter 2 over the nominated temperature range of 0ºC
to 70ºC.
69
Figure 38 Downward temperature swing measured filter response (0ºC)
Figure 39 Upward temperature swing measured filter response (70ºC)
70
Chapter 7
CONCLUSIONS
This paper presents a 10-section 6-Transmission Zero Dielectric Resonator Band-pass
Filter that successfully rejects Provider B’s passband frequencies in order to transmit
Provider A’s passband frequencies with maximum power. The innovative cross coupling
techniques provided allow a high Q/volume ratio compared to other known filter
topologies. The assembling repeatability, manufacturing cost and ease of tuning are also
achieved by the development of the tunable cross couplings, iris dimensions, and
input/output coupling structures. The non-adjacent couplings are analyzed in triplet and
quadruplet sections which are cascaded to form symmetric transmission zeros outside the
filter passband.
The coupling matrix derivation through the in-house synthesis program is
essential in the development of the filter. The irises are developed to minimize the effects
of unwanted non-adjacent resonators coupling to each other that can cause degradation to
the filter. Temperature compensated cross couplings is employed for further stability of
the filter over the desired temperature range and excellent measured performance is
presented. The high Q of the filter is maximized by two ways: designing the unit cavities
as rectangles rather than squares and minimizing the iris’ tuning screw penetration.
For future applications that deal with co-channel interference, the same
techniques are advisable. Maximizing the filter Q, temperature compensating cross
couplings, designing filter components for repeatability and developing irises for
71
optimum tunability will optimize the design of dielectric resonator filters for co-channel
interference rejection.
72
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