Dielectric
Bandstop
Resonator
Richard
Filters
Chan
Kayip
Submitted in accordance with the requirements for the degree of Doctor of
Philosophy
The University
School
of Electronic
Leeds
of
and Electrical
April
Engineering
2011
The candidate confirms that the work submitted is his own and that
has
beengiven where reference has beenmade to the work of
credit
appropriate
others.
This copy has beensupplied on the understanding that it is copyright material
and that no quotation from the thesis may be published without proper
acknowledgement
1
Abstract
Dielectric resonators have been widely employed in wireless and satellite commuloss
low
fashion
large
Q
due
to
inherently
them
to
their
allowing
nication systems
in
bandwidth
filters.
Recent
has
these
resonators
adopted
progress
and narrow
The
demanding
low
for
specifications.
volume and mass
applications requiring
dielecfilters
bandpass
using
technology at present consists of an assortment of
filters
little
but
bandstop
is
there
employing
tric resonators
published material on
front
filters
frequencies
the
Bandstop
desirable
to
at
are
suppress
such resonators.
end of wireless communication
imperait
is
demands,
future
To
systems.
meet
dielectric
filters
both
in
these
the
to
tive
reduce
costs of
volume and weight using
resonators.
This thesis presents compact mono-mode and dual-mode bandstop dielectric resonator structures.
The former consists of a dielectric-loaded
filter that offers a miniaturised
ters requiring
waveguide cavity
fildielectric
typical
to
resonator
version
cavity
high unloaded Qs. The niono-mode filter described is ideal for
Q
lower
specifications
a
resonator to replace common coaxial
relaxed
requiring
filters.
high
For
bandwidth,
requiring
applications
resonator
this resonator is im-
A
by
line.
dielectric
to
transmission
coupling
ring resonator
a
proved
a coaxial
dual-mode
bandstop resonator is developed taking advantage of the geomnovel
etry of a cylindrical puck within a single shielded cavity to create two degenerate
modes with equal resonant frequency, effectively replacing two mono-mode cavities. Miniaturisation
is achieved by sitting the dielectric puck at the base of the
cavity and correct phase separation between the orthogonal modes is produced
from a curved uniform transmission line.
Abstract
11
The mode behaviour is observed in the physical realisations using a 3D FEM
Advanced
filtering
solver.
functions using prescribed reflection zeros is demon-
dual-cavity,
dual-mode
bandstop
the
with
simulation
resonator where
of
a
strated
inter- and intra- cavity couplings are controlled.
discussed in this thesis will provide cost-reduction
highQ
bandstop
filters.
requiring
systems
The miniaturisation
techniques
for microwave communication
111
Contents
Acknowledgments
vii
List of Figures
viii
List of Tables
xvii
1
1 Introduction
1.1
Applications
of Microwave Filters
..................
1.2 Review of Dielectric Resonators .....
1.2.1
Background
1.2.2
Dielectric Resonator Filters
.....
.....
......
5
. .....
........
.....
.....
1.3 Scope of the Study
.....
3
6
......
.....
...
...
.....
17
................
18
1.4 Organisation of Thesis
........................
2
Filter
20
Design
2.1 Introduction
8
...
...
2.2 Types of Filters
. ...
.....
...
2.3 Impedance Transformations
...
....
.....
.....
......
.......
. ..
........
......
.....
. ....
. ...
20
21
23
iv
Contents
2.4
Lowpass to Bandstop 'Transformation
2.5
Transfer Functions
2.6
................
24
..........................
2.5.1
Butterworth or Maximally Flat Approximation
2.5.2
Chebyshev Approximation
2.5.3
Inverse Chebyshev Response
2.5.4
Generalised Chebyshev Response
Direct-Coupled
2.6.1
3 Dielectric
Bandstop Filters
Quality Factor
Resonator
. .....
.....
. ..
.....
...
29
..............
...
. .....
.........................
Quality Factor
3.3
Coupling to a transmission line
3.4
Configurations
...
. .....
.....
. .....
3.5.1 Cohn's Model
........
...
.......
HFSS Finite Element Model
Compact
....
Bandstop
.......
.....
43
. .....
44
......
...
...
53
................
. ..........
. .....
Filter
. ....
TElos Rectangular Waveguide Resonator
46
50
..............
3.5.3
...
.....
. ..........
Mode-Matching Model
...
.....
. ..........
3.5.2
Dielectric-Loaded
38
39
.............................
. ...
30
38
Filters
....
27
36
3.2
4.2
......
26
. ....
Basic Properties of Dielectric Resonators
4.1 Introduction
25
..................
3.1
3.5 Resonant Modes
4
23
55
59
. .......
..............
. ...
59
60
y
Contents
4.3
Configuration
4.3.1
Single Resonator Design
4.4 FEM Simulations ......
4.6 Fabrication of Filter
5
......
. .....
......
91
...........
94
Filter
...
. .....
....
.
.....
.....
94
95
...........
5.3 Configuration of Proposed Resonator
.......
Single Cavity Design
88
. ..
.....
.....
5.2 Dual degenerate HEEII mode
. ........
5.4
74
.
............
Bandstop Resonator
DR Bandstop
5.1 Introduction
69
......
. ..........
....
Coaxial Dielectric-Loaded
Dual-Mode
66
...................
4.5 4th Degree Chebyshev Design . ......
4.7
64
Filter
Proposed
of
...................
.
........
96
102
.........................
106
5.4.1
FEM Simulations for single cavity
. .........
5.4.2
113
Fabrication and measurements of dual-mode single cavity
.
5.5 4th Degree inverse Chebyshev Design
5.5.1
5.7
Fabrication of filter
5.8
Direct-coupled
....
.....
117
................
Inverse Chebyshev element values
5.6 HFSS optimisation
. ...
. ....
...
. .....
...........
...
...
127
..................
6 Conclusions
6.1 Future Work
120
125
..........................
DR bandstop filter
118
137
......
.....
.......
. .....
...
...
139
Contents
A
Conferences
References
vi
and Publications
141
142
Vii
Acknowledgments
Firstly I would like to thank Ian Hunter for his invaluable supervision and guid-
ance throughout this work. Thanks also to Filtronic for funding this work.
Many thanks to Terry Mosely and Nick Banting for the amount of time spent
discussing the construction of the filters.
I would also like to thank Richard
Cameron for his comments in this thesis.
A big thank you to my Mother and Father for making all this possible.
viii
List of Figures
1.1 RF front-end of a cellular radio base-station . .....
1.2
...
4
...
4
Typical diplexer response
.......................
1.3 TEola resonant mode dielectric resonator ......
. ..
.....
1.4 E-field plots of shielded TEO,& mode dielectric resonator ...
1.5 Structure of 6.9 GHz DR filter ..............
1.7 Configuration of a TM016 mode DR filter . ....
1.8 Dual-mode configuration of a DR filter
....
.9
. ...
....
. ...
. ....
...
.....
7
. ..
.....
1.6 TEola DR filter for cellular base-station application
6
...
9
10
11
1.9 Tuning screw orientations for cross couplings in an elliptic function
DR dual-mode filter
..........
........
...
.....
11
1.10 Conductor-loaded dual-mode DR filter configuration
........
12
1.11 Quadruple-mode DR filter configuration
13
. .......
...
...
1.12 Configuration of a 6th degree mixed-mode elliptic function DR filter 14
1.13 Structure of 6th degree mixed-mode DR filter
. .....
. .....
1.14 Configuration of 41' order combined conductor and dielectric-loaded
filter
..................................
14
15
ix
List of Figures
1.15 Bandstop filter with DRs placed transversely along waveguide
1.16 Bandstop filter with DRs placed outside waveguide
16
..
16
........
1.17 Microstrip DR bandstop filter with quarter-wavelength unit elements 17
2.1
Lowpass prototype ladder filter networks
21
..............
2.2 Impedance inverter terminated in a load
........
2.3
General Nth degree inverter coupled lowpass prototype
inductors (b) capacitors
....
.....
2.4 Lowpass to bandstop transformation
.
. ....
. ....
(a)
with
. ...
. ....
.......
22
...
. .....
22
24
2.5 Bandstop transformation of an inductor and capacitor
.......
24
2.6 Frequency responseof butterworth lowpass filter for varying N
..
25
2.7 Frequency response of a Chebyshev lowpass filter
26
2.8 Frequency response of an inverse Chebyshev filter
2.9 Highpass prototype for inverse Chebyshev filter
...
. ...
2.10 Frequency response of an elliptic lowpass filter
.....
2.11 N+2 multicoupled resonator circuit
......
. ...
. ....
.....
28
......
29
......
29
......
...
...
2.12 4th degree N+2 coupling matrix with all possible cross-couplings.
Core NxN matrix within double lines
.....
...
...
.....
2.13 Direct-coupled
(4-2) bandstop filter : (a) coupling-routing
(b) realisation with coaxial cavities
......
.....
Transmission
bandwidth
response displaying
. ...
...
...
.....
31
diagram
35
......
2.14 Direct-coupled cul-de-sac (4-2) bandstop filter (a)
:
coupling-routing
diagram (b) realisation with waveguide
cavities ....
...
...
3.1
31
36
resonant frequency and 3 dB
.....
.....
...
...
42
List of Figures
3.2
X
43
Magnetic field coupling of a DR to rectangular waveguide
.....
3.3 Magnetic field coupling of a DR to microstrip line ........
44
.
3.4 Three DR configurations: (a) rectangular resonator, (b) cylindrical
resonator, L<D,
3.5
(c)
and
cylindrical resonator, L>D...
44
...
45
Commonly used DR structure
.....................
3.6 Field plots of common DR modes
.........
3.7 Typical DR mode chart
. ....
...
...
. .....
.......
47
48
...
. .....
3.8 Mode chart of a DR in cavity as a function of aspect ratio
48
....
3.9 Mode chart of a DR in cavity as a function of aspect ratio with
improved spurious performance
. .......
49
......
.....
3.10 Classification of HE modes showing E-field component for (a) electric wall (b) magnetic wall
...
. .....
...
.....
.....
49
3.11 Cohn's second-order DR model showing a DR inside a magneticwall waveguide below cutoff
............
51
. ...
. ....
3.12 Improved model for a shielded DR
..................
51
3.13 Generalized multilayer cylindrical DR
.......
54
...
...
...
3.14 Mesh with tetrahedral elements for maximum flexibility to approximate shape of 3D dielectric puck
.......
......
.....
56
3.15 Finite element method analysis of dielectric puck with axial hole:
(a) basic geometry, (b) view of mesh with 0.2A
(c)
view of
mesh,
mesh with 0.1A mesh .......
....
...
...
.....
...
4.1 Field distribution of TE101rectangular cavity
.....
...
57
61
...
4.2 Schematic of third-degree strip transmission line bandstop filter
.
65
List of Figures
xi
65
4.3
Schematic of third-degree cavity waveguide bandstop filter
4.4
Schematic of (a) Circular coaxial transmission line coupled to DR
cavities (b) Cross-section of feasible realisation
....
66
...........
4.5 Structure of TE10 mode dielectric bandstop resonator
66
.
.....
4.6 Frequency responseof air-filled square coaxial TEM line with circular centre conductor, D=
10 mm and r=4.68
mm . .....
4.7 Details of TEIOamode dielectric bandstop resonator
....
69
.
70
....
4.8 Electric field of TEloa mode DR: (a)Vector Lines (b)Magnitude
71
.
4.9 Magnetic field of TE106mode DR: (a)Vector Lines (b)Magnitude
.
71
4.10 H-field plots of fundamental mode DR coupled to coaxial line: (a)
Magnitude acrosstransverse plan (b) Vector view cut through middle (c) Magnitude cut through middle
......
72
..
. .......
4.11 Resonant frequency versus DR length for various coupling gaps
..
73
4.12 3 dB bandwidth versus coupling gaps for different DR lengths
..
73
4.13 Ladder network
............
76
......
..........
4.14 Transforming resonators of equivalent Q (a) Reactance slope parameter (b) Transformation of capacitor to magnetically-coupled
resonator .....
. .....
....
......
79
. ..........
4.15 Prototype circuit for 4th degree Chebyshev bandstop filter
4.16 Simulated results of prototype
bandstop filter
.....
82
....
network for 4th degree Chebyshev
........
.....
.....
.....
.
82
4.17 Normalized reactance slope parameter
against spacing of resonator
from coaxial line
...
.............
.....
......
83
List of Figures
4.18 3 dB bandwidth
X11
in
MHz
MHz
2°d
11t
5.1
8.6
and
resonator
of
=
=
Chebyshev design with fo = 1.85 GHz
...
...
..........
84
4.19 Resonant frequency against spacing of uncoupled dielectric side
with sidewall
85
.............................
4.20 Simulated resonant frequency against depth of tuning screw
...
85
4.21 HFSS simulated tuned 1st resonator, 3 dB bandwidth = 5.11 MHz
fo
GHz
1.8502
and
=
86
.........................
4.22 HFSS simulated tuned 2nd resonator, 3 dB bandwidth =9 MHz
fo
and = 1.8498 GHz ....
...
.....
.....
........
4.23 Schematic of HFSS design of final filter
....
4.24 HFSS simulated response of filter to be fabricated
87
......
.....
86
87
.........
4.25 HFSS simulated wideband response of filter to be fabricated
...
88
4.26 Practical resonator design
89
......................
4.27 Fabricated 4th degree Chebyshev Bandstop filter
. ...
......
4.28 Interior of fabricated 4th degree Chebyshev bandstop filter
4.29 Measured frequency response of Chebyshev bandstop filter
....
. ...
89
90
90
4.30 Measured wideband frequency responseof Chebyshev bandstop filter 91
4.31 TNIo16dielectric-loaded bandstop resonator: (a) Schematic (b) Hfield plot in dielectric region
....
. .....
...
...
.....
4.32 Dimensions for experimental coaxial dielectric-loaded resonator, L
80mm,
W= 40 mm, Ll = 10 mm, L2 9.57
=
=
mm . ...
...
4.33 Simulated transmission response for experimental resonator for
various inner coaxial transmission line radii, r
.
.....
.....
92
92
93
List of Figures
5.1
Field distributions
plots .......
5.2
Xiii
(b)
(a)
H-field
E-field
dual
HEEII
plots
mode
of
...
...
.....
.....
...
.....
...
97
Diagram of dielectric puck in perfect conductor cavity
.......
5.3 Mode chart variation of H/h with frequency
.........
. ..
5.4 Mode chart variation of h2/hl with frequency
.....
...
5.5 Mode chart variation of R/r with frequency
......
96
...
98
99
100
. .....
5.6 Topologies for coupling of transmission line to dual-mode dielectric
(a)
puck:
weakly coupled probes (b) probes for maximum coupling
(c) side view
.....
.............
...
.....
...
100
5.7 Coupling, of right-angle transmission line to dual-mode dielectric
(a)
(b)
top
puck:
side view ...................
view
101
5.8 Coupling mechanism for dual-mode HEEII bandstop resonator: (a)
top view (b) side view
5.9
102
........................
Circuit model for coupling post
102
...................
5.10 Structure of HEEII mode dielectric bandstop resonator: (a) Corner
(b)
Cross section (c) Top view
view
...
......
...
.....
5.11 Mode chart variation of ri/r
with frequency . .....
...
...
103
104
5.12 Coaxial transmission line with various centre conductor curvature
radii (a) c= 40.25 mm, e= 63.2 mm (b) c= 29 mm, e= 68.1 mm
(c) c= 19 mm, e= 72.77 mm
. .....
. ....
5.13 Frequency response of coaxial transmission
. ..
......
104
line, outer and inner
conductor diameters, 13.5 mm and 6 mm respectively, for various
radii of inmost coaxial conductor wall curvatures
....
...
5.14 Details of HEE11 mode dielectric bandstop resonator
. ...
...
...
106
107
List of Figures
XIV
5.15 Field plots of single degenerate HEE11 mode coupled to transmis(b)
(a)
line:
E-fields
11-fields in xy- and
in
sion
xy- and xz-plane
yz-plane
108
................................
5.16 Field plot of first higher order spurious mode, TEO,&: (a) Side view
(b) Top view (c)
. .....
...........
..
. ...
.....
109
5.17 Dielectric puck with removed ring section for improved spurious:
(a) 3D view (b) Top view (c) Side view
......
...
...
...
109
5.18 Diagram of orthogonal frequency tuning and coupling screws arrangement
110
...............................
5.19 Frequency response for penetration
110
of cross-coupling screw ....
5.20 Frequency response for penetration of single resonant mode tuning
111
screw ..................................
5.21 Optimisation of coupling rod diameter
5.22 HFSS simulation of experimental
......
. ........
filter for fabrication
. ......
.....
.............
113
.......
5.23 HFSS simulation of the spurious mode of the prototype
fabrication
112
filter for
113
......
5.24 Fabricated single cavity of HEE11 dual-mode bandstop filter
114
...
5.25 Measured frequency response of HEEII experimental bandstop filter 115
5.26 Measured Chebyshev responsewith tuning screws of HEEII single
cavity bandstop filter . .....
. .........
...
...
...
116
5.27 Inverse Chebyshev frequency responseof HEEII single cavity band116
stop filter . .....
........
............
.
....
5.28 Spurious frequency responseof HEEII single
filter
bandstop
cavity
117
5.29 Matched inverse Chebyshev filter prototype
118
.......
....
.
List of Figures
xy
5.30 Circuit network of inverse Chebyshev elements
...........
118
5.31 Inverse Chebyshev bandstop filter prototype
118
............
5.32 4th degree circuit model inverse Chebyshev bandstop filter
120
....
5.33 4th degree circuit model inverse Chebyshev bandstop filter
121
....
5.34 Top view of HFSS simulation with variables for optimisation ...
122
5.35 Variation of resonant frequency with DR circular cavity height ..
122
5.36 Variation
of 3 dB coupling bandwidth
with coupling post to puck
123
spacing .................................
5.37 Final HFSS simulated model for inverse Chebyshev bandstop filter 124
5.38 Frequency response of optimised HFSS design for inverse Cheby124
shev bandstop filter ..........................
5.39 Fabricated 4th degree inverse Chebyshev bandstop filter
125
......
5.40 Measured frequency response of inverse Chebyshev bandstop filter
126
5.41 Measured wideband frequency responseof inverse Chebyshevbandstop filter
. ...
........
..........
127
. ........
5.42 Frequency response of direct-coupled (4-2) bandstop filter
....
.
5.43 Coupling routing diagram of a direct-coupled (4-2) bandstop filter
129
129
5.44 Configuration of HEE1I dual mode direct-coupled (4-2) dielectric
bandstop filter
....
. .....
.......
.
.....
. .....
130
5.45 Variation of coupling coefficient with iris width of length 3 cm and
thickness 2 cm
.............................
132
5.46 HFSS model of optimised direct-coupled HEEII dual-mode bandstop filter
. ...
...
.......
. ....
...
.....
. ...
132
List of Figures
Xvl
5.47 Simulated response of optimised direct-coupled
bandstop filter
HEEII dual-mode
133
.............................
5.48 Coupling routing diagram of cul-de-sac direct-coupled (4-2) bandfilter
stop
. ....
. .....
....
....
134
. ...........
5.49 Frequency responseof cul-de-sac direct-coupled (4-2) bandstop filter134
5.50 HFSS model of optimised cul-de-sac HEEII dual-mode bandstop
filter
........
. .....
....
....
.....
.....
..
135
5.51 Simulated response of optimised cul-de-sac HEEII dual-mode band-
stop filter
. ....
. .....
.....
.....
. .........
136
xvii
List of Tables
3.1 High-Q dielectric materials . .......
...
...
........
3.2 Computed and measured resonant frequencies of DRs . ...
...
40
55
banddielectric
TE105
dimensions
Typical
4.1
mode
and performance of
resonator
stop
....
. ...
. ....
. ....
. ..........
69
isofive
frequencies
Qus
first
Simulated
of
4.2
modes
and
of
resonant
lated dielectric rectangular cavity resonator
.......
4.3 First five resonant modes of prototype resonator ....
4.4
Filter specifications
71
......
...
...
74
74
..........................
5.1 First five resonant modes of a dielectric puck
. .....
...
. ..
96
5.2 Typical dimensions.and performance of HEEII dual-mode dielectric bandstop resonator
...
....
. .....
.....
...
...
106
5.3 First five modes in a dielectric puck in contact with base of cavity
109
Filter specification for 4th degree inverse Chebyshev bandstop filter
118
5.4
5.5 Requirements for resonant frequency and bandwidth for each mode 123
5.6 Filter specification for 4th degree direct-coupled bandstop filter ..
131
1
Chapter
1
Introduction
With current trends in communication
systems calling for lower manufacturing
Qs,
factors,
higher
high
performance, resonating elements with
quality
costs and
become a neccessity. These elements play a fundamental
design
in
the
of
role
filters
as the resonator quality factor is proportional
microwave
becomes an important
limiting
to volume and
factor. Typically, waveguide structures have been
high
Q
high
for
their
temperature stability
and
used
bandallowing very narrow
large
frequency
in
domain,
900
MHz
to 100 GHz.
a
widths
The disadvantage
is bulky and cumbersome filters are required that are expensive to produce and
heavy.
Microstrip
excessively
and stripline
technology have been the main con-
in
bulky
these
removing
waveguides in the majority
stituents
of microwave sys-
tems and are used in the high frequency domain, 100 MHz to 30 GHz, to realise
high bandwidth
integration
filters due to their low Q. Their small dimensions and ease of
with microwave circuits are of great interest but their disadvantage
is their low losses are usually compensated by active devices or superconducting
technology.
A miniaturisation technique providing a low-loss solution employs dielectric resDRs,
as they allow a reduction in size inversely proportional to the
onators,
square root of the permittivity
of the dielectric material used. In addition, the
loss in a dielectric-loaded cavity with metallic shielding is dominated by the loss
tangent owing to the dielectric material and minimally dependent on the outer
2
I Introduction
loss.
An
dielectric
improving
losses
is
that
this
conare
advantage
with
conductor
losses
due
being
to.
more advanced materials
produced, whereas metallic
stantly
have remained fairly constant with no signs of improvement,
of superconductors.
with the exception
As a result, these resonators have the ability
filters
but
better
in
terms of minimisation,
are
much
waveguide
as
weight.
This advantage can be seen in satellite communication
inherently high-loss microstrip
equivalent application.
to function
stability
and
systems where
for
DR
disregarded
technology
a
and stripline
are
In recent years, these low-loss DRs have led to the reali-
lightweight
small,
reliable,
of
sation
and stable microwave systems.
In microwave filter technology, DRs have been preferred for their superior high Q,
low loss and miniaturisation
attributes.
In recent years, motivation for more com-
bulk
for
low
demand
have
these
increased
ease
of
manufacture at
cost
pact and
types of filters.
For example, in wireless communications,
a more cost-effective
DR
low-cost
that
can
replace
coaxial air-filled resonators with smaller,
solution
filters is a necessity. Further size-reduction techniques have been developed in
the form of higher-order
mode filters, [1]. These higher-order
filters
are
mode
design
in
and often rely on measured data to implement the recomplex
more
frequencies
resonator
and coupling coefficients that satisfy the equivalent
quired
With
improved
model.
computer speeds, full-wave electromagnetic
circuit
field
becomes
increasingly
software
useful in simulating these 3D structures
simulation
reducing practical test times and enabling the filter designer to observe modalfield behaviour for different parameters.
Although much work has been presented using DRs with bandpass filters, only a
limited number of publications on bandstop filters employing DRs have been published and very little is known about dual-mode dielectric bandstop filters. Filters
DRs
coupled to microstrip line have been presented but require housing that
with
increase their volume, [2] and [3]. A triple mode hybrid reflection filter was also
presented using two cubic dielectric resonators coupled together through a3 dB
[4].
hybrid,
The design requires complex tuning for each mode and
quadrature
is limited as it caters for filters of degree six and above. More conventionally,
3
1 Introduction
Applications of Microwave Filters
for
lines
DRs
have
been
transmission
to
attenuacoupled
waveguide
mono-mode
[5].
It
but
behaviour
DR
increases
tion
volume,
each
requires a cavity which also
is the aim of this thesis to design bandstop filters using DRs making full use of
their high Q and low loss to achieve miniaturisation
techniques suitable for wire-
less systems where the emphasis is on cost and not highly demanding low-loss
dielecThe
first
for
is
to
objective
provide a solution
a mono-mode
performance.
tric resonator bandstop filter providing a low-cost alternative to coaxial bandstop
The
second objective is to incorporate
resonators.
the hybrid dual-mode prop-
dielectric
resonators allowing the reduction in cavity number compared
erty of
to mono-mode resonators. The final objective is to propose an improvement for
type
to address shortcomings and demonstrate realisability
resonator
each
functions.
filtering
This
thesis provides an introduction
vanced
of ad-
to size reduction
for bandstop filters employing dielectric resonators that have potential for further
filtering techniques and, therefore, only provides possibilities for the use of this
implement
fullly
to
advanced filter functions.
structure
1.1
Applications
Microwave
of
Filters
Microwave filters are used to define wanted and unwanted frequency bands. They
important
role in terrestial, radio and satellite communications along with
play an
As
communication
radar systems.
systems improve at a tremendous rate, the
difficulty to meet filter specifications becomes more challenging. In a cellular base
station, they perform important
roles at different stages of the radio frequency,
RF, front-end unit, figure 1.1. Typically,
low loss is required in the passband
high
rejection of signals at the passband edges to give greater selectivity.
with a
This prevents a high level of cross-channel interference between the number of
subscribers that share the spectrum available to them.
A broad stopband and highly symmetrical frequency
responseis usually preferred
for bandpass filters, although asymmetrical designs
be
more adcan sometimes
vantageous when distinguishing between two adjacent bands in the spectrum.
4
1 Introduction
Ap)j)lirat
on. ý of Alicro11(0'(
Filtr
.ý
Antenna
TX Filter
Up-Converter
BTX
Power Amplifier
RX Filter
Down-Converter
-
00 RX
Low Noise Amplifier
TX/RX
Figure
Diplexer
1.1: RF front-end of a cellular radio base-station
This is the case for diplexers where a highly asymmetrical attenuation
specifica-
tion is needed as more rejection is required from each filter over the passband of
the other filter, figure 1.2.
Tx.
Rx"
S,,
Frequency
Figure
1.2: Typical diplexer response
Bandstop filters have been widely used in many microwave circuits and systems
[6], [7].
important
In particular,
narrowband
reject, or notch, filters have become more
in most microwave communications
there
are
as
systems
and radar
interferences
signals
and
unwanted
at air interfaces.
more
Systems that utilise
the spectrum with interleaving spectra require notch filters to avoid interference
between two operators if they are too close. For example, in the Advanced Mobile
Phone System/Global
System for Mobile communications
extremely narrowband
filters often require resonators
factors
Q
with unloaded
AMPS/GSM,
these
in excess of 25 000. To realise such filters, cavity structures measuring 9x9x
9 cm. at 2 GHz. are usually required per resonator leading to physically large
devices. Microwave filters with both a compact size and high Q are desired. The
5
1 Introduction
Review of Dielectric
Resonators
level
dielectric
bandstop
filters
be
to
a
resonator
provide
would
suitable
proposed
band,
the
on
receive
when transmitting,
of rejection
diplexer and amplifiers at communication
1.2
Review
of Dielectric
between
the
and vice versa
system front-end units.
Resonators
Low-loss DRs or superconductor filters are capable of high Qs and although the
latter may produce Qs in the order of 100 000, DRs do have the potential
attain
Qs exceeding 20 000. They are considerably
to
smaller than the size of a
hollow resonant cavity operating at the same frequency, provided the dielectric
is
the
of
material
of an order much greater than unity.
constant
DRs are com-
in
as
short,
solid
shaped
pucks
and
such a geometry, the common resonant
monly
denoted
TEola
is
figure
be
1.3.
dipole,
which
may
observed
as
mode
a magnetic
The electric field lines are concentric circles along the azimuthal axis and for DRs
dielectric
constant approaching 40, the typical stored electric energy
with relative
for TEoia mode is greater than 95% and over 60% for magnetic energy within the
distributed
The
is
remaining
energy
puck.
into the surroundings, rapidly decaying
from
the
Ceramics
resonator
surface.
away
used in constructing
DR filters typi-
dielectric
have
constants in the range 20 to 90, thus, DR filters gain a huge
cally
to
compared
advantage
similar waveguide or coaxial filters when operating.
size
In addition, although planar filters are more convenient to fabricate and, consebulky
in
the majority
replace
can
waveguides
quently,
of microwave systems, their
low Q, only up to 500, limits them to moderate performance and cannot be used
in demanding communication
system applications.
DR filters are then useful to
fill the gap between waveguide and stripline technologies
high
the
accomodating
Qs needed and also a system integrability approaching that
of planar resonators.
Furthermore, they offer versatility and are adaptable to
various microwave structures and coupling configurations.
Unfortunately,
the disadvantage of DRs is
although their geometrical forms may be simple, an exact solution for Maxwell
become
more difficult to obtain than for hollow metal cavities. This is
equations
6
I Introduction
Review of Dielectric
Resonators
for
fields
from
DRs
in
in
the
shielded
metal cavities,
which,
uniform
even more so
isolated resonators become distorted
due to the presence of metal boundaries,
figure 1.4. However, boundary approximations
are possible and simple resonant
frequency equations may be derived. For example, the resonant frequency for an
isolated TE01 mode dielectric cylindrical
resonator is
fo-34(2+3.45)
a
1.1)
Er
1
dielectric
height
is
in
in
is
the
the
the
constant
radius
mm.
mm
a
and Er
where
of the resonator. This formula has an accuracy of 2% for 0.5 < a/1 <2
and 30
< Er <50. For a resonator with radius 18.5 mm and height 23 inin, its resonant
frequency in free space is 1.18 GHz. When the dielectric is placed in the centre
of a shielded cavity with square sides 60 mm and height 50 mm, the resonant
frequency increases to 1.3 GHz.
z
1.2.1
-
Y
.X
Figure
E-field
H-field
1.3: TE016 resonant mode dielectric resonator
Background
The propagation
of guided electromagnetic
waves in dielectric
first
was
media
days
leading
in
the
DR
of
to
the
microwaves
early
the
where
studied
prominence of
functioned
dielectric
[8].
The
term
objects
as
microwave
unmetalised
resonators,
7
1 Introduction
ZL
Review of Dielectric
Resonators
yýlý
LX
x
Figure
1.4: E-field plots of shielded TE1A mode dielectric resonator
dielectric resonator was coined in 1939 but the theoretical work reported failed to
first
interest
DRs
1960s.
the
until
early
were rediscovered and
generate significant
[9],
[10].
in
designs.
Unfortunately,
terms
of
mode
and
resonator
analysed
dielectric constant materials at the time had poor temperature
stability
highcausing
frequency
in
in
As
shifts
spite of
microwave
systems.
a consequence,
unwanted
their high- Q factor and small size, DRs were not considered suitable for microwave
In
the
mid-1960s, theoretical work with experimental
systems.
evaluation of ru-
tile ceramics that had an isotropic dielectric constant in the order of 10(1 was
for
the DR was developed along with
and
a
perfect
magnetic
wall
model
studied
formula
for
between
the
coupling
approximate
coefficient
adjacent resonators,
an
[11]. A bandpass DR filter was also presented by placing TEols mode dielectric
in
TEO,
[12].
As
before,
the
coaxially
a
cutoff
resonators
circular
waveguide,
rod
temperature
problem
of
poor
stability
continuing
velopinent of practical applications.
the first temperature-stable
Raytheon,
by
veloped
[13].
was present preventing the de-
The breakthrough
1970s
in
the
when
came
and low-loss barium tetratitanate
Bell laboratories
reported
ceramics were de-
a modified material
leading
to improved performance,
one
the afore-mentioned
to
[14]. These results
led to the first realisations of DRs as microwave components but these materials
in
for
supply
and
were
short
not
marketable
were
commercial purposes. Murata
Manufacturing Company provided the first commercial DRs
(Zr,
Sa)TiO4
using
that
offered adjustable compositions allowing temperature
ceramics
coefficients to
[15].
+10
between
This
and
ppm/°C,
-12
vary
allowed the desired small control-
8
I Introduction
lable temperature
Review of Dielectric Resonators
coefficients over the useful operational
temperature
range. It
filters,
from
developed
DR
this
in
that
the
point onwards
rapidly
microwave
was
[16,17,18,19].
Furthermore,
filters
dual-mode
filter
technologies,
new
such as
function
[20],
filters
developed,
to
techniques
response
were
along with
and elliptic
improve the spurious response, [21,22,23].
To accomodate these improvements,
full-wave
involving
implemodels
and
were
modeling
analytical
methods
rigorous
[24,25,26].
mented,
1.2.2
Dielectric
Resonator
DR filters play an important
Filters
role in mobile and satellite communications.
A typi-
filter
dielectric
DR
inside
consists
of
a
number
cavities
of
resonators,
mounted
cal
in
Probes
a
metallic
enclosure
are
or
an
evanescent-mode
machined
waveguide.
input
the
to
couple
and output electromagnetic energy and irises are typically
used
for
inter-cavity
resonator coupling. DR filters used in microwave systems can
used
be divided into two configurations:
individual
enclosure
or
a metallic
individual
DRs that are loaded coaxially in
resonators mounted in a planar configuration.
The first practical DR filter was reported in 1975 and a schematic of the 6.9 GHz
filter is shown in figure 1.5, [15].
The mono-mode filter with all resonators operating in the TE016mode provides
low loss and small volume. A planar layout offers many advantages over an
in-line configuration although they are larger in size. These advantages include
layout
flexible
DR
structure,
simple
a
supports and easier tuning mechanisms
for mass production, therefore, these are widely used in base stations for mobile
[27].
A major problem with DR filters is the proximity of
communication systems,
For
instance,
in a filter operating under TEola mode, the ratio of
modes.
spurious
this fundamental resonant frequency to the first spurious HE11smode resonance
is 1.3:1, although this may be improved to 1.5:1 by inserting a hole in the centre of
the DR. Inter-resonator coupling is magnetic and controlled through irises since
a greater proportion of magnetic than electric energy leaks from DRs. A typical
9
1 Introduction
'Adjusting
Review of Dielectric
Resonator.
Screw for Q,
Fine tuning screw
for f,
Tuning screw for the coupling
Higher mode
and neighbouring
O
1.5: Structure of 6.9 GHz DR filter, [15]
Figure
TE0m DR filter for cellular base station applications is pictured in figure 1.6. In
this configuration,
non-adjacent couplings can be used to realise more advanced
filter features. such as elliptic
Quadruplet
responses.
function or asyInilletri(al
be
basic
building
blocks
to generate symmetric
triplet
sections
can
regarded
as
and
for
TE
transmission
zeros
mode cavities.
or asymmetric
J
PI-
ý"
Figure
An alternative
is
Cfir
1.6: TE0Ia DR filter for cellular base-station
application,
structure
consists of grounded
dielectric
This
filter
has a simpler structure
TMoi
mode.
s
single
[281
rods operating
in the
compared to the previous
10
1 Introduction
structure
Reviewof DielectricResonators
dielectric
irises
the
are needed as
since no
other electrically.
rods are coupled to each
A compact DR filter may be constructed
by placing these
high- Q dielectric rods coaxially in a TMOIS circular cutoff waveguide as shown in
figure 1.7.
SRM connector
Tuning screw
TM., cutoff circular waveguide
Figure
1.7: Configuration
Dielectric rod resonator
Resonator support
[29]
TMolb
Dß,
filter,
mode
of a
Even with a dielectric constant of 45, a typical 900 MHz resonator occupies a
8x8x5
of
cavity size
cm which is still relatively
become
factor.
techniques
a
major
size-reduction
large.
As a consequence,
Higher-order
modes are usu-
however,
have
the
as
spurious
modes,
property
considered
certain
modes
ally
to generate multiple
modes for a given structure.
The HElla mode is such a
dual-mode
for
D/L,
diameter-length,
operation
and
ratios
certain
mode allowing
frequency
its
falls
TE01a
below
the
puck
resonant
that
cylindrical
mode.
a
of
of
The dual HElla dual-degenerate mode in cylindrical
DRs was first reported by
Fiedziusko in 1982, [30], as shown in figure 1.8. In this configuration,
only half
the number of physical cavities is needed, offering smaller volume and DRs are
in
the
Low-loss,
in
axially
centre
of
each
circular
mounted
cavity
evanescence.
is
to
mounting
required
assure good electrical and thermal performance.
stable
Coupling between modes within
a single cavity is achieved via a mode-coupling
location
an
angular
with
of 45° with respect to orthogonal tuning screws.
screw
Intercavity
coupling is provided by coupling slots in the form of cruciform irises
situated throughout
the filter such that both resonances are able to couple to
in
adjacent cavities. Elliptic
each other
function responses can also be produced
by cross couplings between non-adjacent cavitites and the
signs of these couplings
by
determined
the orientations of the tuning screws
to
are
each other.
relative
11
1 Introduction
N( cif u' of J), 1 (ir it
R( , otlalovs
The theory used for an empty cavity dual-mode filter based on a coupling screw
design can also be applied here to determine the required couplings as shown in
figure 1.9. [31].
Connectors
%"1C\
ý'Th
Iris
Slots
4ý\
Dielectric
Resonator
(TYP)
Units cm
Figure
Although
3.29 Dia x 10.16 long
[30]
DR
filter,
of a
1.8: Dual-mode configuration
is achieved, unfortunately
good size-reduction
the fundamental mode for this cylindrical
the HEiib mode is not
resonator and a straight 2: 1 reduction
in size is not possible for the same Q. These bandpass filter devices are commonly
used in mobile and satellite communications
applications
due to their low loss
Subsequently, this work has
and small size compared to single-mode realisations.
[33].
been
[18],
improved
[32],
by
Zaki,
Gendraud,
Kobayashi,
upon
since
and
Output
,
?
Coupling
Screws
n
Output
Polarization
is rotated 90°
for
p
n-(4m-2)
m= 1,2,3TE.
Mode
(1)
(Polarization
lll(Input
A1
For Square Waveguide
TE,
(2)
i
Polarization
Figure 1.9: During screw orientations
DR dual-mode filter, [31]
A planar modification
Mode
for cross couplings in an elliptic function
was reported by positioning
the DR on the base of the
12
1 Introductioli
with
cavity
conducting
the DR with conductors
discs placed on top of each resonator,
at both ends, tangential
bottom
top
both
the
and
at
for this structure
theoretically.
Review of Dielectric
of the DR. This allowed
A typical
dual-mode
these metallic
Figure
E fields are diminished
a simple
model to be used
variations
conductors
as shown in figure 1.10. Devices of this
in the metal conductor
It is no surpise that exploiting
greater size reduction.
coaxial filter but, unfortunately
on top of the DR caused frequency
1.10: Conductor-loaded
Electrically.
drifts
due
as high power was applied.
dual-mode DR filter configuration,
multiple
Q
and
Q1A
this
type
of 6300
of
achieved a
resonator
half
the volume of an equivalent
type can occupy
to frequency
By loading
using the TM110 mode to analyse the resonant frequency
6.5 x 6.5 x 6.5 cm cavity
in
MHz
900
a
at
placing
electric,
[34].
Resonators
[34]
degenerate resonant modes will give
the optimum
geometry for a triple-mode
he a sphere but this is not ideal for bulk
would
resonator
manufacture.
To com-
dielectric
be
cube
may
a
used although spurious modes become a detripromise.
here. An example of this is a triple-mode TE0I6 DR filter
factor
inental
operating
[35],
2:
GHz,
1
in
2
offering
a
reduction
size over conventional TEO, & filters.
at
A quadruple-mode DR filter has also been realised and a2 GHz compact filfor
WCDMA
communication systems has beeil reported as shown in
ter suitable
figure 1.11, [36].
13
1 Introduction
Tuning groove
Metal cavity
Review of Dielectric Resonators
Quad mode dielectric resonator
port
Loop probe
Figure 1.11: Quadruple-mode DR filter configuration, [36]
Although
multimode
DR filters have many advantages, they also have a major
drawback in having inferior
additional
out-of-band
spurious characteristics.
lowpass filter is needed to eliminate
increases the size, insertion loss, complexity
Usually, an
the unwanted modes but this
filter.
the
and cost of
Significant
filters,
been
into
improving
has
DR
the
especially
put
spurious response of
efforts
dual-mode filters. For example, both the TE018 mode and HE116 mode filters have
free
but
by
limited
into
them
performance
a mixed-mode
spurious
combining
very
DR filter, spurious performance can be improved. An example uses TEolb monodual-mode
HElla
DRs
filter
in
function
to
as
shown
produce
an elliptic
mode and
figure 1.12, [22]. A lateral offset between the axes of the TEola and HElla mode
because
the magnetic field at the cavity centre
provides
greater
coupling
cavities
is maximum for HE116 mode and minimum for TElla mode respectively.
Unfortunately, an in-line configuration is seen as too cumbersome due to the latbetween
dispositions
dual-mode
the
two
cavitites
the
accomodating
eral
single and
A
is,
therefore, much simpler to implement as
planar
configuration
resonators.
[23].
figure
1.13,
The
in
frequencies
spurious
shown
of the two types of resonators
MHz
500
to
free
produce
a
offset
spurious
are
window, however, since the filter
essentially operates under single-mode operation, the dual degenerate modes are
that
dual-modes
the
is used adding further complexity.
only
such
one
of
split
14
I Introduction
h'f rir ur of Do It ý lI I
J?'r. tiuiiulor.,
Single
Iris
(Msv)
Single
Iris
(M
Figure
f22]
1.12: Configuration
Dielectric
Resonator
12)
of a 6`t' degree mixed-mode elliptic function DR filter,
Toi
HE,
ri
2
---. -Iris
Iris l
Iris 3
0
X
HE,,
M12
f
M23
001
Iris
Iris 2u
In
Mc
JO..
TEo,
Figure
O
M.
LA
.-.
mm"
'J HE,, L-3
TEo,
1.13: Structure of 6h degree mixed-mode DR filter, [23]
Another technique to improve spurious performance is to combine different types
together.
resonators
of
One such resonator is produced on the basis that if the
DR in a dual-mode filter is replaced by a perfect electric conductor, significant
miniaturisation
can be achieved, since the relative dielectric constant of the res-
infinity.
approaches
now
onator
The dielectric-loaded
Q
higher
have
resonators
than conductor-loaded resonators, therefore, low loss is also achievable along with
15
I Introduction
Review of Dielectric
Resonators
impressive spurious performance due to conductor-loaded resonators. Another advantage is these resonators both operate in HE,, dual-mode so that inter-cavity
couplings are simple to realise using cruciform irises. A 1.55 GHz filter is shown
in figure 1.14 where spurious modes are suppressed to below
dB up to 2.8
-40
GHz, [37].
Dielectric Loaded
Cavities
Figure 1.14: Configuration
filter. [37]
Conductor Loaded
Cavities
Dielectric Loaded
Cavities
of 4th order combined conductor and dielectric-loaded
The first waveguide Bandstop filter was proposed by Okaya and Barash, [9], by
placing rutile crystals inside the main waveguide to operate under TE016 mode.
Colin also reported a design configuration
of a waveguide bandstop filter using
Ti02 resonators as shown in figure 1.15. However, problems with these earlier
designs
included too niuch perturbation
waveguide
to the placement of the DRs within
due
the
of
waveguide modes
the main guide producing a poor match in
the passband. Futhermore, unwanted non-adjacent and inter-resonator couplings
were unavoidable as there was no isolation between these resonators.
Chung-li Ren noted the problems of the aforementioned filters, [38], and solved
them by positioning
the DRs outside the main waveguide. In this configuration
the resonators were isolated in their own metal enclosure coupled to the main
waveguide through small apertures on the waveguide walls as shown in figure 1.16.
The couplings between the waveguide and resonators could now be controlled via
apertures and there was now scope for independent tuning for each DR.
In all the above configurations,
the placement of the resonators is seen to be
in
especially
providing
cumbersome
supports for each cylindrical
waveguides are used as the propagation
Also,
as
puck.
medium, a 3/4 wavelength separation is
16
1 Introductimi
-Rectangular
Review of Dielectric
Resonators
Waveguide
OO0b
ýa
Dielectric
Resonator
0aa1o
a
Waveguide
-Rectangular
Figure
1.15: Bandstop filter with DRs placed transversely along waveguide, [38]
Y
1
b
3/41,80
I--
a=2b
(a) Hx Coupling
L
3/4 Xea
a=2b
(b) HZCoupling
Figure
F
a
x
1aT-0
ii
ý-b-4
'Y
1.16: Bandstop filter with DRs placed outside waveguide, [38]
between
between
fringing
field
to
each resonator
avoid excessive
needed
coupling
For
leading
degradation
in
to
in
the
topologies.
the
a
resonators
response
above
TEMPIlines, such as coaxial or microstrip,
needed producing
more compact structures
only 1/4 wavelength separations are
[26].
figure
1.17,
in
shown
These
designs have shown how cumbersome the fabrication process can be to provide the
frequency,
coupling and phase separation between each resonator.
correct resonant
It is, therefore, not surprising that there has been very few bandstop filter designs
involving higher order modes where the coupling scheine involves a large number
for
independent
tuning
elements
control of each degenerate modes. intra-cavity
of
17
1 Introduction
and inter-cavity
Scope of the Study
To date, a triple mode hybrid reflection mode was
coupling.
described but involves coupling bandpass resonator cavities to a3 dB quadrature
hybrid, thus, it is not strictly
a pure dielectric bandstop resonator. To realise a
dual-eiode design, along with correct control of resonant frequencies and couplings
within the cavity, the separation between the tap points of the main transmission
line must also be accurate and the finite dimensions of these tap elements will
provide some measure of unwanted coupling between them.
lý. (:....,...
Figure
1.17: Microstrip
TT-:,
ýý:..
M----
DR bandstop filter with quarter-wavelength
unit ele-
ments
1.3
Scope of the Study
DR filters have been of considerable interests recently but have only evolved
bandpass
filters.
around
There is little published material on DR bandstop fil-
ters, thus, the proposal for this work was to develop and realise practical bandstop
filters using high permittivity
dielectric materials to miniaturise conventional air-
bandstop
in
filters.
resonators
microwave
cavity
Note that the development of
filter
is
Chebythe
this
thesis,
prototypes
therefore,
out
of
scope of
novel
classical
Chebyshev
inverse
approximations
shev,
and direct-coupled
design
The
for
the
process.
majority
used
of the research work centred around the
configurations
factors in the physical realisations using 3D HFSS simulations.
been
has
incorporated
design
mode
using dielectric-loaded
knowledge,
To
the
author's
previously
uides.
lines
forming
transmission
bandstop
to
filter.
a
coupled
Firstly, a mono-
rectangular
only cylindrical
were
waveg-
been
have
pucks
In using the properties
18
1 Introduction
dielectric-loaded
of a
Organisation of Thesis
waveguide resonator, an advantage is seen in the spurious
dielectric
Using
isolated
to
rectangular
as
compared
an
resonator.
performance
DRs also provide ease of manufacturing
compared to cylindrical
for
lower
costs
mass manufacturing.
viding
resonators pro-
The design is much simpler as these
leaving
grounded
cavity
resonators
are
against
only a coupling
walls,
waveguide
face to the transmission line and an open face for tuning. The result is no complex
design is required for the dimensions of the cavity.
A Chebyshev filter was de-
SZ
50
line.
The
to
each
resonator
coupled
with
a
second structure
coaxial
signed
filter
has
DR
dual-mode
knowledge,
to
the
never
which
again,
author's
uses a
been published before. By exploiting the dual degenerate modes, miniaturisation
is achieved through producing two modes in a single cavity as opposed to monodesigns.
its
The
is
in
two
this
coupled-cavity
versatility
novelty of
structure
modes
for
DR
filter
novel
configurations.
as a practical
Measured results produced an
inverse Chebyshev response. To achieve coupling into both modes, a right-angle
designed
line
was
and the resonators were magnetically
coaxial
coupled through
fixing small coaxial probes to metal posts in the base of the cavity.
A number
design
including
HFSS
in
filters
both
the
simulations
were
performed
use of
of
of
the eigenmode solver and parametric analysis to achieve the required dimensions
for fabrication.
The final section leverages the dual-mode bandstop resonator in
direct-coupled
novel
configurations,
lations demonstrating
including a cul-de-sac form, with EM simu-
only a quarter wavelength transmission line is required to
directly couple the source and load resonators to create miniaturised
dielectric
bandstop
filters.
resonator
1.4
Organisation
Thesis
of
Firstly, this chapter has identified the benefits of DRs and how, only in recent
times, they have become popular in the microwave industry due to the availability
of temperature-stable materials. Advantages over bulky waveguide and coaxial
have
been
discussed. The benefits in using higher-order modes includstructures
I Introduction
19
Organisation
of Thesis
ing recent DR filter designs has also been described and this allows a substantial
filters.
in
volumes
of
cavity
reduction
In Chapter 2, a review is presented of filter designs stating the stages from the
initial prototype to the transformed circuit model. Also included is an advanced
technique
using a coupling matrix
synthesis
design
direct-coupled
to
polynomials
to generate generalised Chebyshev
bandstop filters. Note that physical realisa-
tions are not discussed here.
Chapter 3 reviews the properties of DRs and how they are designedusing a variety
Couplings
from
to
simple
models
more rigorous numerical models.
of methods
between these DRs and different transmission lines is also discussed.
Chapter 4 covers the design of a TEloa mode compact DR bandstop filter. First,
is
dielectric-loading
before
the
waveguide
analysed
concept of
a rectangular
is
introduced and the effects on its Q factor are considered. A bandstop filter is
designed based on the Chebyshev characteristic.
Simulated and measured results
for a 4th degree bandstop filter are shown with shortcomings in the fabrication
discussed. At the end of this chapter a novel wideband dielectric-loaded
coaxial
introduced.
is
resonator
In Chapter 5, a novel HEE11 dual-mode dielectric bandstop resonator is analysed
faced
developed
is
in
discussions
the
experimental
cavity
an
with
problems
and
on
design process. A dual-cavity 4th degreebandstop filter is designedand measured.
The direct-coupled bandstop resonator is discussed showing how the dual-mode
bandstop resonator compliments the synthesised coupling matrices for the original
forms.
and cul-de-sac
Lastly, Chapter 6 summarises the fundamental aspects of this thesis, along with
advantages and shortcomings for both filters. Improvements are also discussed.
20
2
Chapter
Filter
2.1
Design
Introduction
Microwave filters are important
to extract the desired frequency spectrum from a
theoThis
describes
basic
and
signals.
concepts
chapter,
wide variety of electrical
[39].
Generally,
filters
RF
design
their
and
considerations,
ries of microwave and
has a brick-wall transfer response with instantaneous transition
filter
ideal
an
due
delay
to
in
impractical
but
is
the
this
bands and constant group
passband
finite-order
limitations
lossy
of
practical
To realise the filter function
filters.
for a lowpass prototype
transfer
the
and reflection polynomials
required,
be established.
It is seen later that a lowpass prototype
must
be
translated
can
to
bandpass or bandstop response as required and the synthesis of a
highpass,
a
lead
to
the
implementation
circuit
will
eventual
physical
prototype
in transmis-
design
line,
filters.
The
procedure
waveguide,
printed
circuit
or
other
media
sion
the required transfer function,
follows from the required specifications outlining
degree of filter and location, if required, of transmission zeros to form
loss,
return
the ideal characteristics
filter
the
of
polynomials.
first introduced to calculate these polynomials
The recursive technique was
for symmetrical
and asymmetri-
[40].
The
into
be
then
translated
polynomials
a prototype
may
performance,
cal
through
[41],
the
either
circuit
synthesis,
network
or the direct coupling matrix
[42]. An advantage of the latter is the
be
transapproach,
coupling matrix may
21
2 Filter Design
Types of Filters
formed to suit the physical couplings required in the physical implementation,
[43] and [44]. This is the case for dual-mode designs where the matrix
can be
form
The
the
then
to
may
necessary
coupling
paths.
prototype
network
arranged
be realised by a physical resonator using 3D electromagnetic,
EM, simulations as
dimensions
for
filter.
Tuning
to
the
the
achieve
correct
methods are
guide
entire
a
for
discrepencies
implemented
to
between
the simulated and
compensate
any
also
fabricated designs taking into account manufacturing
behind
The
theory
errors.
found
be
in
is
these
techniques
but
the
this
thesis
out
of
of
scope
may
of
much
[45].
2.2
Types of Filters
Filters can be classified as one of lowpass, highpass, bandpass or bandstop, [46].
The first is a filter permitting
low frequencies and rejecting frequencies higher
than the rated cutoff frequency and the highpass performs the opposite function.
Bandpass and bandstop combine lowpass and highpass filters to select interested
bandwidths
lumped-element
rad/s, w=1.
The lowpass prototype
and reject others.
operating in a1
In addition,
is defined as a two-port
SZsystem with angular cutoff frequency of 1
it is passive and reciprocal.
These responses can be
by
ladder
the
synthesis
of
networks, of which the simplest is Cauer's
analysed
form consisting of series inductors and shunt capacitors as shown in figure 2.1.
S,
-------------
g
S:
9H
1g4
N-ý
N odd
1!2
N even
9N.,
-
14
rn
Figure 2.1: Lowpass prototype ladder filter
networks
An alternative transformation technique, [47], compliments inverters
with reactive
22
2 Filter Design
Types of Filters
lowpass
ladder
in
a
network where the inverters are coupled with series
elements
inductors or shunt capacitors, figure 2.3. This process provides a good approxibandwidths
for
depending
20%
narrow
upto
on the physical realisation.
mation
An inverter, shown in figure 2.2, is a frequency independent two-port network
between
load
impedance,
input
impedance,
Zen
the
the
relationship
and
where
ZL, is defined by
K2
Zin = ZL
(2.1)
ZL
F
ZIN
Figure 2.2: Impedance inverter terminated in a load
in
(a)
in
(b)
Figure 2.3: General Nth degree inverter coupled lowpass
prototype with (a)
inductors (b) capacitors
23
2 Filter Design
2.3
Impedance
Impedance Transformations
Transformations
For impedance transformation, the 11 impedance of the prototype is converted
to an impedance level of Zo by scaling all the reactive elements in the filter by
ZOusing the following transformations
L -ý ZOL
C
(2.2)
Zö
K -+ZOK
2.4
Lowpass to Bandstop
Transformation
Bandstop configuration allows power to pass through the resonator at frequencies
but
is
resonance
power
absorbed from the coupled line at resonance inoutside
impedance
the
effective
of the resonator leading to more reflections. The
creasing
transformation from the lowpass prototype to a bandstop filter with arbitrary
frequency
bandwidth
and
centre
can be performed where the transmission zeros
for
lowpass
the
infinity
prototype is mapped to wo. The response is shown in
at
figure 2.4 and the transformation is set out below.
w -+
-1
ö- )
(2.3)
where,
wo = (w1w2)1/2
(2.4)
bandwidth
factor,
the
scaling
and
a is given by,
a=
wo
wo
_ Ow
w2 - wl
band
the
w2
and
are
wl
edge frequencies.
when
(2.5)
2 Filter
24
Design
Transfer
152112
Functions
152112
Co,
w,
Co
-1
Co
Figure 2.4: Lowpass to bandstop transformation
Applying this transformation leads to the transformation of elements as shown
in figure 2.5.
L, _aL
wo
L
C, _
aLo
,: =
C
1
1
aCwa
41-
HH -f
C, =aC
Wo
Figure 2.5: Bandstop transformation of an inductor and capacitor
2.5
Transfer
Functions
The transfer function of a two-port network can be written as:
1S21(jW)12
1
°1+
c2F
2
ri
(w)
(2.6)
'a
is
F(w)
e
ripple
constant,
where
represents a filtering or characteristic function
frequency
is
For
the transfer function in equation 2.6, the
variable.
a
w
and
insertion loss response of the filter can be solved using:
LA(w) = 10109
1
dB
ý921(jW)12
(2.7)
2 Filter
25
Design
Since ISll(jw)12 + IS21(jw)12 =1
Transfer
Functions
for a lossless, passive two-port network, the
filter
loss
is
the
of
return
2.5.1
Butterworth
(2.8)
IS21(jw)12)dB
LR(w) = lOlog(1-
or Maximally
Flat Approximation
filter.
low
ideal
is
butterworth
the
to
The
pass
response
simplest approximation
an
The response is flat at d. c. and rolls off to 3 dB at w=1
before flattening out
figure
in
2.6.
infinity
shown
as
at
again
IS121
=2
=4
6
0
we
G)
Figure 2.6: Frequency response of butterworth lowpass filter for varying N
The transfer function describing this response is given by:
IS21(jw)12 =1
1 +. W2N
.
(2.9)
loss
insertion
is
the
and
LA(w) = 10log(1 + w2N) dB
degree of the network.
N
is
the
where
(2.10)
26
2 Filter Design
rnnsfer
Design formulae for both lowpass prototypes
Functions
for a general Nth degree with in-
(b)
(a)
by
inductors
figures
2.3
in
and
or capacitors, shown
verters separated
for
G,.,
below.
the
given
are
element
values,
respectively,
G, = L,. or C,. =2 sin l
Kr,
2.5.2
Chebyshev
A better approximation
is one containing
r+l =1
)7r
(2r
2N
(2.11)
(r = 1, N)
...,
(r = 1, N...,
(2.12)
1)
Approximation
than the maximally
flat to the ideal transfer function
a rippled response in the passband region.
Chebyshev
approximation
a
The response of
is shown in figure 2.7 and the insertion loss at the
defined
by
is
level
ripple
(2.13)
LA = 10log(1 +w2TN(w))
1
IS.,I2
WO
(! )
Figure 2.7: Frequency response of a Chebyshev lowpass filter
An expression for the transfer function of this response is given by
IS (jW) 12=1
21
1+
ý2TN(w)
(2.14)
Thznsfer Functions
27
2 Filter Design
defined
is
in
as
level,
the
the
and
passband
the
e,
ripple
controls
ripple
where
e_
(10LR/10
(2.15)
1)-1/2
-
Chebyshev
Nth
is
TN
the
polynomial and e<1
order
where
is a real constant.
These polynomials are defined in terms of a real variable w as
TN (c)
cos[N
=
(2.16)
cos-'(w)]
the
below
be
to
in
terms
of
either
Element values,
of rj, are given
applied
and can
Nth degree lowpass prototypes asfor the butterworth design.
Kn, n+i =
[712+ sin 2(r7r/N)]
77
r=1,
...,
N-1
(2.17)
is
impedance
inverters.
KR,
the
the
of
R+l
where
[(2r
1)ir
L, =2 sin l
2N
77
r = 1, ..., N
(2.18)
where
1
rý = sinh
2.5.3
Inverse Chebyshev
sinh-1
(2.19)
Response
This approximation is the inverse of the normal Chebyshev in that it is maximally
flat in the passband but is equiripple in the stopband as shown in figure 2.8.
This function is used in applications where a non-infinite stopband attenuation is
tolerated and a symmetrical stopband can be achieved by controlling the ripples
in the stopband using zeros in a low pass transfer function.
2 Filter
Transfer Functions
28
Design
12
IS12
1
.2
HS2
-a
Figure 2.8: Frequency response of an inverse Chebyshev filter
The transfer function is defined as
IS21(jW)12=11
1-F
(2.20)
ý2T2 (1/W)
and
LA
1
20 1og
(2.21)
A highpass prototype is shown in figure 2.9, [41], and the element values are
calculated using
Cr
217sin[(2r - 1)7r/2N]
( (2r 1)ir ,
B,. = Cr cos L
2N
Kr,
r+l =1
(2.22)
(2.23)
(2.24)
29
°LFilter Design
Transfer Functions
to
is
Figure 2.9: Highpass prototype for inverse Chebyshev filter
2.5.4
Generalised
Chebyshev
It is possible to realise a polynomial
adjacent cross couplings.
Response
function using extra resonators with non-
The response of elliptic filters has rippled approxima-
tions in both the amplitude of the passband and stopband regions. This provides
filter
to
selective
attenuation
more
slopes
as
of equal
compared
any other
much
degree. The frequency response is as shown in figure 2.10 with finite-frequency
transmission zeros present in the stopband.
is.X
1
Minimum Attenuation
Attenuation Floor
VIW
Figure 2.10: Frequency response of an elliptic lowpass filter
a disadvantage of this response is transmission zeros are prescribed
frequencies.
Thus,
basic
Chebyshev
the
at certain
polynomial is considered too
filter
for
designs.
The
advanced
generalised Chebyshev transfer response
simple
Unfortunately,
for a lowpass prototype is,
IS21(.
7w)12-11+
FN(w)
for
+1
<
<
<w<
with -1
-1
+1
e2FN(w)
(2.25)
30
2 Filter Design
for
FN(Wr)
r=1,...,
and
Direct-Coupled Bandstop Filters
N
frequency
is
the
transmission
the
of
rth
zero.
w,
where
The cross couplings can be made in an inverter-coupled
inductive,
or
positive,
capacitive,
negative,
couplings add transmission zeros or
Adding
transmission
ther
to
real
response.
poles
increase
selectivity.
can
network where additional
zeros in the frequency doman
The design for such a filter can be approached through
the addition of cross-couplings to a Chebyshev prototype, performing an analysis
and optimisation
program to achieve the response. This technique is suitable for
basic structures but for more complex designs requiring asymmetric or multiple
further
is
technique
transmission
a
zeros,
of
required.
pairs
2.6
Direct-Coupled
Bandstop
Filters
In conventional Chebyshev bandstop filter designs, each resonant element is couA/4
to
a main transmission line. An advanced approach
of
multiples
odd
at
pled
between
the
transmission line and resonant cavcouplings
of
number
can reduce
ities dramatically,
therefore, wideband performance is potentially
better.
Since
the resonant frequencies are tuned within
the stopband, the main signal need
input
through
the
travel
and output
only
tap points, bypassing direct-coupled
high
handling
to
give
power
and minimum
resonators
insertion loss.
The technique stems from generating transfer polynomials
for
the
solving
and
filter function as described in [40] following the Darlington
synthesis procedure
the
[31]
around
coupling
matrix
model,
and revolves
and [42]. This can be applied
to the asymmetric case and to singly and doubly terminated
That
is,
networks.
filter
networks for any type of filter function including:
the method produces
1. Even and odd degree
2. Prescribed transmission zeros
3. Asymmetric or symmetric characteristics
31
2 Filter Design
4. Singly or doubly terminated
Direct-Coupled Bandstop Filters
networks
An example of the 4th degreeN+2 coupling matrix with all possible cross-couplings
is shown in figures 2.11 and 2.12, [45]. The core 4x4 matrix describes the adjabetween
resonators and the whole matrix is symmetrical around
couplings
cent
the diagonal axis. From this matrix it is possible to calculate the element values
in the circuit network using equations described in [47].
Ms.
Mss
Ms.
c
x
Ms.
1
MIL
ýM
M,
w
M,.,,
Figure 2.11: N+2 multicoupled resonator circuit
Si
S
Mss Msl
1 Ms,
2
3
4
L
234L
MS2 MS3 MS4 MsL
Mil
M11
MI3
MIL
,4
MS2
M12
MS3
MIS
M23
M33
Al34
M3L
MS4
Mu
M24
A
M
M4L
MsL
'",
M4L
1v
M22
1v!
M24
23
2L
34
A2L
M3L
L
Figure 2.12: 4th degree N+2 coupling matrix
Core NxN matrix within double lines
M
LL
with all possible cross-couplings.
To generate the exact solution for the filter element values given a set of initial
three
essential steps are required:
parameters,
32
2 Filter Design
Direct-Coupled Bandstop Filters
1. Network synthesis
2. Generation of coupling matrix for Nth degree network
3. Reduction of matrix to represent realisable coupling elements
The network synthesis begins from first considering a losslesstwo-port network
degree
Nth
functions
defining
transfer
the
two
the
and reflection
as
ratio of
and
[45],
polynomials,
F(s)/ER'
Sll(s)
_
P(S)
S21(s)
E(s)
(2.26)
-
cE(s)
from
for
is
is
2.19
the
equiripple
general
passband
equation
e
and CR unity
where
for
functions
canonical
where all transmission zeros are prescribed
casesexcept
frequencies
is
finite
ei
given as,
and
at
ER
E
-2-
(2.27)
1
To develop the bandstop characteristic, the reflection and transfer coefficients and
become,
to
exchanged
are
constants
P(s)/c
S11(s)
_
S21(s)
E(s)
F(s)
(2.28)
_
-RE(s)
The shared common denominator of both functions preserve the unitary condition
for a passive losslessnetwork,
5112+S
212 =1
(2.29)
In effect, with respect to a Chebyshev characteristic, the original equiripple return
loss is now transformed to the transfer response and the minimum rejection level
33
2 Filter Design
Direct-Coupled Bandstop Filters
As the degree for top and
is now equivalent to the original return loss level.
bottom of S21 are now equal, the synthesized network is now canonical, thus, the
S11
function
is
the
transfer
of
original
polynomial
new numerator
and can realise
less
figure
is
transmission
this
prescribed
or
of
equal
zeros provided
any number
than the Nth degree. Note that e1 =1
degree. To form the polynomials
for the number of zeros less than the
for a bandstop filter, P(s)/e and F(s)/eR are
in
the
process to calculate the polynomials
exchanged
for a lowpass prototype,
[40].
described
below
in
as
outlined
For a losslessnetwork,
1
S21M' -1
1
(1+icN(w))
(w)
e2CN2
"t-
(2.30)
(1_jCN())
ER
CR
where
Fw
CN ýwý _
7
To generate the polynomials and location of transmission zeros, the recursive
technique is performed on the derived equation 2.31 for the general Chebyshev
through
mathematical techniques described in [45].
characteristic
1
CN (W)
2
[(w
nn
i
-
1/Wn)
+
(1 - 1/wn
1n=1(1
-ý
JIN-
L/W-
O1
-
Zw
-W/Wn)
(2.31)
11
2(w2
1)1/and
w'
wn are the prescribed transmission zeros. These must
=
where
be symmetrical about the imaginary axis of the s-plane for F(w) and P(w) to
be purely real and the number of zeros must be of order no greater than N-2 to
implement the physical filter. The polynomial, CN(w), is of Nth degree and the
be
infinity.
The recursive technique is performed
zeros
must
placed
at
remaining
from n=1
to the Nth degree to yield the polynomials for F(w). PN(W)
may now
J
34
2 Filter Design
be derived
as the denominator
Direct-CoupledBandstopFilters
of CN(W)4
wJ
PN(w) = IIn 1 11wn
L
(2.32)
The next polynomial E(w) is more complex and requires the Hurwitz polynomial
have
they
in
that
the
that
are
negative
so
all
roots
real
parts
s-plane
condition
hand
left
imaginary
The
the
the
located
side
of
on
axis.
complex polynomial
now
p(w)/e - jF(w)/ER is formed and the roots are found positioned alternately and
is
bottom
top
The
the
the
a
root
of
and
of
w
plane.
conjugate
symmetrically on
by
j and E(w) may now be obtained. The coupling
through
multiplying
taken
from
finding
be
the
synthesised
now
admittance parameters, y21(s)
may
matrix
for
for
As
two-port
an even
short-circuit
network.
a
an example,
and y21(s),
load
SZ
impedances,
1
and
source
network with
(F(S)/ER)
Y21n(s)
Y21(S)
=
_
yd(S)
ml(S)
y22n(s)
1122(8) -
yV(s)
(2.33)
_
ni(s)
(2.34)
mi(s)
where
ml(s) = Re(eo+po)+
ni(s) = jIm(eo
jIm(el
+pl)s+Re(e2+p2)s2
+po) + Re(el + pl)s + jlm(e2
+
+p2)82 + ...
N,
i=0,1,2,3,...,
the
P(s)/e
pi,
are
E(s)
and
complex
e;
coefficients
and
and
reof
The coupling matrix is synthesised with
spectively.
one noticeable exception since
S21(s)is now fully canonical, the direct source-load coupling NISL is calculated
from,
35
2 Filter Design
jMSL =
Y21(8)
yd(s)
Direct-Coupled Bandstop Filters
ni(s)
(2.35)
__ ml(s)
For the noncanonical case where the number of transmission zeros is less than the
Nth degree, PN = 0, and from the equations above, yd(s) = 1. Together with the
properties that the leading coefficient F(s) is unity for Chebyshev characteristics,
for
e1
noncanonical designs, therefore, MSL = 1. This provides the
along with
direct-coupled property where the source and load coupled inverter have the same
line.
impedance
be
\/4
transmission
and
can
modelled as a
characteristic
uniform
Note that for the fully canonical case, MSL will have a value slightly below unity
finite
the
return loss at infinite
providing
frequency.
The synthesis technique
by
finding
the residues and eigenvalues of the admittance functions to
proceeds
construct the coupling matrix.
form using similarity
This coupling matrix
is then reduced to folded
transforms, such that it represents the coupling network of
the physical filter. An example of a symmetric 414degree bandstop filter in folded
form is shown in figure 2.13 demonstrating
the signal path is directly
coupled,
MSL.
SL
Coaxial
(a)
Figure 2.13: Direct coupled (4-2) bandstop
diagram (b) realisation with coaxial cavities
(b)
filter,
[48]: (a) coupling-routing
For a doubly terminated network between source and load impedances and if the
less
is
than the Nth degree, then cul-de-sac configuration
zeros
reflection
order of
a
by
formed
be
adding two unity impedance 45° phase lengths at either end
may
36
2 Filter Design
of the network.
Direct-Coupled Bandstop Filters
This represents multiplying
the F(s) and P(s) polynomials by
j that only introduces a 90° phase change without
changing the overall transfer
A
the
typical configuration
response
of
network.
and reflection
filter is illustrated
for the bandstop
in figure 2.14 and clearly shows the core quartet of resonators
for
for
diagonal
the
removing
need
cross-couplings, even
in a square formation
asymmetric characteristics.
As for the original direct-coupled
form, MSL is unity
for the number of reflection zeros less than the Nth degree meaning only a A/4
transmission line is required between the input and output.
The form is defined
by the last resonator in each of the two chains having no output coupling, hence
the name for this form.
SL
M
-º
a
s`
-º
MssýMAL
t
-0----------2143
1®
O
Mýj
(a)
M,
®
"
Mý"
O
(b)
Figure 2.14: Direct coupled (4-2) bandstop filter,
diagram (b) realisation with waveguide cavities
These two configurations
[48]: (a) coupling-routing
demonstrate that only a A/4 length of uniform trans-
form
line
is
to
bandstop
This
filter.
needed
a
multi-resonator
asserts the
mission
lengths
transmission
between
reduced
of
phase
advantage
resonator to transmisline
tap
the
points
removing
need to tune these phase lengths and reduce
sion
transmission line dispersion. In addition, matrix operations can be applied to
the
topology
and performance of the simulated circuit.
reconfigure
2.6.1
Quality
Factor
Practical filters have components with finite resistance producing loss in the sysloss
be
This
can
accounted for by the Q of the filter. In Chebyshev prototem.
Nth
degree
bandpass
for
filter of centre frequency, fo,
an
types,
and bandwidth
2 Filter
if,
37
Design
Direct-Coupled
Bandstop
Filters
the unloaded Q is given by
Qu
4.343foN
_
fILE
gr
(2.36)
r=1
IL
is
insertion
loss
is
the
the value of the rth element of
midband
and
gr
where
the lowpass prototype.
External losses are also evident due to coupling fields
from input probes to the filter and is attributed to an external quality factor,
QL. The loaded quality factor, QL relates any external and internal lossesand is
design
It
for
is
bandpass
filter
bandstop
important
parameter
structures.
and
an
defined as
,L
QU+Q
(2.37ý
ext
U$Y
UNNERSIT`(
LEEDS
38
Chapter
3
Dielectric
3.1
Resonator
Basic Properties
Resonators are important
Filters
Dielectric
of
Resonators
filtering,
in
components
microwave systems acting as
frequency selection in oscilloscopes, amplifiers and tuners. At resonance, stored
fields
leading
to maximum energy stormagnetic
energies
and
are
equal
electric
difference
fields.
Since
internal
by
the
is
to
resonator
reactance
proportional
age
between electric and magnetic energy storage, the input impedance at the resoA
is
dielectric
boundaries
frequency
free-space
purely
real.
can
object
with
nant
due
in
internal
to
modes
various
reflections of electromagnetic
resonate
dielectric
high
the
constant material/air
at
boundary.
waves
The dimensions of a DR
fundamental
dielectric
in
for
the
the
the
of
one
wavelength
order
material
are on
As
Ad
=aE,.,
mode of resonance.
the dielectric,
where Ad is the wavelength associated with
A is the wavelength in freespace and
dielectric
is
the
relative
er
dimensions
become
the
A
to
resonator
as Er
smaller when compared
constant,
increases. Since the dimensions of an air-filled cavity are of the order of A, a DR
has much smaller dimensions than the cavity resonator.
During the previous decade, many advances in dielectric materials have led to
the successfulcombinations of high Qs, high dielectric constant and small temdrift
in
for
materials
suitable
use at microwave frequencies. High Q
perature
dielectric
with
constants ranging from 20 to 90 are now commercially
materials
39
3 Dielectric Resonator Filters
from
various manufacturers.
available
Quality Factor
At microwave frequencies, the classical dis-
increases
dielectric
loss
dielectric
that
the
theory
with
of
materials
states
persion
frequency, f, whilst er remains unchanged, [49]. Therefore, the product of Q and
f can be used to classify the fundamental properties for each dielectric material.
Table 3.1 lists the characteristics of dielectric materials currently available. These
have
highbut
Q
high
dielectric
also good
values and
constants
materials not only
temperature
stability.
By adjusting
proportions
in
the mathe
of
compounds
for
the linear expansion of the ceramic, perfect temperature
terial and allowing
The
is
temperature
possible.
compensation
dielectric
the
material,
of
frequency
the
resonant
coefficient of
r,, combines three independent factors that include
temperature cofficient of the dielectric, Te, thermal expansion of the material, aL,
the
thermal
of
expansion
environment
and
in which the resonator is mounted.
Resonant frequency shifts due to intrinsic material parameters are related by the
in
below,
the
temperature
coefficients
equation
above
Te
Tfý-2
-aL
(3.1)
To advance the technology of these materials, the properties of the material must
be measured accurately. Hakki and Coleman provided a method to measure the
loss tangent of the dielectric,
[51], which was later improved upon by Kobayashi
[52].
Katoh
The
technique involved measuring the
greater
with
accuracy,
and
dielectric
dielectric
properties
of
a
microwave
both ends by two parallel conducting
plates.
rod resonator short circuited
at
This allowed the advancement of
new materials.
3.2
Quality
Factor
Practical filters have components of finite resistance that produce a degradation
in performance. The effects of this resistance can be related directly to the Q
3 Dielectric
Resonator
Materials
Quality
40
Filters
I
E_
0
7`C
(DDm)
r,
(GHz)
.f
7
10
10
MgTiO3-CaTiO3
Ba(NIg,Ta)03
Ba(NIg,Ta)03
21
25
25
8000
16000
35000
0
3
4
Ba(Sn, Mg, Ta)03
25
20000
0
10
0
0
0
5
2
0
2
+5
-5
15
0
+460
+910
+1700
10
12
10
11
6
7
6
5
2
1
Ba(Mg, Ta)03-Ba(Zn, Ta)03
Ba(Zn, Nb)03-Ba(Zn, Ta)03
Ba(Zr, Zn,Ta)03
(Ca,Sr,Ba)Zr03
BaO-Ti02-W03
(Zr, Sa)Ti04
Ba2Ti9O20
Sr(Zn, Nb)03-SrTiO3
BaO-Sm203-5TiO2
BaO-PbO-Nd2O3-TiO2
Ti02
CaTiO3
SRTi03
15000
27
14000
30
10000
30
4000
30
8800
37
7000
38
8000
40
43
5000
77
4000
90
5000
104 40000(Qf)
180 70000(Qf)
304 33000(Qf)
Factor
-
Table 3.1: High- Q dielectric materials, [50]
factor. The definition of the Q factor is given by,
in resonator
energy stored in resonator
energy
stored
27r
Q_W
=
energy dissipated
energy dissipated per cycle
(3.2)
In
figure
dimensionless
Q
is
loss
in
the
providing
order
a
of merit of
circuit.
where
be
the
energy
must
resonator,
coupled into the resonator with either
to excite
To
into
input/output
take
the
coupling.
electric
account
of
effects
magnetic or
factor
the
loading,
of a structure can be broken down into different factors,
quality
Qv,,
Q,
Q,
Qe
The
first
the
QL.
Q,
loaded
the
external
the
unloaded
and
namely
for internal lossesand the external Q accounts for external
Qv,
accounts
unloaded
losses when the resonator is part of an external circuit. The loaded Q is the
into account the loading effects of any external circuits on
factor
taking
quality
itself
includes
both
internal and external losses. This figure
and
the resonator
however,
Q.
Qe
In
be
easily,
be
measured
and
can
cavity
only
extrapolated.
may
dielectric medium, conductor loss
the
and radiation can contribute
resonators,
Q.
These
losses
be
individually
dielectric
If
the
can
the
unloaded
to
classified.
3 Dielectric
Resonator
41
Filters
Quality
Factor
high
DR
is
from
is
the
the
the
enclosure,
and
of
physically
remote
walls
constant
the electric and magnetic fields of a given resonant mode will be confined in and
fields
forming
These
the
the
of
will
material
vicinity
a resonant structure.
around
freespace
distance
to
the
to
values
negligible
within a small
relative
attenuate
Q
As
losses
become
the
a result, radiation
unloaded
minimal and
wavelength.
determined
filter
by
loss
is
dielectric
the
tangent
the
the
primarily
material
of
of
DR
filter.
is
loss
The
the
for
dielectric
to
tangent
material
construct
a
used
defined by
o'
tanb=
WEper
dielectric
is
is
the
the
constant,
ever
a
conductivity
where
frequency.
is
the
radian
w
Note that
(3.3)
of the medium and
Q is inversely proportional
to fractional
bandwidth allowing DR filters with high- Q to have narrow bandwidths.
If all the
is
losses
the
inside
DR
the
of
resonant
energy
mode
stored
occur
no
and
electric
due to external fields, the unloaded Q is
tan S
(3.4)
Dielectric losses then become dominant and largely dependent on Q. For all
DRs,
losses
external
will always occur due to some form of radiation or
practical
dissipation in a surrounding
metal shield. These losses will reduce Q., however,
increase
Q.
energy
stored
will
external
For a permittivity
greater than 100 or
higher, these effects are negligible and equation 3.4 becomes a good approximation
for the unloaded Q of a DR. The benefit of this is that an unloaded Q of 50 000
in
be
a reasonable volume, of which, would be impossible for metallic
obtained
can
filters.
waveguide
For a resonator in bandpass, or bandstop configuration, with resistive matched
load
impedances,
loaded
the
and
quality factor can be obtained from measource
dB bandwidth of the S21,or S11
3
the
suring
as shown below,
Quality Factor
42
3 Dielectric Resonator Filters
f0
QL
=
(3.5)
tf3dB
S21,
frequency
the
Of3dB
dB
bandwidth
fo
is
is
3
the
the
of
resonant
and
where
A
3.1.
figure
is
in
typical
transmission
S11,
response
shown
response.
or
0
M -3
b
N
N
0
a.
u
E
Iw
F
to
Frequency
Figure 3.1: Transmission responsedisplaying resonant frequency and 3 dB bandwidth
The external Q can then be obtained from QL and the insertion loss of the
frequency
by
the
at
resonant
solving,
resonator
ýQw
QL
Qe
-
S21
f0)
or
QL
e=
(3.6)
s11(f0))
S21
is
S11
the
transmission
fo,
the
and
reflection
resonance,
at
coefficient
where
for a bandpass and bandstop resonator respectively. The unloaded Q can then
be found from,
QL
Qu =1-
or
S21(.fo)
(Qe
QL
=1-
Sii (fo) I
(3.7)
For accurate measurements,the coupling should be weak such that any influence
from the loss of the feedline structure has negligible impact on extrapolation of
Q.
The
definitions
three
above
the unloaded
can be related by
43
3 Dielectric Resonator Filters
Coupling to a transmission line
11_1
Qu
QL
(3 8)
Qe
Thus, the Qv of a resonator can be measured.
3.3
Coupling
to a transmission
line
An advantage of DRs is the ease with which they can couple to common transA
DR
lines.
be
in
typical
TEola
transversely
the
operating
can
mode
mission
inserted into a rectangular waveguide and by coupling to the magnetic field, a
filter
formed
is
figure
bandstop
in
3.2.
Coupling
the
to
magnetic
as
shown
simple
field in the waveguide can be adjusted by rotating the resonator or moving the
In
the
the
line
the
towards
side
of
waveguide.
applications,
microstrip
resonator
Rectangular
tic Field
TE,,, Dielectric Resonator
Figure 3.2: Magnetic field coupling of a DR to rectangular waveguide
forms
bandstop
DR
figure
in
filter
3.3.
magnetically
couples
and
a
same
as shown
This is the simplest way to incorporate a DR into a microwave network. In this
by
is
lateral
the
adjusted
coupling
movement of the resonator from the micase,
A
low-loss
line.
low
dielectric
be
support
with
crostrip
may
material
constant
the
increase
to
which
resonator
the Q. In order to prevent losses
would
raise
used
due to radiation, the entire device is enclosed in a metallic box, often aluminium.
The resonant frequency may be calculated using equations from [53] and may
be increased through perturbing the magnetic field via a tuning screw, or metal
the
down
in
frequency
resonator
or
shifted
above
by moving the resonator
plate,
Configurations
44
3 Dielectric Resonator Filters
howis
10%
A
tuning
typical
from
possible,
the
plane.
range
of
ground
away
Q
degrading
be
temperature
of
taken
to
performance
or
avoid
must
ever, care
DR.
in
by
the
to
the
close proximity
moving
metal plates
the resonator
M
S
Figure
3.4
3.3: Magnetic field coupling of a DR to microstrip
line
Configurations
DRs are the basic building blocks in DR filters.
Fields inside a resonator store
frequency
the
resonant
where equal storage of electric and magnetic
energy at
is
An
DRs
cavities
advantage
of
over
corresponding
wall
metal
energy occurs.
it
fields
inside
be
the
to
the
whereas,
perturb
shaped
they can
evanescent cavity,
Typically,
hollow
inserting
to
impossible
is
cavity without
shape a
extra materials.
DRs have a disc form that can be modified to include notches, chamfers and holes
in
and
multiple-order
modes
spurious
to control
inter-modal
issues
of
address
couplings.
devices, these perturbations
Three conventional
may
for
DR
a
shapes
figure
in
3.4
the
theoretically
the
and
among
geometries,
explored
shown
are
L<D,
is considered the most advantageous as a resonator
shape,
cylindrical
filter structures.
in
element
c
T
L
bý
(s)
(b)
ODI
(c)
DR
Three
(a)
3.4:
configurations:
Figure
rectangular resonator, (b) cylindrical
L<D, and (c) cylindrical resonator, L>D
resonator,
45
3 Dielectric Resonator Filters
Configurations
At microwave frequencies, any physical entity can be used to realise a resonator,
boundary
the
shape,
size
and
whereby,
conditions
applied will determine the
internal electric and magnetic fields. The most common type of DR. structure is
the cylindrical suspended DR structure as shown in figure 3.5. A 'Shielding is used
losses
from
to
prevent
radiation
enclosure
an
as
aluminium
and copper.
and typical metals used include
If the walls of the outer conductor
are moved closer
to the resonator, the resonant frequency of the TEola mode is increased due to
the cavity perturbation
theory.
This theory states that when a metal wall of a
is
inward,
frequency
if
decreases
the stored
the
moved
cavity
resonant
resonant
displaced
field
is
the
predominantly
of
energy
electric. Otherwise, if the majority
fields
frequency
displaced
is
the
increases
the case
magnetic,
are
resonant
as
of
here for the TEolb mode resonator.
The relative dielectric constant is typically
between 20 to 80 and the DR is remote from conductive walls, usually about
twice the largest dimension of the DR. This is important
as any current induced
by
field
the
the
metallic
surface
external
of the resonator may incur serious
on
frequency
the
effects
on
resonant
and also reduce the high intrinsic
adverse
Q of
the resonator.
Conducting
"Enclosure
,
a,
co
z
Lr
1
fa
1
alil
Figure 3.5: Commonly used DR structure, [28]
Since most of the electromagnetic energy is stored within the dielectric at the
frequency,
frequency
this
largely
is
resonant
controlled by the dimensions and
dielectic constant of the dielectric material itself. By assuming that the lateral
DR
behaves
ideal
the
as
of
an
magnetic boundary, the resonant frequency
surface
be approximately calculated
field
may
patterns
and
since it is now assumedthere
is zero tangential magnetic component on the curved surface of the DR. In all
filter configurations, preventing Q degradation requires
dielectric
the
mounting
46
8 Dielectric ResonatorFilters
resonator
3.5
ResonantModes
on special supports.
Resonant
Modes
Similar to conventional metal wall cavities, an infinite number of operating modes
DRs
boundary
be
in
excited
satisfying
conditions.
exist and may
These modes
(TE),
distinct
known
into
three
transverse
be
electric
groups
as
classified
may
(TM),
Each
hybrid
(HE)
of
and
electromagnetic
modes.
transverse magnetic
has
families
three
an infinite variety of individual
these
individual
suit
will
modes
applications.
modes, thus, particular
Plots of the field distributions
[54].
figure
3.6,
For
in
L<D,
a
puck
where
shown
are
modes
for these
the lowest frequency
has
TEola
distribution.
field
is
the
mode
which
a
circular
electric
resonant mode
The magnetic field is strongest on the axis of the puck and maintains a magnitude
distance
The
field
the
outside
puck.
to a sufficient
resembles that of an axial magis commonly used. For L>D,
dipole
this
mode
and
netic
the fundamental mode
is the TMola mode which has an equivalent magnetic dipole moment transverse
interest
is
The
the HEI, s in which both the electric and
of
the
other
mode
to
axis.
direction.
field
the
azimuthal
over
vary
magnetic
has distinct
This dual-mode configuration
advantages over single-modes offering better performance, smaller
fundamental
[55].
less
filters,
TE
than
TM
classical
weight
or
mode
size and
Comprehensivestudies of modes in DRs have produced mode charts for the cylindrical system and a few examples are illustrated in, [56], [57], [58], [16] and [59].
design
important
tools for filters and other applications. A
These charts are
[28].
is
in
figure
3.7,
shown
chart
typical mode
The most commonly used mode in a DR is the TEolb mode in a cylindrical resin
TE116
the
mode
a rectangular resonator since the former has the
onator, or
for
frequency,
certain diameter/length, D/L, ratios, and is therelowest resonant
,
fundamental
the
mode. The HElla degenerate hybrid mode
fore, classified as
smaller
of
the
volume
advantage
and weight, half the number of cavities,
offers
Resonant Modes
47
3 Dielectric Resonator Filters
08
(0,15)
.
TEE,
TT
0
@1
"o
T"T
T"T
T
1T'
T1
v
T_r
HE,,,
EH,
a
.r
T
T
03
l'
.1
T"r
T"T
r
r
111
T
TIr
T
{ý.
týýýJ
ii
Tý
1%
Vrý.
hilt
I
T"T
r
"r
ýI
Tr=2
1
T
HE,,
Figure 3.6: Field plots of common DR modes, [54]
devices.
This
is
to
single-mode
possible since each resonator
when compared
independent
in
is
DR
two
A
drawback
the
and
orthogonal
of
modes.
resonates
proximity
of resonant modes to each other and in order to make the DR useful
for practical applications,
a goal in resonator design is to separate the resonant
frequency of the operating mode as far as possible from higher frequency modes.
little
to
exhibit
shown
Side walls were
effect when placed at a distance greater
DR,
however,
diameter
the
the
have
the
of
the
aspect
can
than
a
ratio of
puck
improving
in
the
spurious
In
TEola
performance.
effect
mode operation,
positive
diameter,
height
H/D,
the
for
both
over
0.4
is
of
of
around
recommended
a choice
3 Dielectric
Resonator
48
Filters
Resonant
Modes
iss--------------'_"_
-qri$
I
Figure
optimum
M. i-
fnetlwd for
%
ao
Q.
o,w
.,,
waq ayüidn
---"Motif
r
3.7: Typical DR mode chart, [28]
Q and minimal interference of spurious modes. A chart depicting this
is shown, figure 3.8. [24]. By introducing
a hole at, the centre of the DR, the spu-
between
the fundamental
separation
rious
TEol s mode and higher-order modes
be
Figure
improved.
3.9 shows how the spurious characteristics are improved
can
function
diameter,
of
as a
ring
[17]. This property can be used to improve the
spurious performance of dielectric loaded filters.
ýZ
ri
U
Er = 36 Er =1
,
, 2
D/A=I. 5
ýn
5'
L/13.0
» h:
--TE02
V
2
HE 12
HE13
C
C
C
ýý
TMOI
5
HEIL
TEOI
1
1
1.5
2
2.5
d// (Diameter
Figure
3
DR/Length
3.5
4
4.5
of DR)
[24]
3.8: Mode chart of a DR in cavity as a function
of aspect ratio,
Even for a radially symmetrical
anode such as the TE01 which only has three
,
3 Dielectric
Resonator
49
Filters
3r
-
ýrý
ý rT-r
Resonant
rT
Er,
36, Er2=1
d/l=3.5
ddD
ý2
Modes
TE02
D/d = 1.5
L/l-3.0
5
HE13
L
T
U
C
U
C
U
HE12
TMO1
2
U.
C
A
C
0
H
..
S
HE11
TEOI
-. 1
0
.1
.2
d, /d (Diameter
.3
.4
of Ring/Diameter
.5
of DR)
.6
Figure 3.9: Mode chart of a DR in cavity as a function of aspect ratio with
improved spurious performance, [17]
components of the electromagnetic
various simplifying
field, rigorous analysis is still a problem and
assumptions are required. The situation is more complex for
higher order modes that are generally hybrid, usually degenerate, and have all six
components of the electromagnetic
field. To identify and distinguish the hybrid
modes with strong axial magnetic or electric fields, Kobayashi proposed a naming
convention using EH and HE notations, [58], respectively. A modern classification
system proposed by Zaki, [59], is more simple and defines HEE,,,,, and HEH7,,,,
with the first two letters indicating
the symmetry wall, z=0,
a hybrid mode and the third letter, E or H, if
is an electric or magnetic wall, respectively, as shown
in figure 3.10. The first subscript, n, indicates order of angular variation of the
fields and the second subscript. in, is the order of the resonant mode. This system
is used in the study of the hybrid modes for the proposed dual-mode resonator.
Z=o
Z=o
(a)
(b)
Figure 3.10: Classification of HE modes showing E-field component for (a) electric wall (b) magnetic wall
50
3 Dielectric Resonator Filters
3.5.1
Resonant Modes
Cohn's Model
An accurate prediction of the resonant frequency is possible only when all boundary perturbations
are taken into account in the theoretical
A preferred practical approach
intensive.
orously complex and mathematically
is
rigand
analysis
is to find solutions for the DR in simple ways to produce results close to actual
At
high
the
of
surface
regions
of
permittivity,
values.
PEC,
conductor,
or short-circuit
a perfect electric
the boundary behaves like
boundary when observed from
the air to dielectric regions. The reflection coefficient of a plane wave normally
incident at the dielectric to air boundary is given by,
rho-? 1
=
+7
770
-1
N+
er +1
(3.9)
impedance
the
dielectric,
are
waveand
rj
of
71o
air
and
respectively, and
where
boundary,
The
from
dielectric
1.
»
to air, can now be approxiwhen
observed
er
hypothetical
by
a
mated
perfect magnetic conductor, PMC, on which the normal
field
the
of
electric
and tangential
components
components of the magnetic field
boundary.
This
internal
the
in
total
the concauses
at
reflections resulting
vanish
finement of energy in the high permittivity
hypothetical
be
as
a
explained
can
object. To a first approximation,
a DR
perfect magnetic conductor, PMC, waveguide
field
distribution
the
therefore,
cavity,
be
calculated analytically.
onator can
and resonant frequencies for such a resThe magnetic wall waveguide below cutoff
dielectric
in
the middle is as shown in figure 3.11.
resonator
situated
a
with
In reality, electromagnetic fields leak out of the resonator and eventually decay
This
leaking
be
described
by a mode subscript S and the
may
exponentially.
is
model
modified to account for this by removing two lateral
wall
magnetic
Thus,
the
the effects of the top and bottom covers
resonator.
of
walls
magnetic
dielectric
the
and
support or substrate are factored in to improve the
puck
of
figure
in
the
3.12.
model
as
A simple mathematical model of
shown
of
accuracy
below
is
introduced
waveguide
cutoff
in which a second-order model
a magnetic
3 Dielectric
Resonator
51
Filters
Resonant
Modes
3.11: Cohn's second-order DR model showing a DR inside a magneticbelow
cutoff
wall waveguide
Figure
of a cylindrical
DR is used, [11] and [60]. This model reduces to Cohn's standard
model when the two plates are moved to infinity,
L1 = Do and L2 = oc with air
occupying spaces on each side of the dielectric, 6,1 =1
and Ere = 1. Thus, an
isolated resonator in free space is assumed. Both the TE016 and HEI1 modes of
DR
be
can
a
solved using the modified Cohn's model.
for
the TE016 mode is approximately
accuracy
A calculated frequency
6%, [61].
fz
PEC, Enclosure
r
Figure
3.12: Improved model for a shielded DR
The EM field within each region can be expressed as
Hz = (Aeryz
+
Be-rynz)J0(knp))
(3.10)
52
3 Dielectric Resonator Filters
HP --P
P
(Ae')"pz- Be-"pz)Ji (kPP))
tt"(AeYPz
E4,_J
Resonant Modes
+Be_ Pz)Jl(kpp))
(3.11)
(3.12)
P
fixed
index.
is
The
is
the
the
region
mode
radial propagation constant of
where p
by the PMC wall at p=a,
and for TE016mode to be solved,
(3.13)
kPa = Xoi = 2.4048
HE118
be
for
to
the
mode
solved
and
(3.14)
kpa = X11= 3.832
The separation constants are
Q2 = -rye = köe,.
2-
71
12 -
(Xa 1)
2-k,.
(Xa l)
2
(X-')
2
(3.15)
aI
(3.16)
1
(3.17)
kj
r2
Using the properties of the perfect electric wall, PEC, at the top, where z=
L1+L+L2, and bottom enclosure plates, where z=0, and applying the boundary
dielectric
the
Ll
at
surface,
z=
conditions
and z= Ll + L. This ensures the
tangential components of the electric and magnetic fields are continuous at the
interface. Solving the field equations, the following can be obtained.
01
01
ßL
= tan-1
= tan-1
L'L2
+2+
(cotiviLi)
(3.18)
(coth2L2)
17r, 1=0,1,2,3,
(3.19)
"""
(3.20)
3 Dielectric
Resonator
53
Filters
Resonant Modes
For generality, the added angle 17rgives all possible resonance conditions. When
1=0, the mode is the lowest fundamental mode TE016or TElla with the desired
6
than
smaller
constant,
propation
where
nonintegral
signifies
a
number,
radial
for
lowest
As
1=0
desired
the
the
shown,
mode,
of
radial propagation
unity.
field
in
DR
less
half
the
than
variation
a
wavelength within
undergoes
a
constant,
the resonator length, L, due to the end effects of the air-filled region. This model
by
improved
further
the
leading
the
to
removing
of
calculations
circular
wall
was
frequency
[62]
[61].
to
1-2%,
an
accuracy
within
and
resonant
3.5.2
Mode-Matching
Model
A simple DR model is helpful during the initial stages of the analysis or design
lacks
but
design.
In
the
for
accuracy
needed
modern microwave circuit
process
housing
is
to
configurations,
resonator
a
metal-wall
necessary
cavity
or
actual
the
Q.
Due
field
degradation
in
electromagnetic
of
radiation
of
resulting
prevent
to recent progress in computer technology and computer aided design, CAD,
tools for microwave engineering, many EM simulation software and methods have
been developed and can be used to compute the exact resonant frequency and
field patterns for a DR. The model described previously was modified leading to
for
formulae
frequency
distribution
field
resonant
and
accurate
electromagnetic
in the structure through mode matching method, [63] and [53].
The radial mode matching method is used to analyse any cylindrical DR configu[64]
described
in
using a general multilayer configuration with adjustable
ration as
layers
in
both
longitudinal
material
of
number
and radial directions as shown in
figure 3.13. The resonator structure is partitioned
by
boundaries.
appropriate
terminated
into a succession of waveguides
Region ii of the resonator is filled with a
dielectric material with relative permittivity,
e, t
and loss tangent, tan6; j. The
layers and material properties
of
can be assigned individually
number
to the resonator structure.
The top and bottom
according
planes of the structure can be
PEC,
electric
conductor,
perfect
or perfect magnetic conductor, PMC.
either
54
3 Dielectric Resonator Filters
Resonant Modes
The variations of the TE and TM fields of the modes contributing
to resonance are
first expressed in each radial region and are matched at each interface to establish
the continuity
of the fields tangential
to a discountinuity
of the medium.
To
simplify the analysis, the normal mode fields are decomposed into two orthogonal
These
TE,
Ez
the
0, and TM, modes, where
are
solutions.
modes,
of
where
sets
=
z
H, = 0. Finally, the orthogonality property of the modes is applied providing
z
linear
infinite
These
set
of
equations.
are then rearranged and truncated to
an
form a matrix whose determinant
will be zero at the resonant frequencies of the
field
The
field
be
the
to
then
coefficients
of
each
mode can
obtain
solved
cavity.
distribution
and unloaded Q.
Z
bN-
er
Pr
b"
bý
I1Nz
/N.
Cr
gr
2Ns
2N:
Er
gr
Er12
Er22
Er
tr
I. 12
Rr
22
9,
Cr
Er
21
Er
I
b
1
T
Rr
11
11
"O
Fr 21
NrN:
NrN.
N, 2
N.2
PEC
or
PMC
Nr1
Nrl
P
NnJ
Figure 3.13: Generalized multilayer cylindrical DR, [64]
In advanced models, additional
factors such as dielectric
supports and tuning
into
taken
The
are
account.
resonant frequency of the DR in these
mechanisms
be
can
calculated using the mode matching method with accuconfigurations
Recently available electromagnetic
1%.
better
than
racies
simulation programs
improvements
in
the calculations of relatively complex strucadditional
enable
tures. Using such programs, the resonator housing, tuning and coupling elements
be
precisely modelled obtaining accurate results taking into account practical
can
design.
An
the
additional advantage is the electromagnetic field disaspects of
55
9 Dielectric Resonator Filters
Resonant Modes
Table
3.2
be
dissipated
power,
easily.
tribution,
etc. can
visualised and plotted
Cohn's
frequencies
both
DRs
by
the
simple
computed
of
several
resonant
presents
model and rigorous mode matching method.
Mode
6,
DR Radius
(mm)
DR Length
(mm)
L1, L2
(mm)
Cohn's
Model
MM
Method
Measured
(MHz)
TEol
TEol
HE,,
HE,,
36.2
3.015
4.16
3.411
7419
7941
7940 [61]
36.2
37.6
38.2
3.995
8.00
6.80
2.14
6.90
5.60
4.43
inf
inf
7159
4373
5152
7758
4210
4980
7790 [61]
4196 [30]
4994 [30]
Table 3.2: Computed and measured resonant frequencies of DRs, [65]
This method is one of the most efficient and precise methods for DR analysis and
design but for complex three-dimensional designs, 3D, with non homogeneous
is
is
time
there
to
this
a
vary a number of
consuming
need
where
method
media,
dynamically.
parameters
3.5.3
HFSS
Finite
Element
Model
The finite element method, FEM, is used to solve Maxwell's equations in the
three-dimensional
from
transfinite
the
this,
arbitrary
structure
of
and,
volume
be
determine
field
to
the
two-dimensional
can
used
method
solution to
element
input and output ports, [66]. This method has been successfully used to analyse
dielectric-loaded cavity resonators using one-dimensional FEM and is economical
for dielectrics extended along the length of the cavity, [67]. 2D and 3D FEM have
been applied to evaluate and design high quality TM and hybrid DR modes and
full
3D
for
is
the
for
of
a
analysis
structure
shown
need
greater accuracy of
a
[68]. Resonant frequencies for TE
devices,
and TM modes of axisymasymmetric
dielectric
been
containing
common
have
structures
resonators
calculated
metric
in different environments with tuning screws, [69].
HFSS is a software simulation package that uses the generality strength of FEM
to analyse arbitrary, complex voluminous or planar 3D closed device with var-
Dielectric
Resonator
Filters
Resonant
56
Modes
ious levels of resolution in the problem space. This allows the user to address
large
in
based
problem
spaces
efficiently
problems
on the adaptive mesh
minute
refinement method.
The inner materials must be homogeneous and linear but
dielectric
losses.
The
be
possess
and
or
metallic
studied structure
anisotropic
can
is generally closed by perfect magnetic and electrical conditions or excited by
The
lines
or
waveguides.
obvious advantage is the ability to visutransmission
be
include
fields
thus,
the
to
modes.
the
resonant
structure
of
may
modified
alise
This
fields
tool
in
the
true
the
approximates
problem space
modes.
or suppress
by discretizing the field domain into basic elements that are roughly 1/10 of a
guide wavelength.
The finite elements are contactual
domains,
in
1D
line
triangular
elements
as
such
3D
in
problems.
elements
volume
their flexibility
form
the
simplest
and of
in 2D domains and tetrahedral
The advantage for these simple elements is
to subdivide any arbitrary
geometry, figure 3.11.
Components
of elements
of field tangential to edges
stored at vertices
explicitly
of field tangential to faces
and normal to edges of elements explicitly
stored at midpoints of edges
Components
'-"
Value of interior point vector field
interpolated from nodal values
Figure 3.14: Mesh with tetrahedral eleiiieirts fur tiiaxiiºiiiºii
imate shape of 3D dielectric puck
flexibility
to approx-
The solution is found by summing the magnitude of t lie fields or potentials at
junction
each
of elements.
It computes the eigenmodes at each port by using
by
the user and the S-parameters, for the structure,
modes
chosen
of
the number
by
to
tolerance
the
within
a
set
user. The finite-element, mesh is
calculated
are
desired
the
number
of
passes
a
tolerance is achieved. Once a
until
over
refined
frequency,
is
the
at
one
created
raine mesh can be used to sweep a range
mesh
frequencies
impedances
the
and
are calculated at each port for eac11
of proximate
An adaptive pass is run at the frequency
S-parameters.
set of
of interest to create
frequency sweep is
finite-element
mesh
and
a
performed acrosss the interested
a
Adaptive
be
passes
range.
can
run at the end frequencies to check the
spectral
57
Filters
Resonator
3 Dielectric
Resonant
Modes
the
mesh.
of
validity
HFSS has different frequency domain solvers. For a driven problem, an external
is
applied at a physical access port and a matrix
energy
source of
is built and
inverted to find the solution at each frequency of interest, of which the scatterA sourceless problem can also be solved using an
ing parameters are calculated.
defined
with
short circuited planes. The solutions to the solver
eigcnnlode solver
from
derived
stationary
are
field configurations
and formulate cutoff frequencies
for
frequenconstants
waveguide
structures
propagation
and
resonant
natural
and
Qs
field
For
dielectric
in
and
of
plots
resonators.
a
situated
resonator puck
cies,
frequency
between
produce
can
mode
one
charts
of
variations
resonant
a cavity,
the
of
resonator.
variable
any
and
The mesh algorithm
topologies
boundary
density
and in the vicinity
becomes high,
coefficients
depicted
allows it to predict
in that
thus,
area.
in figure 3.15(b).
This
time is required.
accuracy
and computational
(e)
the energy
of the solution,
is very sensitive
finer subdivisions
The resolution
to elements of 0.2. E in figure 3.15(b).
tive mesh, a convergence
of a singularity
requires
for particular
density
mesh
the value of the functional
figure
in
3.15(c)
as
shown
aceiiu"acy
longer computational
the required
for better
to the
accuracy
as
for
he
the
greater
varied
of
mesh can
where the elements
The compromise
E
0.1.
in comparison
are
for greater
resolution
is a
Also, to ensure the accuracy of each adap-
value is required
that
also has a compromise
between
time.
(b)
(a
Finite
3.15:
element method analysis of dielectric
Figure
hole:
with
axial
puck
(a) basic geometry, (h) view of mesh with 0.2A mesh, (c)
view of mesh with 0.1A
mesh
3 Dielectric
Resonator
58
Filters
Resonant
Modes
There are some drawbacks to HFSS, notably performing a frequency sweep with
dependent
frequency.
frequency
Eigenmodes
on
are calculated at each
eigenmodes
but
to
in
HFSS,
the
the
according
propagation
mode numconstant
ordered
and
bering may become erroneous towards a higher frequency.
For example, eigen-
2
in
low
frequency
is
1
remain
will
shown
and
order
mode
at
until
an
extra
mode
in the structure that has a frequency less than eigenmode 2. This new mode will
be
labelled
Furthermore,
2.
and
will
as
eigenmode
replace
now
impedances are.
HFSS
in
lines
These
impedance
defined
the
unless
ports.
are
on
not calculated
the
lines
difference
points
connecting
of
maximum
voltage
at each port and
are
for
Only
for
defined
different
impedance
lines
mode.
each
one
set
all the
of
are
are
frequencies in a sweep and must be defined in the same order as the corresponding
When
during
lines
impedance
the
modes
are
switched
a
switch,
are no
modes.
longer valid at each frequency and no impedances will be calculated.
factor
is
time
as the simulation
tion
a
Computa-
must subdivide the whole volume, thus,
more solutions are required at each node in the mesh. The material properties
[70],
in
HFSS,
[71],
dielectric
have
been
design
filters,
DR
resonators
and
of
of
latter, a combination
For
the
analysed.
of the accuracy of HFSS and rigorous
inter-resonator
has
couplings
of
produced slotted-DR filters without tunanalysis
ing. Unfortunately,
a frequency shift of 0.2% between simulated and measured
that
HFSS
is
although
shows
promisingly
responses
accurate in 3D simulations,
for dielectric-loaded cavity resonators, tuning must be present to compensate for
imperfections.
practical
With
regards to this, sensitivity
simulations should be
to
the
understand
efifect of physical tolerances on the response of the
performed
device.
59
Chapter
4
Dielectric-Loaded
4.1
Compact
Bandstop
Filter
Introduction
Proposing the use of dielectric loading within
waveguide sections is not uncom-
[50],
[72]
the
filters
in
as
size
and
of
resonant
sections
and other components
mon,
dramatically
are
reduced. However, energy is now strictly
confined to metallized
Q
by
least
the
the ratio of 1/
values
are
reduced
at
and
sides
losses. Since resonances are fully supported within
that
of a conductor-loaded
exceeds
performance
is because energy is not in substantial
E,.neglecting metal
the dielectric region, high Q
or cavity metal resonator. This
contact with metal except on enclosure
filter
A
bandstop
by
realised
means of rectangular
walls.
dielectric-loaded
res-
inner
to
the
rod of a coaxial transmission line with square outer
coupled
onators
described.
Commonly,
is
coaxial resonators are normally realised for
conductor
base station filters but conventional waveguide components are used as they offer
lower loss. The existence of a dielectric-loaded
waveguide allows for near perfect
For
hollow
example,
walls.
when
a
magnetic
waveguide is transversely cut, the
but
in
the
high
radiate
ends
presence
open
of a
Cr medium, the open ends approximate a near perfect magnetic wall and will not radiate, although a small
leaky
fields
of
are present. Maximum reduction is obtained by the
percentage
loading
the
of
rectangular waveguide resonator cavities and although
complete
Q. values are smaller, calculated values are acceptable for
base
station
mobile
4 Dielectric-Loaded Compact Bandstop Filter
applications.
60
TE10b Rectangular Waveguide Resonator
This physical arrangement allows a simplicity
design where rectangular
dielectric-loaded
line.
to
the
coaxial
coupled
cavities
in the mechanical
resonators are fitted into prescribed
The narrow rectangular
resonators allow
for inter-resonator spacings of A/4 offering further miniaturisation.
For example,
dielectric
resonators
waveguide
and
pucks, when coupled to a transconventional
[3].
[73]
3A/4
line,
flexibility
The
design
require
spacings,
and
adds
mission
in
that the resonators may be positioned at any distance along the transmission line
for adjustable phase lengths.
Also, the cavities may be easily machined to in-
dielectric
different
shaped
resonators, metal-loaded or completely unloaded
clude
Initial
designs
have
focused
dielectric
narrowband
slabs of permiton
resonators.
tivity, 44, exciting the TE10 mode at 2 GHz. Preliminary
bandwidths
dB
3
coupling
produced
data
have
simulation
in the region of 25 MHz for a 4th degree
filter. Possible applications for this device include UNITS base stations and other
communication
applications where rejection of signals is necessary. The advan-
tages of this filter are that more complex designs can be carried out based upon
this simple structure,
i. e. layering coaxial lines and resonators on top of each
forming
multiple
other
instances of bandstop behaviour over a broad frequency
layout
similar to end-coupled bandpass filters. The physical structure
range with
also allows ease of positioning
of tuning screws for both input coupling and res-
frequency
is
which
neccessary to ensure the response meets the required
onant
In
designs,
fabrication
all
practical
specifications.
tolerances can make the mea-
different
to
the
response
simulated response, thus, some form of tuning is
sured
required.
4.2
TEios Rectangular
Waveguide
Resonator
The design for the TElos dielectric-loaded rectangular resonator begins by finding
the dimensions for the required resonant frequency. The rectangular waveguide
is a hollow-pipe waveguide where an air-filled, or dielectric, region of width, a,
height, b, and length, l extend indefinitely in the axial, z, direction and is enclosed
61
Dielectric-Loaded Compact Bandstop Filter
TE106 Rectangular Waveguide Resonator
by conducting boundaries on four sides. In this one-conductor guiding structure,
TEM, wave exists since no axial field components
no transverse electromagnetic,
for
TE
TM
do
and
modes
propagate through this waveguide.
which
unlike
exist,
The TE10 is the dominant
mode in this waveguide for a>b
propagating
it is the lowest cutoff in this rectangular
structure,
since
figure 4.1. By shorting the
two ends of a segment of waveguide, a rectangular cavity resonator is formed with
two groups of resonant modes, TEmnp and TMmnp, and these correspond to TEmn
first
in
The
TMmn
propagation
modes
open-ended
waveguides, respectively.
and
two subscripts, m and n, follow from TEmn and TMmn modes, representing the
directions.
the
along
x
and
cycles
y
changing
the
along
z axis.
cycles
changing
fundamental mode for b<a<l
The TE101 mode corresponds to the lowest
[74],
field
the
of which
solutions are,
Ev = -2
Hý
The third subscript, p, denotes
A wµa
sin
(äx )
Aa
(äx)
sin
1
_
Hz = -j2A cos
Ca
sin
cos
sin
(7Z)
(4.1)
(äz)
(4.2)
(7Z)
(4.3)
Ey=Ez=Hy=O
(4.4)
u
/I
b
,ýZ1
x
4-
a -*
Figure 4.1: Field distribution of TElol
rectangular cavity
In such cavity resonators, the resonant frequency for
be
TE101
may
cavity
a
62
4 Dielectric-Loaded Compact Randstop Filter
TE10b Rectangular Waveguide Resonator
[75],
from,
calculated
fmnp =
21rc
2+ (Plr)2
(-.
µr
r
-)
\aJZ+
(4.5)
The rectangular waveguide should be designedto operate at a considerably higher
frequency than the cutoff frequency which is given as
[m1r'2
ý-(nlr)2]'/2
b(4.6)
-a1
light
dielectric
for
in
is
typical
the
of
aspect
velocity
medium
a
v
a
and
where
free
in
by
2b
is
space,
w,,
given
a=
ratio of
we =ä
(m2 + 4n2)112
(4.7)
The reason for this design factor concerns the group velocity of the waveguide,
by
v9, given
1/z
2
A9=dý=vf1-(w°)1
(4.8)
As shown, as vg approaches zero, w approaches w, and 0 tends to zero leading
to phase distortions as the signal frequency approaches too close to the cutoff
frequency. The guide wavelength for a TEIG waveguide is defined as
2ic
IN9 ==Q
Ao
[1
-
(wc/w)2]1/2
(4.9)
free
is
A0
the
space wavelength, ,ß is the propagation constant and w, is
where
For
frequency.
the E field to be zero at z=0
the cutoff
to form a
and z=l
TEloi mode cavity resonator, l must be one half-guide wavelength and knowing
frequency
of a mode in a rectangular waveguide, this length is given as
the cutoff
63
4 Dielectric-Loaded Compact Bandstop Filter
TE10b Rectangular Waveguide Resonator
xO
12
(4.10)
2[1 - (o/2a)2]1/2
/w)2]1/2
2[1 - (wý\O
frequency
be
from
to
the
resonant
calculated
which allows
C
fo_ To
c(a
_
2+
12)1/2
(4.11)
2al
Q
determine
losses
finite
in
the
the
The effects of
unloaded of the
conducting walls
determine
EE
be
by
forming
integral
to
This
calculated
a
volume
of
can
resonator.
dividing
dissipated
in
by
due
it
the
to
the
currents
energy
and
the stored energy
[76].
be
The
factor
the
the
estimated
quality
of
resonator,
resonancemay
walls of
from,
[(m)2
b
Q-=X
ý0
+
abc
(a)2]
{(m)2
(2)2
+
4
J
}
[(4)2
+
ac{(d)2ýc)2+
+bc
+
(n)2,2
(4.12)
222
nl2
ý/
\l
54
(P)2]
+[()2+
`b/
[G;
+ab(E)2
) 2+
(n)2]
following
the
leads
to
This
result for the unloaded Q for a TElol mode cavity,
Aabl
Q"lol =S2ä
U-7+
3/2
(a+ 2b) +a (l + 2b)
(4.13)
free space wavelength to the
is
the
A/b
of
ratio
skin depth of the conductor
where
frequency.
To
find
the
Q,
lossy
losses
dielectric
overall
the
in
the
resonant
any
at
for
be
found from equation 3.4 and the total loss
is
accounted
and
must
medium
from,
be
calculated
may
64
Q Dielectric-Loaded Compact Bandstop Filter
(_1
Qioi =+
Qu1o1
Configuration of Proposed Filter
1
-'
Qu
(4.14)
The design equations above have produced initial dimensions based on a dielectric
waveguide resonator with short-circuited ends to approximate the TElol mode,
however, the resonator used in this filter has open-circuited ends to allow coupling
to the transmission line to produce the required attenuation transfer response.
These open ends allow a small leakage of magnetic fields outside the dielectric
boundary. Although the resonator length was designed to be l= a9/2, such
that there was a half cycle in the z-direction, for classification correctness the
dielectric-loaded
defined
is
the
TEloa
as
mode
mode. The subscript, S, denotes
2l/a9
in
the z-axis to account for the leaky fields, how<1
ratio
noninteger
a
from
this
section are still applicable in the design of the initial
calculations
ever,
dimensions of the TElob mode dielectric-loaded resonator.
4.3
Configuration
Proposed
of
Filter
The proposed filter follows the classical design of bandstop filters with a planar
topology consisting of a main transmission line capacitively coupled to inductive
[73].
figure
4.2,
The
shown
as
same design can also be realised using a
stubs
series of waveguide resonator cavities positioned periodically along a waveguide
transmission line, figure 4.3. The principal objective is to load the waveguide
high
dielectric
with
cavities
e,.
resonator
material to reduce the volume of the
form
dielectric-loaded
to
segments
resonant
resonators coupled to a transmission
line. From circuit theory, these segments must be spaced
at odd multiples of a
to
cover a relatively narrow bandwidth at the centre frequency.
wavelength
quarter
As reported previously, [73], a disadvantage with the
waveguide transmission line
is a minimum resonator separation of 3A/4 is required to
reduce interaction effects
if the resonators are wide with respect to the transmission line. This increasesthe
length of the transmission line but by using rectangular DRs,
only A/4 separa-
4 Dielectric-Loaded
Compact Bandstop
65
Filter
Configuration
of Proposed Filter
(2n-1))L
v,
Figure
4.2: Schematic of third-degree strip transmission line Bandstop filter
Figure
4.3: Schematic of third-degree cavity wavegi ide haixlstop filter
tions would be needed reducing the length of the line leading to miniaturisation.
is possible but physical realisation would be
For the TE106 DRs, a inicrostrip
complex and weak couplings between the resonators and transmission line would
be problematic, even for narrowband designs. Also, shielding is needed to confine
the fields leading to a larger volme.
A coaxial line would be more advantageous
for
is
high power, allows ease of coupling and a uniform
it
suitable
as
section offers advanced configurations
discussed
later.
resonator,
coaxial
conductor, rather than circular,
cross-
dielectric-loaded
broadband
the
such as
An air-filled
coaxial line with a square outer
is chosen as the square shape compliments the
DR
for
waveguide
coupling purposes. If a conventional circular outer
rectangular
fabricated
the
lid
used,
was
conductor
would be positioned in the middle of the
figure
4.4.
line,
in
will
which
the
cause
transmission
spurious
effects
cross-section
In addition, portions of the outer circular coaxial conductor must be removed to
enable a coupling window to the rectangular
resonator.
Removing this section
4 Dielectric-Loaded
Compact Bandstop
discontinuity
a
will cause
Filter
66
of Proposed Filter
Configuration
in the coaxial transmission line at the coupling points.
Thus, a square outer conductor was more suitable.
ýý,
jý
(a)
'
(b)
(a)
DR
Circular
Schematic
line
to
transmission
4.4:
Figure
of
coupled
coaxial
Cross-section of feasible realisation
(b)
cavities
The resonator structure is shown in figure 4.5 with the length of each rectangular
long.
A/2
resonator
The dielectric
is metallised on the four longer faces using
between
inside
the
direct
of
sides
placed
a
and
contact
cavity
with
plating
silver
line
from
These
distance
the
displaced
DR
resonators were
at a
the
and walls.
tangential
DR
face
that
the
the
was
such
narrow
rectangular
of
and positioned
direction
the
of the coaxial line.
to
propagation
Meal
Line
Coaxial
Tuning
Screw,
Plating
vIcicciric
Slab
Figure
4.3.1
Aluminium
Enclosure
4.5: Structure of TEI0e mode dielectric bandstop
resonator
Single
Resonator
Design
from
dielectric
was
made
material
The
a coiiipouiid
a permittivity
of 44. They were manufactured
of CaTiO3-NdAlO3
and have
with a measured Q. f product of 41
Compact Bandstop
d Dielectric-Loaded
67
Filter
of Proposed Filter
Configuration
had
GHz,
be
They
21
000
2
a stable
also
available.
aQ of
would
000, therefore, at
for
dimensions
Initially,
in
isolation.
1
the
a
temperature coefficient of ppiu/°C
frequency
TElob
in
the
of
mode
with
a
resonant
operating
waveguide
rectangular
2 GHz were calculated. To utilise the dominant mode, the width of the rectangular
DR, a, was taken to be at least greater than A/2.
Taking into account the
dielectric loading of the waveguide, the effective wavelength, Aej j, is calculated
from,
8
108
c=3x
f
2x10
Aeff=_
15
e,.
44
22.6
mm
=
(4.15)
However, this length should be kept near the minimum allowable value to ensure
dominant
the
only
mode propagates in the interested frequency range, there-
fore, higher-order modes are avoided. Thus, a was reduced to 14.1 mm and the
height, b, was taken as approximately
half the value of a, therefore, b=7.1
The length, 1, of the resonator was then found by substituting
mm.
these values into
4.11
to
give,
equation
l =
[l
a
-
(iref f/2a)2]1/2
0.0226
18.8 mm
=
2[1 - (0.0226/0.0282)2]1/2
(4.16)
Using the above dimensions, the Q for this resonator was calculated, first by
Q
imperfect
the
ideal
the
of
cavity
with
and
conducting
an
walls
calculating
dielectric material with zero intrinsic loss. Taking into account that silver plating
GHz,
2
was used, at
a_1.479
b
and substituting
x 105
`/7
104581
_
(4.17)
into equation 4.13,
Qloi = 2586
(4.18)
4 Dielectric-Loaded Compact Bandstop Filter
Hence,
as tans
68
Configuration of Proposed Filter
= 0.000048,
Quloi
1
1+1
(Q.
101
Qu
(4.19)
2302
Thus, a large unloaded Q. for a compact resonator is produced allowing the delosses
for
that
to
should
a
narrowband
response
compensating
any
achieve
signer
irregularities
to
a
system,
coupling
surface
occur such as
and other perturba-
line
between
line
A/4
The
transmision
was a coaxial
enabling
separations
tions.
line.
This enforces the objective to achieve miniaturito
the
coupled
resonators
lines
in
to
3A/4
transmission
avoid
separations
are
needed
waveguide
sation since
fordesign
To
line,
inter-resonator
the
the
couplings.
empirical
coaxial
unwanted
line
inner
for
with
conductor
square
conductor
coaxial
outer
and
round
a
mula
is,
770
Zo =
In [(1.0787D/r)]
21r Fcr
(4.20)
free-space,
impedance
D
is
is
is
the
the
the
wave
of
and
rho
square
r
side of
where
inner
A
the
diameter
of
conductor.
system impedance of 50 SZand a dimenthe
defined to give r=4.68 mm and a simulated response as
10
D=
was
mm
sion
The coaxial transmission line achieved greater than 20 dB
4.6.
figure
in
shown
GHz
bandwidth
loss
GHz,
2
frequency
a2
thus,
over
at
an
operation
of
return
line
for
design
the
was
suitable
transmission
the
and these dimensions were used
for the physical realisation. Details of the typical dimensions and physical performance for the resonator with coaxial connectors are shown in figure 4.7 and
The
the
tuning screw has also been included, however, for
4.1.
of
position
table
in preliminary HFSS simulations.
it
omitted
was
simplicity,
4 Dielectric-Loaded
Compact
Bandstop
69
Filter
FEM Simulations
0
0
-5
-5
-10
-10
-15
-15
-20
-20
CO -25
-25
in
-30
-30
-35
-35
-40
-40
-45
-45
-50
-50
-55
-SS
1.5
2
Frequency GHz
3
2.5
co
4.6: Frequency response of air-filled square coaxial TEM line with circular
centre conductor. D= 10 mm and r=4.68
inin
Figure
Typical Dimensions
14.1nini
a
b
7.1 min
1= 18.1mm
al = 30 mm
bi = 45.1 mm
b2 = 47.1 min
b3 =5min
Table
4.1: Typical
Typical Performance
11 45mm
d1 = 1.3 mm
d2 =4. lmm
T = 1.7 mm
2.61 mm
s
D
10 mm
4.68 mm
r
dimensions
foý=1.85GHz
Er44
Q,
1=2200
First spurious frequency 2.5 GHz
and performance
of TE10
dielectric
mode
Band-
stop resonator
4.4
FEM
Simulations
Electromagnetic
field simulation
the interaction
of electromagnetic
has proved to be a useful tool for predicting
fields in microwave filter designs. By using
the eigenmode solver of HFSS, FEM simulations
of a TE106 mode rectangular
DR with the calculated dimensions, produced field plots as shown in figures 4.8
fields
The
4.9.
shown clearly represent those of a TElol mode rectangular
and
half-wave
there
are
as
variations
resonator
direction
and no variations in they
and z
both
in
the
E
the
x
of
component
direction.
The tangential electric field
4 Dielectric-Loaded
Compact Bandstop
FEM Simulations
70
Filter
C'
--.
r
--------------
Lx
..............
b,
-º
- b, ..-
b --
1ý
1
........
I_-. y
ý..
................
Figure 4.7: Details of TEloa mode dielectric bandstopresonator
vanishes at x=0
and x=1
long.
half
is
the
wavelength
guide
confirming
one
has
field
is
E
the
the
zero
at
end
walls
and
Thus,
one maximum at the centre of
favourably
how
figures
fields
The
the
store electric
also
show
modal
the cavity.
disperse
boundary
to
its
is
walls
whereas
magnetic
allowed
energy
within
energy
interface.
five
The
first
frequencies
the
the
natural
modes
beyond
air-dielectric
of
in
broad
4.2
first
table
the
shown
showing
and
a
advantage of
were simulated
MHz
885
fundamental
the
frequency.
at
above
response
spurious
between
the transmission line and the rectangular DR was
dominant
coupling
The
Dielectric-Loaded
Compact Bandstop
ýý
Filter
71
FEM Simulations
v
(a)
Figure
=o
(b)
4.8: Electric field of TE10a mode DR: (a)Vector Lines (h)Magnitude
ý.
ý, `ýI
p
I
(U)
1.9: Magnetic field of TE10 mode DR: (a)Vector Lines (b)Magnitude
Figure
Table
(b)
Mode
Resonant Frequency GH,
Q
TEIG,
2.0024
2554.1
TE102
TEo11
TE201
TM 110
2.8847
3.3937
3.415
3.5533
3628.5
2457.6
2879.1
3050.1
4.2: Simulated
dielectric
rectangular
resonant frequencies
cavity resonator
and Qs of first, five triodes of isolated
has
been
it
that
TE10
the
DR
already
shown
since
readily stores
mode
magnetic
but
fields to leak. Simulations for the field
allows
magnetic
energy
electric
plots of
line
to
resonator couplings are shown in figure
To
transmission
achieve the
-1.10.
the rectangular DRs were orientated
coupling.
maximum
such that the magnetic
fields from both the resonator and transmission line were not orthogonal.
When the rectangular DR was coupled to the coaxial line, the resonant frequency
4 Dielectric-Loaded
Compact Bandstop
Filter
72
FEM Simulations
a fl..
(a)
P
k
==
(b)
(c)
Figure 4.10: H-field plots of fundamental mode DR coupled to coaxial line:
(a) Magnitude across transverse plan (b) Vector view cut through middle (c)
Magnitude cut through middle
decreased in frequency from 2 GHz to 1.85 GHz. This was expected as the couby
dominated
fields
has
inverse
inductance
magnetic
relationship
was
and
an
pling
The
fast
frequency.
FEI\i
is
advantage
as
apparent
of
using
an
now
solver
with
be performed to observe the relationships
can
simulations
between physical di-
found
It
the
frequency.
the
that
resonator
and
of
required
resonant
was
tnensious
frequency
of the rectangular
the resonant
DRs was determined by their lengths
dependence
distance
Figure
line.
the
4.11
to
the
on
coupling
minimal
coaxial
with
frequencies
DR
for
different
the
length
resonant
simulated
against
values
shows
ranging
of coupling
spacing
bandwidth
was simulated
ranging
from 1=
from
s=0.5
mm to 10.5 min.
to find the coupling
12.8 inin to 18.8 uim, figure
The 3 dB coupling
needed for different
4.12. The simulation
for shorter DR. lengths, greater coupling bandwidth
DR lengths
showed that
can he attained, however, the
for this is the unloaded Q vVott1d
compromise
The first five modes and their resonant frectuencies for the experimental
resonator
4.3.
The
in
table
mode
classification has reverted back to
shown
are
classical
Filter
Bandstop
Compact
4 Dielectric-Loaded
FEM Simulations
73
1.9
1.88
1.86
N
0 1.84
u
c
1.82
LL
1.8
1.78
1.76'
2
.r.. -.. y........
length
for
DR
frequency
Resonant
various coupling gaps
versus
Figure 4.11:
2:
21
N
I
Z
0
C
to
Co
m1
V
M
n
0.5
1.5
2.5
4.5
5.5
3.5
Coupling Gap mm
6.5
7.5
8.5
DR
lengths
bandwidth
dB
for
different
3
4.12:
coupling
versus
Figure
gaps
distinguish
between
to
variations
modes
with
wavelength
waveguide
rectangular
The
is
direction.
the first spurious resonance
significant
observation
in the z
bandwidth
MHz
650
spurious-free
of
approximately
above the
has maintained a
these
resonators are superior to conventional
and
confirms
mode
fundamental
DR resonators where poor spurious performance often gives rise to more complex
4 Dielectric-Loaded Compact Bandstop Filter
Mode No.
1
2
3
4
5
74
4th Degree Chebyshev Design
Name Resonant Frequency GHz
1.850
TElol
2.494
TE102
3.336
TEoll
3.356
TE201
3.363
TE103
Table 4.3: First five resonant modes of prototype resonator
designs, [77].
4th Degree Chebyshev
4.5
Design
inverter-coupled
designed
using
was
a shunt capacitor,
A Chebyshev prototype
from
(b).
follows
figure
design
2.3
The
that
the
network,
network to synthesise
[39]. The specifications of the filter were assumed to have a centre frequency of
bandwidth.
MHz
loss
dB
3
insertion
40
than
GHz
greater
at
1.85
and a stopband
GHz,
At
in
1.85
the sepa4.4.
table
The complete specifications were as shown
line to resonator tap points were calculated to
transmission
between
the
rations
be a quarter wavelength long to avoid unwanted inter-resonator coupling.
E
Filter Specifications
Centre frequency
1.85 GHz
Passbandbandwidth
d.c. - 1.844GHz, 1.861GHz - 2.5 GHz
Passband return loss (La)
20 dB
Stopbandbandwidth
3 MHz
Stopband insertion loss (LA)
System Impedance
> 40 dB
1c
Table 4.4: Filter specifications
filter
the
degree
needed to meet the requirements was calculated from,
The
of
[39],
N
LA+Lß+6
201oglo[S + (S2 - 1)1/2]
3.68
(4.21)
75
4 Dielectric-Loaded Compact Bandstop Filter
4th Degree Chebyshev Design
S,
defined
is
N
is
the
the
required
order
and
selectivity,
ratio of passband
as
where
4th
degree
therefore,
a
network was required and the ripple level, e,
to stopband,
following
for
from
lowpass
the
equation
a
prototype,
was calculated
(10LR110
1)-1/2
0.1005
6_
=
Hence
[sinh_1(1,
77= sinh
(4.22)
(4.23)
e)] = 0.8201
Using,
Cr =2 sin
77
Kr, r+l
(2r2N )'ý
(4.24)
L
712 + sin2(rir/N)]1/2
(4.25)
=
7)
giving
Cl = C4 = 0.9332
(4.26)
C2 = C3 = 2.253
(4.27)
K12 = K34 = 1.3204
(4.28)
K23 = 1.5769
(4.29)
For unity admittance inverters, a technique is used to scale the nodal admittance
force
ladder
for
to
inverters
the
network
a
to have the same value. A
matrix
is
figure
in
ladder
4.13 with N+2
shown
network
typical
nodes.
4Dielectric-Loaded
4th Degree Chebyshev Design
76
Compact Bandstop Filter
11
In
Figure
4.13: Ladder network
for
ladder
is,
the
network
matrix
The general admittance
Yoo
-Yoi
0
-Yoi
Yll
-Y12
00
-Y12
0
Y22
0
-Yr_l,
[Y,
-Yr-l,
r
Yrr
Yr,
r
Yr,
r+l
r+l
N
-YN-1,
-YN-1,
N
YNN
-YN,
N+1
-YN,
YN+1,
N+1
N+1
internal
the
the
rth
row
and
using
column
required constants,
By multiplying each
be
terminal
the
characterscaled
negligible
can
with
effect
on
admittances
nodal
Note
is
it
that
input
to
the
the
not
possible
and output
network.
scale
istics of
loads
be
N+1
transformers
the
0
as
respectively,
must
at
source and
nodes, and
independently.
The
inverters may be constructed from a
scaled
appropriately
line
discontinuities
from
transmission
isolated
length
the
with
no
of
and
single
for improved response. Consider the nodal admittance matrix for the
resonators
design,
d Dielectric-Loaded
Compact Bandstop
Clp
[Y] _
77
Filter
4th Degree Chebyshev Design
-jK12
C2p
-jK12
0
-0:
23
00
0
-3K23
ß!
3p
-3K34
The scaling is performed through multiplying each row and column by a constant
factor, A and B respectively. In this case, appropriate scaling is performed on
the first and last nodes, therefore, the technique was also performed on the first
in
the
last
matrix.
columns
and
4A
Clp
[Y} _
'. B
-jIC12
00
I{i
-j
2
0
0
A2Clp
[Y]
ýB
-jABK12
0
0
C2P
-j
K23
0
-jABK12
B2C2p
-jB2IC23
0
.. A
t-- A
K23
-j
C3P
E--B
0
B
IC34
-j
A
CO
-jK34
0
0
K23
-jB2
0
B2C3p
-jABK34
-jABK34
A2C4p
Scaling the middle two rows and columns, the following equations are obtained
4.30
from
4.31,
for
A
B,
the
and
equations
values
and
constants,
and
are found
that satisfy the condition for unity inverters. The constant, A, was used to
load
impedances
in
for
the
the
the correct
and
source
circuit
scale
simulations
impedance.
K23B2 = 1,
B=0.7963
(4.30)
K12AB = 1,
A=0.9511
(4.31)
4 Dielectric-Loaded
Compact Bandstop
Filter
78
4th Degree Chebyshev Design
The new element values with unit inverters were then calculated
Cl = C4 = 0.8441
(4.32)
C2 = C3 = 1.4287
(4.33)
K12=K23=K34=1
(4.34)
These element values have been calculated for a broadband lowpass prototype.
For this particular
design, the TEloa filter is coupled to the transmission
through magnetic coupling and is narrowband,
approximately
line
5%, therefore, the
lowpass prototype was modified by the reactance slope parameter method.
The
determines
the
the
parameter
slope
reactance with
rate
of
of
change
reactance
frequency.
A steep gradient expresses a fast changing reactance when varying
the frequency, which corresponds to a high-Q resonator.
A comparison of two
having
frequency,
figure
the
ff,
4.14(a).
in
is
same
resonant
shown
resonators
A high Q resonator equates to a steeper reactance slope. The reactance slope
is
tool
to
the
a
useful
relate
resonance properties of any circuit
parameter
lumped
circuit.
a simple
to
Any dual types of resonator with the same reactance
frequency response. For a series resonant circuit,
demonstrates
a
similar
slope
definition
of the reactance slope parameter, x, can be written as, [57],
the general
Iwo
x2
dw
(4.35)
By forcing the impedance inverters to be fixed at unity to allow a broader out-ofband bandpass response, it is necessary to use a decoupled structure to control
between
line
transmission
and resonator. Although the DR should,
the coupling
be
modelled as an open circuit stub of length \/2, calculated elements
strictly,
79
¢ Dielectric-Loaded Compact Bandstop Filter
4th Degree Chebyshev Design
for a magnetic coupled resonator is used in the circuit
inductive
between
the transmission
coupling
model to simulate the
line and DR. The two circuits in
figure 4.14(b) are now considered.
CT
ZA-. o--ý
I---I11
1
ZB--º
(a)
(b)
4.14: Transforming
(b)
Transformation
rameter
Figure
resonators of equivalent Q (a) Reactance slope paof capacitor to magnetically-coupled resönator
For two circuits to have the same Q value, it is required that their reactance slope
ZA
is
input
be
impedance
to a lowpass to bandstop transformed
an
equal.
should
2.3,
using
equation
which may be expressed as
capacitor
aw
ZA(iw) = C,
r
wo
Wo-w)
(4.36)
ZB is the input impedance of the magnetically-coupled transmission line resbe
can
expressed as
onator, which
ZB(p) = Lip +1
C+ 1/L2p
Lip
+
L2p
(4.37)
+ CL1L2p3
1+ CL2 p2
(4.38)
Hence
ZB(jw)
[w(Li + L2)
- w3CL1L21
1- w2CL2
4)39
.
,ý
Dielectric-Loaded
Compact Bandstop
80
Filter
4th Degree Chebyshev Design
Equation (4.35) states the reactance slope of the resonator can be found by differentiating the reactance expression of such a resonator, thus
dZdw w)
-
(4.40)
,ro+
W2UJO
and
dZA(jw)
dw
2a
(4.41)
=
uCrwo
Also,
dZý w) lw=wo
LL
LL2
2
2Li
=
ia
(4.42)
At resonance,ZB = 0, thus
Wo
Substituting
(4.43)
CL iaL2
(4.43)
into (4.42) and equating with (4.41) yields
equation
(4.44)
= wöCLi
C, WO
The value of C can be chosen for physical realisabilty
L2
Ll
and
are found
and
(4.43)
equations
through solving
and (4.44) simultaneously.
From (4.43)
Li+L2
L1L2
(4.44) and (4.45)
from
and
2C
=w
(4.45)
4 Dielectric-Loaded Compact Bandstop Filter
Ll + L2
L1L2
81
4th Degree Chebyshev Design
a
woCTL1= woC
(4.46)
Hence
Ll,
C
0
w3C
(4.47)
and
L2r _2
The bandwidth
be 3 pF in a11
scaling factor is a=
Li,
(4.48)
woCLir -1
fo/Of,
system, the transformed
and choosing all the capacitors to
element values are calculated from
(4.47) and (4.48)
equations
L11 = L14 = 8.80 nH
(4.49)
L12 = L13 = 6.76 nH
(4.50)
L21 = L24 = 3.43 nH
(4.51)
L22 = L23 = 3.88 nH
(4.52)
The final prototype circuit is shown in figure 4.15 with all unit elements a quarter
long at the centre frequency and have
wavelength
characteristic impedance of
50 Q. A circuit simulation produced a frequency repsonse of the ideal 4th degree
filter,
figure
bandstop
4.16.
Chebyshev
Compact Bandstop
4 Dielectric-Loaded
Filter
82
lath Degree Chebyshev Design
11
10
4.15: Prototype circuit for 4th degree Chebyshev baudstop filter
Figure
0
0
-10
-10
-20
20
-30
30
-40
-40
-50
-50
-60
-60
-70
-70
-80
'-80
1.88
Co
1.83
1.84
1.85
Frequency GHz
Figure 4.16: Simulated results of prototype
bandstop filter
1.86
1.87
N
Cl)
x 109
Chebyshev
degree
for
4th
network
In order to realise the dielectric filter, a technique was used to equate equivalent
normalized reactance slope parameters of individual
between
the
cirresonators
EM1
simulated models, commonly used to design microstrip
cuit and
bandstop
filters, [78]. The required coupling between each resonator to the transmission
line was dependent on the spacing deterinined by finding the normalized reactance
frone
following
the
parameter
slope
expression,
Xi
Zo
fo
(4.53)
20 fags
/Zo
is
the normalized reactance slope parameter
x;
where
of a resonator coupled
83
4 Dielectric-Loaded Compact Bandstop Filter
4th Degree Chebyshev Design
to the coaxial line, fo is the centre frequency and f3dB is the 3 dB bandwidth of
Parametric
the coupling resonator.
simulations were used to produce frequency
for
between
dielectric-loaded
line
the
transmission
spacings
various
and
responses
The
from
extracted
resonator.
normalized
parameters
reactance slope
rectangular
these frequency responseswere taken from which the desired coupling gap was
interpolated from figure 4.17.
600
550
500
450
400
350
300
250
200
150
100'
0.5
1
1.5
2
2.5
3
3.5
S mm
4
4.5
5
1
5.5
Figure 4.17: Normalized reactance slope parameter against spacing of resonator
from coaxial line
know
the physical parameters that control the frequency and
to
important
is
It
bandwidth for each resonator independently. The coupling bandwidth was dedistance
between
by
the
DR
the
termined
and coaxial transmission line and the
frequency was at first determined by the space between the
end wall and
resonant
the
that
resonator
of
end
could accomodate a tuning screw. Following
the open
frequency
determined
by the depth of the tuning screw.
was
the
resonant
this,
FEM
solvers is simulations can be performed to observe variaAn advantage with
to
the
dimensions
in
obtain
optimised
parameters
tions
needed. A limiting factor
these
simualations is determined by computing power, thus,
of
the
in
accuracy
best,
only
provide,
at
optimum solutions. As the filter was
these simulations
for the first two
simulations
only
resonators for optimisation were
symmetrical,
4 Dielectric-Loaded
Compact Bandstop
Filter
th
Degree Chebyshev Design
4
84
figure
4.18.
required,
-10
-20
-30
co
-40CO
-50-60-70-80
1.848
1st Resonator
2nd Resonator
1.8485
1.849
1.8495
1.85
1.8505
Frequency GHz
1.851
1.8515
1.852
x 109
Figure 4.18: 3 dB bandwidth of 15t = 5.1 I\iHz and 2°d = 8.6 I\'1Hz resonator in
Cliebyshev design with fo = 1.85 GHz
The relationship between the resonant frequency and spacing between the uncoupled side of the resonator and wall of cavity is shown in figure 4.19. Fields in
this region may be modelled as a series inductance, thus, a tuning screw inserted
here will effectively increase the resonant frequency. The end cavity wall must,
therefore. he at a greater distance from the open face of the rectangular resonator
such that the resonant frequency is lower than centre frequency in order to tune
frequency.
A plot of resonant frequency against tuning screw
the
to
correct
up
depth is shown in figure 4.20.
The next step was to optimise the dimensions of the dielectric resonator and the
tuning screw such that the simulated response curve closely matched the ideal
As
the
of
circuit
model.
response
shown from figure 4.21 and figure 4.22, a close
approximation
between the circuit
for
individual
achieved
model response and 3D model response was
first and second resonators.
between each resonator, initally
The length of separations
calculated from A/4, provided an asymmetrical
response and was corrected through
final
The
91°.
an optimised separation of
filter was simulated in HFSS meeting the specifications
filter
bandstop
the
as
of
4th Degree Chebyshev Design
85
Bandstop
Filter
Compact
Dielectric-Loaded
4
N
S
0
C
C
m
lL
1.5
2
2.5
3
T mm
3.5
4
4.5
5
dielectric
frequency
Resonant
4.19:
side
against spacing of uncoupled
Figure
with sidewall
1.86
1.855
1.85
1.845
1y
1.84
1.835
1.83
1.8251.82L
1.815
0
2468
10
W mm
12
14
Figure 4.20: Simulated resonant frequency against depth of tuning screw
figure 4.23.
in
shown
filter
the
simulated
was
final
with
optimised tuning screws as shown
The
practical
dB
bandwidth
the
4.24
simulation
showed
a3
figure
and
in
GHz.
The
input
1.85
and output
frequency of
MHz
10.9
at centre
of
couplings were also optimised to
low loss in out-of-band performance and a1 mm gap was the optimised
achieve
inner
the
between
coaxial conductor and the outer cavity walls.
distance
Q Dielectric-Loaded
Compact Bandstop
Filter
86
4111Degree Chebyshev Design
0
3
-10
-5
-20
-10
-30
-15
-40`
1.82
-20
Co
U,
1.83
1.84
1.85
Frequency GHz
1.86
1.87
Figure 4.21: HFSS simulated tuned Ist resonator, 3 dB bandwidth
fo
GHz
1.8502
and
=
0
-.
N
MHz
5.11
=
0
-5
-5
-10
-10
co
Co
-15
-15
-20
-20
-25'
1.82
-25
1.83
1.84
1.85
Frequency GHz
1.86
1.87
Figure 4.22: HFSS simulated tuned 2nd resonator, 3 dB bandwidth
GHz
fo
1.8498
=
and
=9
MHz
A wideband response was also simulated for and the location of the next spurious
2.49
GHz,
thus, leaving a 640 NlHz spurious free window as
at
situated
was
mode
figure
4.25.
Compared
in
to DR filters, this spurious free band was quite
shown
Compact Randstop
4 Dielectric-Goaded
Figure
Filier
87
;th
llryir
Figure
3
-10
-10
-20
-20
-30
-30
Co
v
-40
-40
-50
-50
-60
-60
-70
-70
-80
1.82
igin
4.23: Schematic of HFSS design of final filter
0
U,
by.+lu r I)e
r (li
1.83
1.84
1.85
Frequency GHz
1.86
1.87
r4
U)
-80
4.24: HFSS simulated response of filter to be fabricated
DR
filter
typical
designs
high considering
require modifications
spurious-free performance.
to improve their
4 Dielectric-Loaded
Compact Bandstop
Filter
88
0
0
-10
-10
-20
-20
-30
-30
-40
-40
-50
-50
-60
-60
-70
-70
-80
Figure
4.6
of Filter
Fabrzcatiou
1.5
1.75
2
2.25
Frequency GHz
2.5
2.75
-80
3
4.25: HFSS simulated wideband response of filter to be fabricated
Fabrication
Filter
of
It was essential the filter was precisely machined since any discrepancy could cause
fixed
frequency
To
at
the
shifts and couplings.
unwanted
ensure
resonators were
the required coupling distances from the transmission line. two fabrication
tech-
height
implemented
figure
in
Since
4.26.
the
niques were
as shown
cross-sectional
line
designed
the
to be smaller than the height of the rectangular
coaxial
was
of
in
the
indent
into
base
lid
the
the
an
was
sections
machined
resonator,
of
and
vicinity
between the transmission line and DR. This ridge prevented the dielec-
tric resonator from shifting too close to the coaxial line, therefore, maintaining
its coupling bandwidth.
In addition, small aluminium
plates were machined and
fabricated
The
the
in
rectangular resonators
secured
position using small screws.
filter is illustrated
in figure 4.27 with brass tuning screws. A picture of the interior
filter
is
the
also provided as shown in figure 4.28.
of
The measured response is shown in figure 4.29 with 3 dB bandwidth of 19.6 MHz
frequency
1.8501
GHz.
At 40 dB, the stopbaind bandwidth
centre
at a
MHz
be
3
to
which achieved the required specifications.
sured
was mea-
However, a low Q
4 Dielectric-Loaded
Compact Bandstop
Filter
89
Fabrication
of Filter
Lid
duminium
3ody
DF
Coupling
Edge
Figure
4.26: Practical resonator design
'i;
ºý-
'ý
ý°ý'ý
,rýyi
9
Figure
IQ
11
nupngniýinipu
12 , 13 14 15
r'ahricated
1.27:
4"'
('Ii(-by
1i'v tºal(Iktop lilt(+r
ci('grve
.
This was largely clue to the poor silver nietallisation
216
measured.
was
of only
dielectric
between
resonator
and
air
gaps
the
rectangular
apparent
were also
of
the cavities they were placed in leading to poor
dielectric
and
slabs
the
electrical
To improve the Q, improved inetallisat. ion techniques
are required
grounding.
hybrid
than
rather
a
nietallisatioii
Nickel
spattering
as
using a sticking
such
coni-
¢ Dielectric-Loaded
Compact Bandstop
Filter
90
Fabrication
(uý
uuiý
12
of Filter
5
Figure 1.28: interior of fabricated 4`h degree Clieb shev ban(Istep filter
It may also be feasible to solder the DR into its resonator
before
silver.
poiin(l
he
thus,
grounding
proper
will
obtained.
space,
0
0
-10
-10
-20-
-20
Co
-30
-40-
-40
-so
-50
-60
1.82
1.83
1.84
1.85
Frequency GHz
1.86
1.87
N
-60
1.88
x 10°
Figure
4.29: Measured frequency response of Cliebysliev bandstop filter
The spurious performance of the filter is also examined. The TE,
02 mode was
leaving
GHz
2.41
a
spurious-free range of 59() MHz as shown in figat
observed
Thus. a favourable spurious-free range is
4.30.
ure
achieved without the need for
5I..
vw
x
-
Compact Bandstop
4 Dielectric-Loaded
91
Filter
Coaxial
Dielectric-Loaded
Bandstop
Resonator
DR
in
filters.
The
filter
demonimprovements
required
as
commonly
physical
handstop
high-Q
dielectric-loaded
a
compact
using
the
of
rectprinciple
strated
high
Q
the
unloaded
allows
and
miniaturisation
over
coaxial
waveguides
angular
designs.
or cavity
0
-10
-10
-20
-20
to
fV
-30
-30
-40
-40
-50
1.9
2
2.1
2.2
Frequency GHz
2.3
2.4
2.5
-50
x 109
1.30: Measured widebaud frequency response of Chef) sliev
Figure
filter
4.7
1.8
Coaxial
Although
Dielectric-Loaded
the TE106 dielectric-loaded
Bandstop
rectangular
l)aiidstop
Resonator
handstop rctioiºýitor is sliital)le
bandwidth,
for
narrow
applications requiring greater handfor designs requiring
between
the
space
resonator and transmission line provides
the
coupling
widths,
bandwidth.
It
is
possible to intersect the rectangular
maximum
on
limitation
a
line
improve
to
but
it is difficult to insert the
the
coaxial
coupling
with
resonator
line through the rectangular resonator at the optinnnn position for niaxicoaxial
A better option would be to use dielectric pucks to take
advantage
niurn coupling.
An
field
broadband
handstop
experimental
pattern.
novel
resonator
of their radial
figure 4.31 with the H-field plot of the dielectric ring displaying the
in
is shown
fundamental
Tl'toia mode. The structure
comprises a coaxial transmission
line
4 Dielectric-Loaded
Compact
Bandstop
to
a cylindrical
coupled
Filter
92
Coaxial Dielectric-Loaded
Bandstop
Resonator
dielectric ring resonator replacing the rectangular
res-
The DR had the same material properties as for TE106 mode resonator
onator.
hole
height.
inner
dimensions
13
5
9
of
radius,
mm, and
radius,
mm,
mm,
and
the same coaxial transmission line, with outer diameter 10 mm and inner diamdimensions
fundamental
These
4.68
was
mm,
also
used.
allowed
a
eter
resonant
frequency of 1.85 GHz.
Dielectric ring
Iresonator -\ ,,
Coaxia
(a)
(b)
Figure 4.31: TMoia dielectric-loaded
field plot in dielectric region
(a) Schematic (b) H-
Bandstop resonator:
--L
L,
--L,
--
WI
Yý
ýx
_Z
Figure 4.32: Dimensions for experimental coaxial dielectric-loaded
W=
40
L,
L2
80mm.
9.57
10
inm,
mm
nun,
=
=
Due to the discontinuity
resonator, L
at the dielectric resonator intersection, the TEA1 proper-
ties of the coaxial transmission line become distorted and is affected by dielectric
loading.
HFSS simulations
can optimise the dimensions of the coaxial line to
discontinuity
these
the
problems
such
as
matching
address
prove the selectivity
of the rejection skirts.
segments and also im-
This is shown in figure 4.33 where
bandwidth
coupling
of 200 MHz is possible for a smaller inner conductor radius
line
DR
transmission
to
junction. An eignciunode solver calculated the unthe
at
loaded Q of this structure to be 2670. The coupling bandwidth
is superior to the
4 Dielectric-Loaded
Compact
Bandstop
93
Filter
Coaxial Dielectric-Loaded
Bandstop
Resonator
-10
-20-
C,
4
Co
-30-
-40
-50
-60
Figure
4.33:
r=1.34 mm
r= 1.84 mm
2.34 mm
1.5
1.6
1.7
1.8
1.9
Frequency GHz
2
Simulated
inner
coaxial
various
2.1
2.2
for experimental
transmission
response
line radii, r
transmission
resonator
for
TE, ()b dielectric-loaded rectangular resonator where only 18 MHz is possible for
0.5 nim spacing, figure 4.12, thus, TM016 mode coaxial dieletric-loaded Bandstop
TEio
the
can
easily
replace
previous
resonators
mode resonators for applications
that require the removal of a high band of undesired spurious components, such
as harmonics, parasitic effects and intermodulation
These are required in transmitter
become important
distortion
paths in communication
devices for future communication
through a system.
satellites and also will
systems as the frequency
increasingly
becomes
for
the
congested
requiring
need
spectrum
widehand interference suppression in front end of communication
Q resonators will also provide miniaturisation
for
filter
design.
commercial
objective
systems.
Using these high
and reduce costs, a paramount
94
Chapter
5
Dual-Mode
5.1
DR Bandstop
Filter
Introduction
A novel dual-mode DR bandstop filter is described in this chapter offering a high
weight
less
Q, better performance, small volume and
compared to conventional
filters
TETM-mode
and
cavity
air-filled
filters.
These benefits are due to the
dimensions of the filter reduced by a factor of 1/
E,. and the high Q. prop-
Although
dielectric
to
materials
metallic
compared
an
empty
enclosure.
erty of
dual-mode DRs are commonly used in bandpass filters, there has been very little
in
bandstop
DR
bandstop
the
only
mono-mode
and
material
sector
published
been investigated, [5]. It is the aim of this chapter to present the
have
structures
dual-mode bandstop resonator compared to a mono
of
a
advantages
-mode strucflexibity
its
to realise advanced filter functions. One distinct drawback
ture and
for such a structure
is the complexity
highlighted throughout
in the realisation
process and these are
from FEM simulations to fabrication.
The DR structure
dielectric
below
in
puck
situated
cavity
a
a
waveguide
cutoff coupled to
considers
line through coupling elements. The fundamental resonance is the
transmission
a
dual-degenerate HEE11 mode and FEM simulations have been used to generate
field patterns for this resonator and perform frequency response simulations aiding in the design of the filter. Bandstop filters are necessary in rejecting unwanted
interference.
When
low
and
cost, size, weight and simplicity
signals
are required,
95
5 Dual-Mode DR Bandstop Filter
Dual degenerate HEE11 mode
high
frequencies
filters
DRs
design
targets
meet
the
at
can
cost
using
of such
large
Qs.
filter
The
for
is
their
superior
new
structure
well
suited
rejecting
with
frequencies
carrier
of a communications
unwanted
system.
Although
design
itself
is
incredibly
the
may
seem
process
arduous,
struction
the con-
robust using
to
posts
as
opposed
magnetic coupling wires, where vibration
coupling
metal
impact in a mobile environment
can distort the frequency behaviour.
and
The main
transmission line is isolated from the DRs, thus, reducing impact of unwanted
interference from stray coupling fields that were a problem seen in open transmisThis
designs.
isolation
line
and miniature
sion
coaxial coupling tap points allows
the resonators to be spaced a/4 apart, unlike in open-transmission
3X/4
spacings are obligatory
where
distortion
5.2
to avoid transmission
line structures
line, inter-resonator,
of the signal.
Dual degenerate
HEE11 mode
To understand the properties of the hybrid mode HEE1I dielectric resonator, the
be
An
FEM
initial
must
modes
studied.
eigenmode solver calculated the
resonant
first five resonant modes for a dielectric puck of height 23 mm, radius 18.5 mm
dielectric
For
44,
5.1.
HFSS
table
permittivity
of
accurate
simulation results,
and
the puck was enclosedwithin a loo mm3 airbox and perfect magnetic layer, PAIL,
boundaries were introduced on the airbox as absorbing conditions for the open
The
free
TEola
in
space.
mode is the fundamental for the specified dielectric
puck
different
for
but
diameter
length
to
aspect
ratios
of
puck
of the dielectric puck,
the HEEII mode can be the fundamental mode in shielded cavities.
The fields for a single degenerate polarisation of HEEII, have been generated
figure 5.1. The orthogonal polarisation has identical field plots but are normal to
the plots shown. Coupling between these two polarisations may be controlled by
introducing a suitable perturbation either internally in the puck, [35] and [71],
located
in
45°
the
surroundings,
at
angle with respect to the direction of each
or
Tuning
have
screws
generally been used but recent advances have
excitation.
5 Dual-Mode
DR Bandstop
96
Filter
Configuration
of Proposed Resonator
Mode No.
Name
Resonant Frequency GHz
1
2
3
4
5
TEoia
HEE11
HEH
TNlo16
HEE21
1.178
1.342
1.649
1.740
1.771
Table 5.1: First five resonant modes of dielectric
a
puck
included metallising the exterior of dielectric shapes, [79].
-_
Jam'.;
I-
-:
-
¶: iIII
- _-
:ýý
V
ý+
(7/
;4i;
p$t
\';
4,
(a)
Figure
(b)
5.1: Field distributions
of HEED 1 dual mode (a) E-field Plots (b) H-field
plots
5.3
Configuration
of Proposed
Resonator
In the design of a microwave Bandstop resonator, anode charts
are essential to unbehaviour
the
derstand
of the resonant frequency in the
proposed DR structure
in
design
the
prerequisites
of bandstop filters. A cylindrical dielectric
which are
in
is
the common configuration
a
cavity
puck suspended
for a DR }nit,
unfortu-
fundamental
in
the
a
structure
such
nately,
mode is the TESa mode, figure 5.2.
A FEM simulation is produced to understand the frequency behaviour
of the di-
5 Dual-Mode
DR Bandstop
97
Filter
Configuration
of Proposed Resonator
faces
between
in
the
the
of the
a
cavity
respective
when
spacings
electric modes
top and bottom cavity walls relative to the dieletric
figure 5.3. The dielectric
puck used was as before and placed in an air-filled,
box
with perfect conducting
cavity
H=
With
63 nim.
consideration
by
a relatively
supported
puck surfaces, are varied,
walls of widths,
to realisation,
2W = 65 mm and height,
the dielectric puck would be
low dielectric constant support but as its effect is in-
for
its
to
the
the mode chart
compared
resonator,
effect
was removed
significant
In the range H/h
simulations.
< 1.2, with the top and bottom
height
but
the
cavity
as
node
the dielectric surfaces, TM0I is the fundamental
increases equally in both z-directions,
fundamental
the
comes
mode.
walls close to
this mode rapidly increases and TEO, be-
A slight increase in H/h
from unity
causes a
dramatic change in modes HEE11, HEE21 and TM0, as their axial E-fields are
for
from
boundaries.
fields
As
further,
H/h
the
increases
the
conductor
removed
final
distributions.
into
their
stabilizes
mode
each
For the specified dielectric puck
for
h/2r
HEE11
0.35,
this
first
the
ratio,
mode
aspect
remained
spurious
=
with
for
between
various
equal
spacings
structure
upper and lower cavity walls and the
dielectric puck.
Av
A7
"--- r --
Top
View
Side
Ea
View
Eo
h
E,
Er
hH
h2
--º
x
Figure
Although
5.2: Diagram of dielectric puck in perfect conductor cavity
a dielectric puck with different r/h
HEEii
force
aspect ratio could
to
be the fundamental mode, to preserve the dimensions of the puck, an alternative
lower
is
the
to
puck to the cavity floor reducing h2 =0 whilst hl = 20 min
method
kept constant. This increases the frequency
32.5
R=
below
TM01
mm
are
of
and
5 Dual-Mode DR Bandstop Filter
98
Configuration of Proposed Resonator
1.7r5
1
N
i
UU
U
7
Q
U-
25
LL
1g
TEO,
--$. - HEE11
HEH,
t
TMO,
o.,
-ý-
a
i
i.
t
HEE21
i"V
i.
V
H/b ýLL.
Figure 5.3: Mode chart variation of H/h with frequency,
h2/h1 < 0.8 and leaves the resonant frequency of HEEII
relatively unchanged as
becomes
first
TEO,
fundamental
figure
the
5.4.
mode
and
spurious
mode,
the new
The disadvantage of this is that Q. will decrease due to the interaction
between
dielectric
but
face
by
lowering
both the
the
bottom
puck
and
cavity
wall
of
the
further
is
height
the
the
of
volume
reduction
cavity,
gained
and
reduces
and
puck
foundation
dielectric
for
Thus,
for
is
support.
a
solid
mechanical
a
stability
need
provided.
The conductor sidewalls must be at a distance from the dielectric puck such that
dielectric
losses
the
fields
in the conconcentrated
at
are
region
and
resulting
the
ductor walls are minimised, however, the sidewalls must also be near enough for
miniaturisation
to be effective.
A mode chart showing the effect of conductor
DR
R/r
in
the
that
1.3,
frequency
the
the
<
shows
range
on
of the
sidewalls
by
due
the
to
their
affected
vastly
conductor
walls
are
near proximity to
modes
figure
5.5.
For
R/r
1.5,
frequency
dielectric
the
for HEEII
>
puck,
resonant
the
mode varies constantly
with conductor
walls indicating
the fields are concen-
fields
the
puck
and
only
weak evanescent
trated within
exist in the vicinity
of the
conductor walls.
bandstop
configurations, each resonator is located at an odd mulIn conventional
99
5 Dual-Mode DR Bandstop Filter
Configuration of Proposed Resonator
.8
.7
.6
N
x'
.4 -
Cl
m
7p
IL
.3 .2 6-
i .1
1
-
HEEII
H
E
-ir-
HEH11
TMot
9
-ýis
E
0
0.2
0.4
0.6
HEE21
0.8
h1h,
Figure 5.4: Mode chart variation of h2/hl with frequency
tiple of a quarter-wavelength
line
transmission
travelling in one direction.
along a
For the dual-mode configuration,
the conventional design produces two physical
by
A/4
figure
but
(a),
5.6
the
experimental
coupling
probes
offset
with
topogies
,
fields are not focused on the surface of the puck and resulting coupling
coupling
be
too poor for filtering applications. The height of the coubandwidths would
be
that
they
the
may
raised
such
extend
over
upper surface of the
probes
pling
however, this would cause increased spuriincreased
for
coupling
surface,
puck
both
between
bandwidths
The
be
increased
probes.
coupling
may
coupling
ous
input
the
couplings perpindicular to each other such that the probe
by placing
figure
(b),
but the A/4 separation between the
to
5.6
the
puck,
faces are normal
be
difficult
would
resonant probes
to realise at the transmission
line and extra
higher loss within the cavity. The solution was to bend
lengths
cause
would
probe
line
90°
face
lateral
the
around
transmission
of the puck, figure 5.7. This is
the
input and output ports required for canonical dual-mode DR bandto
similar
[18], and allows minimum length coupling probes to directly
filters,
excite
pass
dual
for
in
mode
A
maximum
coupling
a
orthogonal
square
cavity.
small
each
is
this
the nature of the transmission line curve would cause
with
disadvantage
a
in the transmission response, however, FENI
discontinuity
simulations can
slight
DR Bandstop
5 Dual-Mode
100
Filter
Configuration of Proposed Resonator
1
1
1
.7
1
.6
Ni
S
0
>1
U
C
.4 -
7ý
.3 u
-i
.2
-
TEO,
.1
HEE11
1
HEH11
-*-
TM01
0
HEE21
0
R/r
Figure
5.5: Mode chart variation of R/r
frequency
with
dimensions
for
frequency
the
the
optimum
response.
optimise
X/4
X/4
Transmission
LInc
Coupling
Probes
DR
Xý
xt
Vf
y
(a)
(b)
(c)
5.6: Topologies for coupling of transmission line to dual-mode dielectric
(c)
(a)
(b)
for
side view
weakly coupled probes
probes
maximum coupling
puck:
Figure
A waveguide transmission
line is commonly coupled to a DR situated in a cav-
ity using irises but require 3A/4 separations to avoid transmission line spurious
inter-resonator
dispersion.
line
increases
transmission
couplings which
resonator volume and
A coaxial transmission
lar inner conductor,
line with square outer conducter and circu-
as described from the TE106 filter in the previous chapter,
The
be
ideal.
benefits
physical
are it offers a uniform cross-section, when
would
diinto
through
be
a curve, and coupling elements may
shaped
rigidly supported
inner
the
to
coaxial conductor.
rect contact
A coupling mechanism to isolate the
i Dual-Mode
DR Bandstop
101
Filter
Configuration
of Proposed Resonator
ýý
Transmission
Line
Coupling
Probes
DR
DR
ýx
y..
(a)
(b)
5.7: Coupling of right-angle
(b)
(a)
top
view
side view
puck:
Figure
degenerate mode excitations
transmission
line to dual-mode dielectric
and provide controllable
coupling is required.
The
design of the coaxial probe can also be isolated from the transmission line such
that dielectric loading is insignificant
and no physical changes in the main traiisIn the past, input and
line
are required to achieve acceptable rejection.
mission
output coupling elements to DRs have consisted of simple electric or magneticfield dipoles using wire probes or loops to excite the correct mode, [26]. The
disadvantage with these elements is that in filter structures, wires may vibrate
Although
is
the
thus,
cavity,
within
a more robust coupling structure
considered.
electric coupling pins would be more simple as only one end is fixed to the coaxial
line, the dielectric-air
boundary of a dielectric puck allows more magnetic energy
to couple out. Thus. it was beneficial to make use of magnetic coupling to niaximise the coupling bandwidth
available.
The coupling mechansim was designed
base
tapped
to
the
to
of the cavity
probe
a metal post and grounded
as a coaxial
figure
5.8.
in
as shown
A tuning element was also needed to correct any imperfections
design. therefore, coupling screws were also introduced
in the realised
to time the capacitive
A
figure
5.9.
in
the
for
is
the
probe.
circuit model
element of
coupling model shown
This is equivalent to a resonant circuit such that as the tuning screw approaches
the inductive post, the capacitance increases, effectively reducing the resonance
from
the
the transmission
allowing
more
post
coupling
of
line to the dielectric
5 Dual-Mode
DR Bandstop
102
Filter
Single Cavity
De. sigri
Inductive
Coupling
Element
Coaxial
Transmission
Line
-º
X/4
ýx
,ý
y
ýa)
fib)
5.8: Coupling mechanism for dual-mode HEE11 Bandstop resonator: (a)
top view (b) side view
Figure
Non-resonant
S/C Stub
Figure
5.9: Circuit model for coupling post
To
aid with the positioning
puck.
introduced
was
Tuning
Screw
in the puck.
hole
floor,
the
the
a centre
of
puck on
cavity
The filial proposed HEE»
bandstop structure
is
figure
5.10.
in
shown
5.4
Single
Cavity
Design
The dimensions for a single cavity dual-mode resonator were calculated based on
the same properties of the dielectric puck in the previous section with an additional circular hole along the axis of the puck. This modification
for
positional
was
purposes to align the puck at the centre of the cavity but to ensure the spuriThis
figure
5.11.
was
unaffected,
a mode chart was produced,
ous performance
insignificant
there
was
showed
variation
in resonant frequency against increasing
hole diameter for both HEE11 and TEoj modes, thus, the spurious-free bandwidth
MHz
It
250
is interesting
was
conserved.
of
to note that for operation of TEo1
improve
hole
in
increases
TMo1
will
a
spurious
performance since
mode,
mode
frequency due to removal of the axial electric fields of the TM0I mode.
103
5 Dual-Mode DR Bandstop Filter
Single Cavity
Tuning
Screws
Design
Aluminium
Enclosure
Metal Coaxial
Line
cý
Dielectric
Puck
2
LX
y.
(a)
Y
L-. x
ýbý
1c)
Figure 5.10: Structure of HEEi1 mode dielectric Bandstop resonator: (a) Corner
(c)
Cross
Top
(b)
section
view
view
For ease of design, the sidewalls of the cavity were fixed to accoinodate the righttransmission
coaxial
angle
line. In the design for this particular
27,
37
diameter
diameter.
mm,
providing
a
suitable
cavity
=
of
dielectric puck
a factor greater
than 1.5 of 2R = 65 mm was suitable to minimise the effect of conductor losses.
A prescribed cavity height spacing of It, = 20 min gave a resonant frequency of
1.07 GHz for the HEE>> mode, figure 5.4. One should ii<ºte that this frequency
was simulated
there is minimal
for a puck in a box-shaped
change in frequency
cavity
when a cavity
but
future
corner
simulations
is curved
shows
inwards
to
frequency
line
This
the
transmission
bend.
to
was
used
calculate the
accornodate
length of transmission line separation between the two modes as A/4 =7 cm. The
line needed to be large enough to accomodate the coaxial
transmission
coaxial
dimensions
from
the
A
4.20.
were
and
equation
calculated
square outer
probe
13.5 111111
inner
defined
6.35
width
of
and
conductor
round
of
inne
were
conductor
thick
between
conductor
innn
a1
wall
outer coaxial conductor and cavity
with
sides.
5 Dual-Mode
DR Bandstop
104
Filter
Single Cavity
Design
1.6
1.5
1.4
N
S
HEEll
ý-
1.3
S
TEO,
Ui
TM01
1.2
HEE21
1.1
0
0.04
0.08
0.12
rilr
0.16
0.2
0.24
5.11: Mode chart variation of r1/r with frequency
Figure
t
(a)
(b)
(c)
Coaxial
line
transmission
5.12:
with various centre conductor curvature
Figure
(a) c= 40.25 inin, e= 63.2 min (b) c= 29 iiini, U= 68.1 iiini (c) C= 19 iiiiii,
radii
72.77
min
e=
The complexity
in the design of this structure
is now shown as the total length
transmission line separation, including the right-angle
inter-mode
of
bend, must
their respective cavity sidewalls.
tap
the
the
of
points
coupling
at
centre
position
by
length
line
determining
be
transmission
the
to undergo
of
controlled
This can
the right-angle transformation.
Ideally, the transmission line is straight but devi-
into a curve causes a discontinuity at which point, the pure TEN1
from
this
ating
down into components of electric and magnetic fields along the axis
breaks
mode
It
bend causes changes in the electromagbend.
that
the
was
reported
the
of
inversely proportional to the radius of the curvature, [80], therefore, a
fields
netic
5 Dual-Mode
DR Bandstop
105
Filter
Single Cavity Design
transmission line of maximum curvature radius is desired to limit the sharpness
bend.
To
the
conform with the symmetry
of
of the dielectric puck and cavity,
the maximum radius must be directly proportional
to the radius of the puck at
the sidewalls. Figure 5.12 shows a possible range of curve radii for this structure
with each corresponding to a different separation between the degenerate modes
at the centre of the coaxial conductor.
In order to conserve the properties of the
puck inside the cavity, the designer may increase the radius of the transmission
line, 40.25 mm, to fulfill the A/4 separation and keep the maximum curvature of
the bend, however, this would increase the volume of the structure.
option is to decrease the radius in the transmission
The second
line and introduce straight
line sections to preserve the 1 mm cavity wall between the cavity sidewall and
outer coaxial conductor,
figure 5.12 (c).
FEM simulations
filled coaxial transmission line with aluminium
for a practical
air-
SMAs
at each end
conductors and
frequency
responses for various inmost coaxial conductor curvatures.
produced
Results show there is little variation
in the transmission line response of differ-
ent radii curves producing a range of separation values around the required A/4,
figure 5.13. Although
there is poor isolation at high frequencies above 2 GHz,
loss
better
than 20 dB in the region of operation, 1 GHz, is achieved and
return
the second option was used to minimise volume.
Dimensions for the tuning element must also be considered to provide the correct
bandwidth coupling to the DR puck. Coupling probes of miminum size were
ideal to avoid impedance loading of the transmission line and unwanted spurious
in
effects the cavity at the coupling tap points. The well-known coaxial impedance
line equation was used to calculate the initial diameters for the circular coaxial
These
points.
were initially configured to be 1.3 mm and 3 mm for the
coupling
inner and outer conductor, repectively. An introductory rod length between the
inner
conductor and tuning post was 10.8 mm and the post diameter was
coaxial
3 mm. Based on the above discussions, the typical dimensions for a single cavity
dual-mode HEEII bandstop filter are shown in table 5.2.
5 Dual-Mode
DR Bandstop
106
Filter
Single Cavity
Design
-10
2cm
2.45cm
2.9cm
3.35cm
-12
-14
-16
-18
-20
-22
-24
-26
-28
-4n
VÖ.5
2.5
2
1.5
Frequency GHz
1
3
line.
transmission
inner
Frequency
5.13:
of
coaxial
and
response
outer
Figure
diameters, 13.5 inm and 6 mm respectively, for various radii of inmost
conductor
curvatures
wall
conductor
coaxial
Typical Performance
Typical Dimensions
h=23
in"
r=18.5min
6.5
mm
n
65
inin
c=
52.5 min
R=
57 mm
25 min
H
l=
hi
G=
=
14
13.5
g=6.35
Table
min
min
min
5.2: Typical
h= 18.5 min
12= 10.8 mm
13=3 Inns
l4 = 1.5 nun
f0=
1.07 GHz
F,. = 1.1
Q=
9000
First spurious frequency 1.35 GHz
15 = 1.3 min
d, =1.3min
d2 = 4.1 Inns
71.7
e=
el
=
19
min
min
q1=1min
dimensions
haii(lstop
resonator
5.4.1
FEM Simulations
and performance
of HEE1I
dual-ino d' dielectric
for single cavity
behind the proposed dual-anode l)andstop filter. it is useful
ideas
the
To confirm
the behaviour of the fields of the proposed resonator cavity using
to understand
The
fields
in
excite
posts
radial
coupling
the
FEM
magnetic
simulations.
3D
dual-modes. The field plots for a single HEE11 degenerate
anode
two orthogonal
E-field
is
maximum near the centre of the top surface, and at
the
radial
show
5 Dual-Mode
DR Bandstop
107
Filter
Single Cavity
4W
Design
R
ý-Gý
-------------
h,
iy
14
1h
`JI
ZLý
X
91
e,
o
1,d,
1
#15
-,
Figure
5.14: Details of HEE11 anode dielectric bandstop resonator
the circumference of the bottom puck. The H-field is concentrated through the
centre of the transverse plane towards the cavity base, figure 5.15. There is greater
fields
dissecting the ti-axis than in the axial direction of the puck
the
variation of
which indicates that, in a fixed cavity, Er and the diameter of the puck have more
frequency
the
than the puck height.
resonant
effect on
The eigenmode solver was used to simulate the resonant frequencies of the first five
bandstop
DR
the
modes of
resonator, table 5.3, with dimensions from table 5.2.
For the structure
described, HEEii
is the fundamental
mode but the resonant
frequency increased from 1.07 GHz to 1.11 GHz caused by the interaction between
the coupling posts. The Q,, of the fundamental
bottom
8100
the
as
mode was
face of the puck was now in direct contact with the cavity. The spurious response
for DRs is generally poor and the first spurious TE0ý16
MHz
247
mode occurred at
5 Dual-Mode
DR Bandstop
Filter
108
Single
Cavity
Uesiyn
yt
YL.
x
i
ol
;!;:: --
,
=W
,4-ý
---
Zý
ZL
X
(a)
(b)
Figure 5.15: Field plots of single degenerate HEE1I mode coupled to transmission
(b)
H-fields
in xy- and vz-plane
in
E-fields
(a)
line:
xy- and xz-plane
fundamental frequency. However, the axial path varies with the TM10»
the
above
frequency
hole
increase
the
this
thus,
a
centre
would
of
spurious
mode,
spurious
by
improve
It
is
to
the
the
response
removing
possible
portions
spurious
of
mode.
[81].
The
fields
E-fields
for the spurious TE1116
spurious
of
modes
exist,
where
puck
figure
By
5.16.
E-field
in
to
terminate
the
removing
sections
paths, the
are shown
bandwidth will increase. An example is shown of the saine dielectric
spurious-free
figure
design
in
5.17.
dimensions
The
the
removed,
with
a
ring
small
used
puck
7
14
inner
height
5
outer
the
are
radius,
radius,
mm,
nine,
ring
and
of
mm
of
below
5
the puck. This modification produced
the
top
mm
surface
of
at
situated
increase in the spurious bandwidth
MHz
50
a
without
affecting the fundamental
frequency.
Figure 5.18 presents the tuning screw arrangement required for dual-mode cavity
designs, [30]. The orthogonal modes are initially
designs, the bandwidth
uncoupled but for cross-coupled
of this coupling may be controlled by placing a metallic
the
perturbed
opposite
screw
edge of the cavity at 45° with respect to the two
5 Dual-Mode
DR Bandstop
109
Filter
Single Cavity
Mode
Resonant Frequency GHz
HEE11
TEola
TMola
HEE21
HEH11
1.111
1.3578
1.483
1.562
1.7913
Design
Table 5.3: First five modes in a dielectric puck in contact with base of cavity
Z"
rt-
ILS
x
X
(a)
(b)
Figure 5.16: Field plot of first higher order slniriouti iiiode, TEO»b: (a) Side view
(b) Top view (c)
(bi
ui
Figure 5.17: Dielectric puck with removed ring section for improved spurious:
(a) 3D view (h) Top view (c) Side view
polarization
axis. 'Tuning disks may also be used as the larger surface area will
tuning
effect.
more
provide
As most of the fields lie within
be
tuned
to
close proximity
must
screw
variation
the dielectric,
to have a desired effect. This coupling
can clearly be seen in figure 5.19 where a penetrating
the two frequency modes together, splitting
frequency for each orthogonal
the
them further
anode may be controlled
dialing screws opposite each coupling post on the xy-plane.
apart.
screw couples
The resonant
individually
by placing
Figure 5.20 shows the
disk
tuning
a
penetration
of
of
with a silver circular disk of 5 nine radius and
effect
1 mm thickness attached on the end on mode 1. As the disk moves from 6.5 min
5 Dual-Mode
DR Bandstop
110
Filter
Single Cavity
Design
frequency
14
the
towards
the
to
the
resonant
puck,
of mode 1,
min
inside
cavity
fl, decreases by over 3 MHz, while the frequency of mode 2, f2, increases slightly
by 1.5%. For greater tuning
bandwidth
for each mode, a large screw is ideal
but care must taken not to hugely distort the frequency of the second othogonal
frequency
have
but reduce the Q
Metal
tuning
screws
a
greater
effect
on
mode.
of the resonator.
To maintain
the Q. dielectric screws may he used but have a
Metallic
to
tuning
capacity
when
compared
metal
screws.
smaller
in
the
experimental
used
screws were
resonator structure.
Input
Coupling
Elements
Frequency
Tuning"
Screws
Mode
Coupling,
Screw
Figure
XtY
5.18: Diagram of orthogonal
frequency tuning and coupling screws ar-
rangement
0
-5
-10
-15
M
-20
-25
-30
-35
t=15 mm
t=20mm
t= 25 mm
-40
-451.11
Figure
1.115
1.12
Frequency GHz
1.125
5.19: Frequency response for penetration
The amount of bandwidth
1.13
of cross-ccoupling screw
is controlled by the coupling rod length and the diatu-
5 Dual-Mode
DR Bandstop
111
Filter
Single Cavity
Design
0
-10
-20
f2
-30
-40
N
N
f2f2f2
-50
{'
f1
-60
f1
6.5 mm
9 mm
11.5 mm
14 mm
-70
_an
1.114
Figure
1.118
Frequency GHz
1.116
5.20: Frequency response for penetration
1.12
1.122
of single resonant anode tuning
screw
between
dual-eiode
The
isolation
the
input
the
achievable
post.
maximum
of
eter
limited due to the right-angle directions of the coupling elements
is
separation
This
limits
the
the
within
coupling
cavity.
measure
of
spurious
some
producing
handstop attenuation but this problem can he reduced by optimising the size of
the coupling
the resonator
elements,
structure,
l min, the frequency
bandwidth.
in particular
the coupling
figure 5.21. For rod diameters
response achieves acceptable
As a result,
rod diameters
the coupling
for
0.9
5.2,
to
mm
a, coaxial
table
rod diameter
outer conductor
between
attenuation
be
can
varied
15 = 0.8 mum and
over the handstop
was optimised
diameter
in
frone 1.3 min,
of 21.1 =3
mm.
The original A/4 transmission line separation for 1.07 GHz was changed to accoGHz. The separation between the
increased
frequency
1.11
the
centre
at
modate
from
7 cm to 6.94 cm with a2 cm radius bend in
tap
was
reduced
points
two
To
line.
accomodate this reduction in the bend, the cavity walls were
the coaxial
increased to 6.5.1 cm. HFSS simulations
were used to adjust all these physical
distance
single
and
a
cavity
was
resonator
simulated
with
a
coupling
parameters
between
inductive
the
5
min
of
post and the puck.
All dimensions were opti-
HFSS
including
in
the
size of the cavity, the post sizes, input and output
mised
5 Dual-Mode
DR Bandstop
112
Filter
Single Cavity
Design
0
-10
-20
N
-30
-40
15= 0.6 mm
15= 0.8 mm
15=1mm
-50
15=1.2mm
-60
1.115
Figure
1.117
1.119
Frequency
5.21: Optimisation
1.121
GHz
1.123
1.125
of coupling rod diameter
The
frequency
the
phase
separation
changed.
and
was
also
response
of
couplings
filter is shown in figure 5.22. The bend at one edge of the cavity to
experimental
line
the
right-angle
caused a reduction
coaxial
accolnodate
in the volume which.
GHz.
The
frequency
1.119
increased
the
to
simulation
in turn,
bandwidth
produced a3 dB
loss
MHz
3.6
of
of 0.18 dB. In addition,
and a mid-band return
in
dual-mode resonators, if the external surroundings are uniform and svini lctrical,
degenerate
the
frequencies
of
the
modes can be identical leading to correct couHowever,
in
between
two
discontinuity
the
orthogonal
modes.
cases
where
a
pling
imperfection
in
the
cavity,
such
as
an
occurs
in the symmetry of the cavity or an
being
inserted, this would distort the orthogonality
object
external
of the dual-
behaviour
Tuning
their
coupling
slightly.
affecting
screws were introduced
modes
in the simulation to de-couple the modes.
The wideband performance of the filter was observed and a higher order mode
GHz
1.432
figure
This
in
5.23.
as
shown
gave a spurious-free window of
at
occured
higher
is
MHz
than the eigemnode solution. In fact, this mode was the
313
which
TM0, from observation of the field pattern of this mode at its resonant frequency.
The TEO, mode was not apparent because the inductive
insufficient electric coupling.
coupling post provided
5 Dual-Mode
DR Bandstop
113
Filter
Single Cavity
0
0
-20
-10
-40
-20
N
N
0,
-60
-30
-80
-40
-Inc
Figure
"II
1.11
1.12
Frequency GHz
_cn
1.13
1.14"
5.22: HFSS simulation of experimental
filter for fabrication
0
0
-20
-10
-40
-20
N
N
0)
-60
-30
-80
-40
-100.
1.1
1.15
1.2
Figure 5.23: HFSS simulation
fabrication
5.4.2
Design
Fabrication
1.35
1.25
1.3
Frequency GHz
1.4
1.45
-50
1.5
of the spurious mode of the prototype
and measurements
dual-mode
of
filter for
single
cavity
The resonator mounting had to be mechanically robust and simple to fabricate.
For this prototype
it was found that applying a thin layer
between
the
glue
of
DR Bandstop
5 Dual-Mode
114
Filter
Single Cavity
A small pocket island was also raised
base
provided adequate rigidity.
puck and
in the machining of the cavity for positional
to avoid unrepeatable and uncontrollable
Design
purposes.
One should note that
effects on the resonant frequency, this
be
due
between
to
the
the puck
not
adequate
would
presence
of
air
gaps
method
To remove these unwanted effects, a solution may be provided by
and cavity.
the base of the puck and depositing a layer of solder on the base
silver-plating
of the aluminium
cavity.
Next the puck may be clamped to the base and the
baked
high
temperature
under
structure
whole
to solder the puck to the cavity
base. This realises a good mechanical support of the puck, providing
frequency
for
the
temperature
high
Q.
The
as
well
good
over
as
electrical
contact
a
stability
filter
is
figure
in
5.24.
shown
manufactured
W
,.
!
'A"
"
.:
eýp
r
Figure
1
5.24: Fabricated single cavity of HEEi1 dual-iiiod('
l)aiidstop filter
The measured frequency response of the experimental handstop filter is shown in
figure 5.25. In this first measurement, no tuning screws were used and a centre
frequency of 1.131 GHz was produced along with a3 dB bandwidth of 4.59 AMHz.
The filter produced an attenuation
of 18.56 dB. This figure incorporated
any
losses and dielectric losses of the resonator
and its surroundings. In
conductor
between the top plate of the filter
the
air
gap
particular,
and the body also creates
5 Dual-Mode
DR Bandstop
115
Filter
Single Cavity
Design
line
between
the
in
the
the
loss,
coaxial
main
cavity.
and
vicinity
especially
much
The losses here are due to the formation of the 1 nim diameter holes between the
halves,
into
two
line
the top
that
as
machined
one
cavity
are
and
transmission
in
A
here
the
the
bottom
symmetry
change
will
small
create a
enclosure.
of
and
face
flow
the
in
the
of the wall leading to loss.
along
discontinuity
current
0
0
-5
-5
-10
v
-10
15
-157N
-20
-20
-25
-25
-30
1.12
1.13
Frequency GHz
1.125
30
1.14
1.135
x 10°
Figure
5.25: Measured frequency response of HEE1 i experimental
Tuning
screws were used to produce
thogonal
width
dual modes to create a peak attenuation
MHZ,
2.74
of
response with
4.3 MHz
figure
5.26.
1% fractional
GHz,
1.13
at
figure
For a rippled
bandwidth
5.27.
higher-order
the
next
measured with
spurious
the maximum
free passband
attenuation
Bandstop filter
between
of 25.05 dB with
response,
was produced
The spurious
with
an inverse
tli e or-
3 dB bandChehysllev
a3 dB bandwidth
performance
of the filter
of
was
1.3689
GHz,
figure 5.28. offering
at
mode
a
of 240 MHz.
it
these
was apparent how versatile this structure was since asnlnnnresults,
From
functions
be
filter
can
realised through creating coupling paths between
ber of
intra- or inter-cavity
modes. However, for more complex functions, such as the
the phatie of the transmission line may be varied in the
approximation,
elliptic
filters
but
direct-coupled
for
A/4,
than
changes
phase
much
of
tllVV
smaller
case
5 Dual-Mode
DR Bandstop
116
Filter
Single Cavity
C
0
-10
-20
m
N
-20
-40
-30
-60
-40'
1.12
Design
1.125
1.13
1.135
Frequency GHz
co
v
04
N
Co
'-80
1.14
x 109
5.26: Measured Chebyshev response with tuning screws of HEE, I single
filter
bandstop
cavity
Figure
D
0
-5
-5
-10
-10
co
U)
-15
-15v
-20
-20
-25
-25
-30
-, an
1.12
1.125
1.13
Frequency GHz
1.135
7
N
N
1.14"
x 109
Figure 5.27: Inverse Chebyshev frequency response of HEED i single cavity handfilter
stop
line
be
may
scaled up by odd multiples of A/4. In the HFSS simulatransmission
tions this was easily implemented through changing the radius of the transmission
line bend which enabled the dual-mode separation to shift away from A/4.
By
5 Dual-Mode
DR Bandstop
4 Ih Degree i,tiver, +e Clirbysli. cv Design
117
Filter
C
u.
-10
C
-20
- -20
-30
-30
-401.1
Figure
-10
1.15
1.35
1.3
1.25
Frequency GHz
1.2
1.4
1.45
N
Co
-40
1.5
x 109
5.28: Spurious frequency response of HEEL I single cavity bandstop filter
inter-cavity
it
is
to
possible
create
cavities,
cascading
cross-couplings to create
between
to
cavities
model complex coupling matrices where rejeccross-couplings
be
the
to
stopband
of
controlled
on
either
side
control selectivity.
can
tion zeros
5.5
4th Degree
For applications
inverse
requiring
Chebyshev
higher bandwidth,
Design
a 4tß' degree filter was designed
for
design
into
the single cavity resonator.
the
consideration
results
taking
design
had
bandwidth,
narrow
very
single cavity
it is possible to increase the bandwidth
The
therefore, by increasing the order
of the stophand of the filter.
to achieve a wide stopband, the inverse Chebyshev approximation
In order
was used as it
flat
to
passband
skirt
produce an equiripple stophand
maximally
and
steep
a
offers
for a symmetrical
response.
The design follows from the transformation
of a
highpass matched inverse prototype, figure 5.29, to the ladder prototype network,
figure 5.30, [41]. The network then translates to a symmetrical handstop filter
formed from an inverter-coupled
network with each inverter equivalent to a unit
figure
The
5.31.
filter
for
the two cavity design are shown
specifications
element,
118
Filter
Bandstop
DR
Dual-Mode
5
4th Degree inverse Chebyshev Design
in table 5.4.
In
is
Figure 5.29: Matched inverse Chebyshev filter prototype, [41]
93
91
ýn
S:
in
S+
ti
Figure
5.30: Circuit network of inverse Chebyshev elements, [41]
C2
Figure 5.31: Inverse Chebyshev bandstop filter prototype, [82]
Filter Specifications
Centre frequency
1.15 GHz
Passband bandwidth
24 MHz
Return loss (Lß)
20 dB
Stopband bandwidth
Insertion loss (LA)
6 MHz
30 dB
for
Filter
4th degree inverse Chebyshev bandstop filter
5.4:
Table
specification
5.5.1
Inverse Chebyshev
element values
for
design
have been calculated from [41]. Specifications
the
The synthesis values
degree
Chebyshev
4th
that
filter,
4.21,
required
a
produced
equation
were
N>
30+20+6
>3 68
201oglo[4+ (42 - 1)1/21
(5.1)
119
5 Dual-ModeDR BandstopFilter
4th DegreeinverseChebyshev
Design
hence, a filter of degree 4 was required and a two cavity dual-mode structure was
Next the bandwidth
suitable.
factor,
be
191.7
to
a,
was
calculated
and
scaling
the element values were as follows,
1B1
Ap
+p=
...
9r
Cp +
(5.2)
LP
The element values are derived from the following approximate
frequency trans-
formation to realise the frequency invariant reactance from figure 5.29. The transformation is based on the approximation
that a lumped inductor or capacitor of
frequency
behave
invariant
to
the
will
similar
reactance
equal
vicinity
of wl <w<
w2 where wl
w2. The immitance
reactance in the
of the rth element is
from
calculated
2a + Cos0,
`4 - 4wo?
I sin Or
B
for r=1,0
for r=2,0
for r=3,0
wo(2o
_
-
)
8,.
cos
4rßsin B,
(5.3)
r
\5.4
= 7r/8,
Al = L1 = 2.8185e x 10-8 H
(5.5)
A2 = L2 = 1.1658 x 10-8 H
(5.6)
A3 = L3 = 1.1635 x 10-8 H
(5.7)
3ir/8,
=
= 57r/8,
120
Filter
Bandstop
DR
Dual-Mode
5
HFSS optimisation
forr=4,9=77r/8,
(5.8)
A4 = L4 = 2.8049 x 10-8 H
The same 0 values were used to calculate the rest of the elements.
Bl = 1.4644 x 1012,Cl = 6.8284 x 10-13 F
(5.9)
B2 = 6.0745 x 1011,C2 = 1.6462 x 10-12 F
(5.10)
B3 = 6.0867 x 1011,C3 = 1.6429 x 10-12 F
(5.11)
B4 = 1.4715 x 1012,C4 = 6.7957 x 10-13 F
(5.12)
figure
The
in
5.32.
is
SZ
the
circuit approxcircuit model shown
In a1
system,
Chebyshev
is
in
inverse
ideal
the
shown
response
imation was simulated and
figure 5.33.
11.64nH
11.66nH
28.19nH
/4
-i
X/4
T
6.83pF
T29.05n11
2./4
6.8pF
6.07pF
6.09pF
Figure 5.32: 4th degree circuit model inverse Chebyshev bandstop filter
5.6
HFSS optimisation
dielectric
design
the
to
the
design
using
same
puck,
single cavity
The
was similar
however,
line,
transmission
the
and
coaxial
cavity was modified
elements
coupling
for
FEAT
waveguide
cutoff
cavity
under
conditions
efficient
to use a cylindrical
This is useful as the symmetry of the structure and appropriate
simulations.
boundaries
drathe
to
time
electric-wall
reduce
or
simulation
allows
magneticA top view of the structure allows the dimensions that were varied for
matically.
5 Dual-Mode
DR Bandstop
121
Filter
HFSS optimisation
0
0
-10
-10
-20
-20
a
-30
-30
-40
-40
-50
-50
-60 1.12
Figure
1.13
1.14
1.15
Frequency GHz
1.16
1.17
N
-60
1.18
x 109
5.33: 4tß' cleorec' circuit IflU(1cl üivcrsc Clicl>y&licv i»U1(istO1)filz cl.
in
particular,
Optimisation,
for even heights in loth
cavities, the tililing
depth is
depicted
by
from
first
last
t, to t4, figure 5.34.
the
to
increased
resonant mode
The coupling bandwidths
SI
=
s4
and
S2 =
for each tuning element was adjusted with spacings
S3.
To aid the design. initial simulations were performed to find the o1)timmil cavity
height for the resonant frequency to be slightly above centre frequency to allow
figure
frequency,
down
5.35.
to
the
required
tuning
resonant
bandwidths.
pling
bandwidth
a simulation
For correct cou-
of the tuning element spacing against coupling
was produced to extract the required spacings, figure 5.36.
The reactance slope parameter method, as used for the TE, w bandstop filter, was
filter
from
however,
the
the
to
physical
model,
realise
circuit
eacli resonance
used
be
individually
treated
not
mode could
due to spurious coupling betwe eIl the
degenerate modes in each cavity. The optiniisatioii
technique involved performing
HFSS simulations to equate the frequency response and 3 dB l»andwidtli for each
consecutive
dual-resonator
circuit from the prototype,
figure 5.32, and required
in
5.5.
The
table
first
shown
step was to observe the middle two resonators
results
5 Dual-Mode
DR Bandstop
122
Filtrr
HFSS optimisation
d2
y,LX
LL
Ä
Figure
5.34: Top view of HFSS simulation with variables for optimisation
1.17
x 10'
1.16
1.15
1.14
LL
1.13
1.12
1.11
26
Figure
28
30
34
32
Cavity Height mm
36
38
40
5.35: Variation of resonant frequency with DR circular cavity height
from the circuit
since their symmetrical
bandwidth
and isolation within
their
dimensions
desired
the
cavity
allowed
physical
respective
of their tuning elements.
123
Filter
Bandstop
DR
Dual-Mode
5
HFSS optimisation
N
I
L
V_
CC
W
m
C
O
a
(5
CC
d
Q
m
V
c)
10
123456789
Coupling post spacing from puck mm
Figure
5.36: Variation of 3 dB coupling bandwidth
with coupling post to puck
spacing
Moving into the first cavity, it was now possible to tune the resonant frequency
first
to
the
the
both
for
resonance mode such
coupling
modes and also adjust
bandwidth.
The
the
both
same process was
showed
required
coupling
modes
that
)//4
last
to
the
the
the
to
was
adjust
step
separations
second cavity and
applied
to achieve a symmetrical response.
Mode
Centre Frequency GHz
S21 3 dB bandwidth MHz
1
1.147
2.823
2
3
4
1.149
1.151
1.153
6.787
6.787
2.823
Table 5.5: Requirements for resonant frequency and bandwidth for each mode
At a centre frequency of 1.15 GHz, the length of the separations was taken to be
6.52 cm long. Unfortunately, this separation was too short for the middle resthe
two
intersect,
for
fabrication
therefore,
to
cavities
causing
purposes, a
onators
6.7
to
input
two
the
taps. This was incorcm
was
chosen
separate
centre
of
value
final HFSS 3D model, figure 5.37 and the optimised frequency
into
the
porated
figure
in
is
5.38.
The
produced
out-of-band asymmetry is caused by the
response
3% increase of the separation between the middle resonators. For future designs,
5 Dual-Mode
DR Bandstop
124
Filter
HFSS optimisation
it is proposed that the cavity radii be decreased to accoinodate the separations
required.
Figure
5.37: Final HFSS simulated model for inverse Chebvsliev handstop filter
0
0
-10
-10
-20
-20
to
v
N
-30
-30
-40
-40
-501.12
5.38: Frequency
Bandstop filter
Figure
1.13
1.14
1.15
Frequency GHz
response of optimised
1.16
1.17
-50
1.18
HFSS design for inverse Clielwshev
5 Dual-Mode
5.7
DR Bandstop
125
Filter
Fabrication
Fabrication
filter
of
Precise machining was used for the desired dimensions and the dielectric
were mounted and positioned
to the base of each cavity.
from
the
tolerances
optimisation
sional
impractical,
was
which
through manual tuning.
of filter
pucks
The required dinien-
hundredth
was
a
of a millimeter
process
therefore, the fabricated tolerances must be accounted for
The enclosure was made from aluniiniuni
in three parts with a body, lid and an aluminium
and Was made
rod fixed to the four coupling
filter
figure
5.39.
fabricated
in
The
is
shown
posts.
1
3
Figure
5.39: Fabricated 4th dicgi 'v inverse ('liebysliev
ýý
1)alldstop filter
Tuning was necessary for this filter and the measured response is shown in figfilter
frequency
GHz
dB
1.164
band3
the
5.40
with
offering
of
centre
and
a
ure
MHz.
The
16.3
is
of
performance
comparable to the simulated results but
width
frequency
in
due
fabrication
increase
1%
to
centre
was observed
a
inadequate tuning screws providing insufficient tuning bandwidth.
is
it
proposed that timing
signs.
tolerances and
For futtre
de-
disks with wide surface area to the dielectric
for
be
due
Losses
tuning
to poor tuning screws and
used
greater
were
puck
effect.
between
dielectric
the
the
contact
surface
puck and the base of the cavity.
poor
of
5 Dual-Mode
DR Bandstop
126
Filter
Fabrication
These can be improved by using silver screws and the interior
be silver-plated ensuring conductor losses are miiiiniised.
of filter
of the cavity can
The tuning mechanism
losses
loss
it
increased
in
Of
introduced
the
as
cavity.
note, there
conductor
also
is a reflection zero on the left side of the response caused by the shortening of
the separation between the two middle resonators. The asymmetric behaviour is
due to an occurrence of a susceptance in the transmission line. By changing the
length of the line, this susceptance will be absorbed into the line producing the
required symmetrical
response.
C
0
-10
-10
-20
-30
U)
N
to
-40
-20
-50
-301.13
Figure
1.14
1.15
1.17
1.16
Frequency GHz
1.18
1.19
-An7
1.2
z 10°
5.40: Measured frequency response of inverse Cliehyshev 1)andstop filter
This filter demonstrated
a significant
Bandstop design producing
improvement
in bandwidth
16.3 MHz 3 dB attenuation
to 4.3 MHz for the single cavity filter.
bandwidth
over the first
in contrast
The wideband response showed the first
TMwI,
GHz
in the 1"' degree DR filter giving
1.516
mode,
occurring
spurious
at
free
This
5.41.
352
MIHz,
figure
window
spurious
of
a
spurious frequency has
been driven down along with the fundamental frequency as the puck was moved
towards the base of the cavity. Although adequate for narrowband communication
DR Bandstop
5 Dual-Mode
127
Filter
Direct-coupled
DR bandstop filter
0
-10
m
-20
0
-30
-40
-50 1.1
1.15
1.2
1.25
1.35
1.3
Frequency GHz
1.4
1.45
1.5
1.55
x 109
Figure 5.41: Measured wideband frequency response of inverse Chehysliev handfilter
stop
be
improved
this
as shown earlier through
spurious performance can
systems.
fields
the
A
the
the
with
of
spurious
modes.
of
puck
sections
associated
removing
dual-mode bandstop filter has been designed that offers the hybrid niode as the
fundamental
mode which is an advantage over mono-mode dielectric
resonator
bandstop filters as it offers two resonances in a single cavity. Miniaturisation
has
been shown by moving the dielectric puck to the base of the cavity, thus, nearly
half the cavity has been removed and the filter structure
exhibits an unloaded
high Q of 9000.
5.8
Direct-coupled
DR bandstop
filter
In this section the dual-mode bandstop configuration
synthesis
technique
polynomials
that
as described
generates
in chapter
a l)andstop
is used to realise a network
function
2. The beauty
frone the regular
of this technique
formed
matrix
produces a folded configuration
coupling
lowpass
is that
the
degree
handstop
4tß'
a
of
filter and the main transmission line is of uniform impedance and can lxs modelled
128
5 Dual-ModeDR BandstopFilter
Direct-coupled
DR Bandstop
filter
[48]
from
An
inverter.
specifying a symmetexample coupling matrix
as a unity
filter with 22 dB return loss and two reflection zeros at ±j2.0107
degree
4th
rical
to give an out-of-band return loss of 30 dB is shown confirming the input/output
\/4
transmission
is
therefore,
a
uniform
simple
unity,
coupling
between the transmission line-to-resonator coupling points.
lit=
0
1.5109
1.5109
0
0.9118
0
0.9118
0
00
0
line would suffice
0001
0
1.3363
-0.7985
-0.7985
0
00
0.9118
0
0
0.98118
0
1.5109
1.3363
0
0,
10001.5109
j
For bandstop transfer functions where the reflection zeros are less than the filter
degree, a second solution is provided by performing
the synthesis technique on
The
dual
the
dual
above.
network is established
coupling
matrix
provided
the
of
by multiplying
the reflection numerator polynomials by -1, in effect adding unity
inverters at the input and output.
The coupling matrix is produced below showing
the removal of the negative M23 coupling, to give positive values for all couplings.
This is a unique solution to cross-coupled designs and removes the need for electric
for both solutions is shown
frequency
for
The
response
coupling.
negative
probes
in figure 5.42.
0
1.5109
0
0
0
1
1.5109
0
0.9118
0
0.9465
0
0
0.9118
0
0.7985
0
0
0
0
0.7985
0
0.9118
0
0
0.9465
0
0.98118
0
1.5109
1
0
0
0
1.5109
0
The coupling routing diagram for this matrix is shown in fi gure 5.43. The dual-
129
5 Dual-Mode DR Bandstop Filter
Direct-coupled DR bandstop filter
0
0
-10
-10
-20
-20
-30
-30
-40
-40
-50
-50
-nn
1.12
_an
1.18"
Co
U)
Figure
1.13
1.14
1.15
Frequency GHz
1.16
1.17
5.42: Frequency response of direct-coupled
(4-2) bandstop filter
described,
is
bandstop
filter,
dielectric
to
perfectly
already
suitable
realise
mode
this coupling matrix.
A diagram of the possible realisation depicts the coupling
figure
between
5.44.
the
cross-couplings
each
othogonal
required,
mode
and
paths
One should note that for practical realisation the bottom dielectric puck is now
fixed to the top of its respective cavity, thus, a low permittivity
dielectric support
is
have
filter
The
be
to
to
the
the specifications
assumed
mount
required
puck.
will
in table 5.6.
*
11.5109
1.51091
0.9465
M..= 01
10.9118
0.91181
0.7985
Figure
[45]
5.43: Coupling routing diagram of a direct-coupled
(4-2) handstop filter.
The dimensions of the cavity and coaxial line and dielectric puck were identical to
those from the previous design. To convert between the ccoupling matrix
bandwidth
and coupling
values
for each coupling in the physical
model, the coupling
5 Dual-Mode
DR Bandstop
130
Filter
Direct-coupled
DR bandstop filter
4A
4ß
4
C'
L-
M.:
-ý®
M
rlý
yý_L
x
Bc
Figure 5.44: Configuration
bandstop filter
direct-coupled
dual
HEE>>
mode
of
(4-2) dielectric
[47],
from,
is
calculated
coefficient
Ow
k",j = 111,
j
WO
(5.13)
k;;
is
Mij
from
the
the
the coupling matrix.
coupling
value
coefficiant
and
where
Intra-cavity
couplings are now required from the coupling matrix and mode cou-
disks
tuning
were used in the simulations.
pling
The coupling can be controlled
by the physical dimensions of the disk such as the thickness and diameter but
its position from the dielectric puck will cause the most variation.
An eigenmode
solver can easily compute the coupling coefficients within the dual-mode resonator
[45],
cavity using,
131
5 Dual-Mode DR Bandstop Filter
Direct-coupled DR bandstop filter
Filter Specifications
Centre frequency
1.15 GHz
Return loss (LR)
22 dB
Stopband bandwidth
5 MHz
Insertion loss (LA)
30 dB
Reflection zeros out-of-band 30 dB lobe levels f j2.0107
Table 5.6: Filter specification for 4th degree direct-coupled bandstop filter
f2-fl
=
(5.14)
f2
be
to
irises
inter-cavity
placed
couple modes of the
the
may
coupligs,
To realise
Simulations
for
the
between
two
the
coupling
coefficavities.
polarisation
same
In
figure
the
5.45.
to
iris
coupling
order
calculate
performed,
were
an
of
cient
[45]
has
been
in
The
described
DRs,
the
technique
the
used.
resonant
between
frequenciesfe and f,,,, are calculated by using a perfect electric or magnetic symbetween
find
inter-cavity
the
iris
to
in
the
the
coupling
middle of
metry plane
frone
found
the
is
The
well-known
equation,
coupling
coefficient
modes.
fee - fmg
k= f +f
e2
(5.15)
m2
from
loading
the irises shifting the rescaused
effects
This cross-coupling approach
To
increase
frequency,
frequency.
below
the
the
frequency
centre
resonant
onant
30.5
height
from
bottom
37
to
the
top
mm
was
mm
and
reduced
cavity
cavity
the
height was reduced to 28.37 mm. The optimisation process began by observdimensions
the
top
such that each
coupling element
ing the
cavity and adjusting
for
bandwidth.
The
lengths
irises
from
the
the
correct
calculated
were
produced
figure 5.45 and for K12 = K34 = 0.00246, slot widths of 1.26 inm were required
for irises of length 30 mm and thickness 20 mm. From these initial dimensions,
it was possible to draw an initial model in HFSS and after lengthy fine tuning
involving adjusting positions of tuning disks and heights of both cavities, the fifigures
in
5.46
5.47
model
and
response
simulation
providing
shown
and
are
nal
5 Dual-Mode
DR Bandstop
8
132
Filter
Direct-coupled
DR bandstop filter
x10;
7
6
Y
C5
Ü4
a
C
ä3
2
1
0
0.5
1
2
1.5
Iris Width mm
2.5
3
length
iris
3 cm and
with
width
of
of coupling coefficient
Figure 5.45: Variation
thickness 2 cm
Dielectric
Puck
Metal Coaxial
Line
Aluminium
Tuning
Hollow
Cavities
Screws
Croce-Iris
ý-'
Z
y--ý,
X
Figure 5.46: HFSS model of optimised direct-coupled
filter
stop
HEE>> dual-mode band-
ideal
to
the
Thus,
HEE1I
dual-rnode bandstop
the
comparison
good
response.
a
demonstrates
the principle of the coupling matrix synthesis apreadily
resonator
133
5 Dual-Mode DR Bandstop Filter
direct-coupled
the
to
proach
Direct-coupled DR bandstop filter
bandstop filter.
1oF..... ... .:. _
...........
H....:..
ý..ý.. ;...
:............:......
1.1
..................:.....
.. ý...........
I
f.
..
.40
12
1113
.... . ...........
..........
ýý.. ý: N f.. y...:.
... .....:...........:....
1'14
1.15
Frequency GHz
... 1.10
1.16
i-30
.:...........
........,.
to note that the same structure
form
direct-coupled
the
of
cul-de-sac
matrix.
m
v
N
N
.
-60
1.18
1.17
Figure 5.47: Simulated response of optimised direct-coupled
bandstop filter
It is interesting
1-20
HEE1I dual-irrode
may also be used to realise a
Bandstop filter.
By considering an example
[48], and associated coupling paths, figure 5.48, the same couplings can
he realised in the same structure, described above, for the original direct-coupled
form, figure 5.44.
This shows the flexibilty
dual-mode
the
of
novel
bandstol)
in
their
as
mono-mode
an
resonators
overhaul
realised resonator
requires
resonator
between
direct-coupled
the
two
structure
coupling
0
1.5497
1.5497 0.5155
1ý1=
forms, figures 2.13 and 2.11.
0
0
01
1.2902
0
1.28008
0
00
0
1.2902
-0.0503
0
0
0
0
0.9465
0
1
0
0
0
0.4222
0
0.4222
-0.2057
1.5497
0
1.5497
0
-1.0187
It is also clear that the cul-de-sac form brings an advantage for the dual-mode
bandstop filter in that no M23 cross coupling is required.
This ineans no anode
5 Dual-Mode
DR Bandstop
134
Filter
Direct-coupled
DR bandstop Jilte?
M=0.5155
M22= -0.0503
W=-1.0187
M=
-0.2057
1.29Ul
5.48: Coupling
Figure
[48]
filter.
stopp
routing
diagram
I. LUUö
of cul-de-sac
U. 4Lll
direct-coupled
(4-2) band-
0
0
-20
-20
-40
-a0
-60
-60
m
y
-80 L1.12
Figure
1.13
1.14
1.15
Frequency GHz
1.16
1.17
5.49: Frequency response of cul-de-sac direct-coupled
-80
1.18
(4-2) bandstop filter
filter
disk
bottom
is
in
tuning
the
the
cavity
required
of
reducing the
coupling
design.
The
frequency
ideal
is
the
this
response
of
of
matrix
shown in
complexity
figure 5.49 showing an asyn1n ctrical response. with centre frequency of 1.15 GHz
bandwidth,
MHz
5
and
can he acquired and is perfectly realisable in the dual-
bandstop
dielectric
filter.
resonator
mode
optimisation
Again, performing
criteria as per the former symmetrical
for the cul-de-sac configuration
similar design and
design, the HFSS simulation
was performed with the final optimised structure
figure
in
5.50.
Note
for
design,
improve
loss,
that
to
this
the
the cavity
shown
as
height was used to control the centre frequency of the higher resonant mode in
disk
for
thus,
tuning
this degenerate anode and as
no
cavity.
was required
each
stated, only one cross-coupling tuning disk in the whole structure was required.
The frequency response for the HFSS design, figure 5.51, is comparable to the ideal
5 Dual-Mode
DR Bandstop
135
Filter
Direct-coupled
DR bandstop filter
dielectric
bandstop
dual-mode
therefore,
the
resonator
resonator
novel
response,
is perfectly suitable to realise an asymmetrical cul-de-sac design.
Dielectric
Puck
Metal Coaxial
Line
Aluminium
Hollow Cavities
Z
Y.
i
j-.
__/
x
Tuning
Screws
7',
7
ýI
Eýy
1/
ZL
__
x
Figure
filter
yf
ýyx
-ý
5.50: HFSS model of optimised cul-de-sac HEE11 dual-niode
Bandstop
5 Dual-Mode
DR Bandstop
Filter
136
Direct-coupled
m
v
DR Bandstop filter
m
v
N
U)
Frequency
GHz
Figure 5.51: Simulated response of optimised cul-de-sac HEE11 dual-mode bandfilter
stop
137
Chapter
6
Conclusions
This thesis describes mono- and dual-mode dielectric resonator bandstop filters
offering compact and miniaturised
solutions over convential
coaxial cavity or
filters are necessary in communication
bandstop
Bandstop
resonators.
waveguide
systems, particularly
with the ever-increasing congested radio spectrum, interfer-
between
transmitters
ence
high
harmonics
harmful
power
are
and receivers and
dielectric
fundamental
be
The
the
concept
revolves
around
suppressed.
and must
bandpass
have
filters
but
little
been
in
These
integrated
is
commonly
resonator.
known about their inclusion in bandstop filters.
A dielectric-loaded rectangular waveguide resonator is developed from classical
determine
frequency
Q
for
to
the
and
unloaded
resonant
a cavity wavegequations
It
loading
is
dielectric,
the
through
the dicavity
apparent
with
uide resonator.
by
factor
dielectric
the
the
the
of
cavity
permittivity
reduce
of
a
of
mamensions
terial. In addition, the material properties of dielectric allow them to achieve high
Qs for comparable performance to cavity resonators, even after miniaturisation.
By metallising the four longer faces of a rectangular dielectric resonator, a coinis
pact resonator achieved and observation of the resonant modes indicate TEloa
is the fundamental mode. To create the bandstop characteristic, the rectangular
is
resonator coupled to a coaxial transmission line achieving narrow bandwidths.
It has been demonstrated that the compact resonator allows A/4 transmission line
separations avoiding unwanted spurious inter-resonator coupling. An unloaded Q
138
6 Conclusions
for
less
ideal
miniaturisa2300
where
applications
stringent
performance
offers
of
dielectric
filters
for
Spurious
key
is
the
are typically
many
aim.
performance
tion
poor and require modification
to the resonator structure.
here allowed a spurious free bandwidth
The technology shown
MHz
650
allowing the ease of these resof
Chebyshev
A
degree
band4th
broadband
be
in
implemented
to
systems.
onators
but
fabrication
bandwidth
designed
techniques
1%
filter
poor
achieving
was
stop
have incurred losses in the final filter desgin, notably poor metallisation
of the
dielectric resonator. The drawback of this resonator is the narrowband coupling
is unsuitable for applications requiring large bandwidths.
This is the compromise
for high Q materials where E-fields are mostly concentrated
for
fields
external coupling.
tric and only magnetic
are allowed
dieletric-loaded
a novel coaxial
developed.
was
resonator
within
the dielec-
To counter this,
Investigations
of this
dB
bandwidths
3
Q
2670
have
coupling
and
of
oberved an unloaded
resonator
MHz
200
are achievable, therefore, multi-section
of
bandwidth
designs can provide superior
designs at higher frequencies.
The second area of contribution
is the novel dual-mode dielectric-loaded
filter operating in the HEE11 mode. Due to symmetrical
the
typically
allow
onators
bandstop
geometries, these res-
higher order dual degenerate hybrid modes to resonate
half
frequency
the
the
therefore,
the
within
only
number of cavities
cavity,
same
at
The
in
to
compared
mono-mode
resonant
modes
resonators.
a cylinare required
drical dielectric puck were observed and for an assumed aspect ratio dielectric
HEE11
first
in
the
the
mode
a suspended structure.
was
spurious
puck size,
forcing the puck to the base, the HEEII became the fundamental
integration
ease of
in communication
By
mode allowing
The
drawback
is
to
this
unloaded
systems.
Q decreases due to metallic contact with one side of the puck but an unloaded Q
The
bandstop
9000
achieved.
was
still
response was achieved through magnetic
of
coupling to coupling posts attached to a coaxial transmission line. An experimental cavity was designed highlighting
complexities
to bend the transmission
line
to produce the required coupling separations between the transmission line and
orthogonal modes of the puck. Simulated and measured responses demonstrated
139
6 Conclusions
Future Work
the principle of the resonator and a 4th degree filter was designed. The response
dB
bandwidth
3
showed
design
from
4.3 MHz
improved
the
cavity
single
was
over
to 16.3 MHz. The main drawback to this filter was the poor spurious performance,
however, it was shown this could be improved by physically removing segments
due
DR
The
to
to the
the
a
gave
rise
rejection
puck.
measured
zero
response
of
length
of transmission
extra
line separation between the middle two resonators
but it is proposed future designs should reduce the radii of the cavity walls.
The dual-mode dielectric bandstop resonator was perfectly suitable to realise
direct-coupled bandstop filters. The benefits of this class of filter are the coubetween
direct
the source and
technique
coupling
allows
pling matrix synthesis
load, bypassing the bandstop resonators. The coupling matrix demonstrated the
length
a/4
transmission
implying
a
single
of
only
source-load coupling was unity,
line was required. A full FEM simulation for the novel dual-mode bandstop filter
demonstrated the principle producing symmetrical rejection zeros on either side
of the stopband for greater selectivity. The coupling matrix synthesized a secby
dual-mode
bandstop
the
same
cul-de-sac
configuration
realised
ond
which was
filter with an improvement in the structure where a cross-coupling element was
not required compared to the former design. The principle was demonstrated in
a FEM simulation showing the advantage over mono-mode cavity filters where
the cavity positions must conform to the correct coupling paths. It has also been
for
that
direct-coupled bandstop filthe
technique
using
coupling
matrix
shown
ters, advanced filter functions involving prescribed rejection zeros for symmetrical
and asymmetrical responsesare easily realised by this novel filter.
6.1
Future
Work
The work presented in this thesis has proposed and developed the early development of miniaturised mono- and dual-mode bandstop filters employing dielectric
resonators. The promising results from these designs should be carried forward to
investigate their use in advanced filtering techniques. Foremost, it is imperative
140
6 Conclusions
that future work includes the fabrication
Future Work
direct-coupled
the
of
filters to confirm
their concepts and compare against simulated reponses to adjust for any repetitive
fabrication
be
Also,
interesting
it
that
errors
may occur.
would
direct-coupled
between
the
sults
to compare re-
bandstop filter and cul-de-sac form for the same
difference
in
to
the
performance,
appreciate
specifications
for example, when a
(4-2)
is
in
the
the
second cavity of
not required
cul-demode coupling screw
The
direct-coupled
form.
in
resonators
sac
filters can consist of mono- dual- or
higher order modes to create mixed mode bandstop filters to collectively improve
the spurious performance.
Lossy filter techniques should also be investigated for
the dual-mode bandstop resonator as it allows the realisation of lossy filters with
ideal lossless transmission and reflection response. This technique allows further
miniaturisation
be
bandstop
low
Q
dielectric
would
resonators
required
as only
for ideal responses.
For these 3D structures, FEM simulations can be time consuming, especially during the optimisation
process where a huge number of iterations
are required to
tune the variables to the required response. Computer aided techniques that can
be
followed
3D
should
geometries
such as
readily optimise circuit elements with
space-mapping optimization,
pling matrix
[83]. Also, a computer program to perform the cou-
synthesis technique should be written
to readily produce element
filtering
Chebyshev
for
functions
filter syninvolving
advanced
generalised
values
thesis.
141
Appendix
A
Conferences
Publications
and
R. Chan, I. C. Hunter, "Dielectric resonator bandstop filters, " Filtronic
ing Symposium, September 2006
Engineer-
142
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"
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