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Prof. T. L. Wu
Microstrip Filters for RF
Microwave Application
Instructor: Prof. Tzong-Lin Wu
National Taiwan University
Institute of Communications Engineering
EMC Lab
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Filter networks are used to select/reject or separate/combine signals at different
frequencies in a host of RF/microwave systems and equipment. Although the
physical realization of filters at RF/microwave frequencies may vary, the circuit
network topology is common to all.
it is useful to be able to describe the operation of a microwave network such as
a filter in terms of voltages, currents, and impedances in order to make optimum
use of low-frequency network concepts.
It is the purpose of this chapter to describe various network concepts and
provide equations that are useful for the analysis of filter networks.
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Network Variables
Scattering Parameters
Impedance and Admittance Parameters
ABCD Parameters
Transmission Line Networks
Network Connections
Symmetrical Network Analysis
Equivalent and Dual Networks
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Network Variables
)(1
)(1
)(
)(
)(
nn
on
nn
on
n
nnonnnn
on
nn
on
nn
ba Z
V V Z
I
ba Z V V V
wavereflected Z
V b
waveincident Z
V a
−=−=
+=+=
=
=
−+
−+
−
+
[ ] [ ]***
21Re
21
)(2
1
)(2
1
nnnnnnn
non
on
nn
non
on
nn
bbaa I V P
I Z Z
V b
I Z Z
V a
−=⋅=
−=
+=
Note that the voltage and current variables are complex
amplitudes when we consider sinusoidal quantities.
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Scattering Parameters
n
n
on
on
a
b
Z V
Z V
V
V S ===
+
−
+
−
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Scattering ParametersFor filter characterization, we may define two parameters:
whereLA
denotes the insertion loss between portsn
andm
andLR
represents thereturn loss at port n.
The definition of VSWR is
phase delay, defined by
group delay, defined by
express the reflection parameter
S 11 in terms of the terminal impedanceZ 01 and the so-called input impedance
power conservation condition
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Scattering Parameters
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Example
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Impedance & Admittance
Parameters
j
iij
I
V Z =
j
iij
V
I Y =
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Impedance & Admittance
Parameters
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Example
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Impedance & Admittance
Parameters
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Example
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
ABCD Parameters
22
22
DC
B A
11
11
DC
B A
×
=
×
×
=
×
=
3
3
3
3
22
22
11
11
2
2
11
11
1
1
I V
DC B A
I V
DC B A
DC B A
I V
DC B A
I V
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Some useful two-port networks
and their ABCD parameters
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
TRANSMISSION LINE
NETWORKS
Z02
lossless
an open circuit or a short circuit at one terminal of a two-port transmission line network
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Network Connections
Parallel
Series
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Network Connections
Cascade
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Network Parameter Conversion
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Symmetrical Network Analysis
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Symmetrical Network Analysis
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Symmetrical Network Analysis
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Example
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Even and Odd Mode
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
4-port S-parameters
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Multiport Networks
Networks that have more than two ports may be referred to as the multiport networks.
For a reciprocal network,
For lossless passive network
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Multiport Networks
Assume that anM 1-port network N’ and an M 2-port network N’’ connect each other at c
pairs of ports.
where
all the connections satisfy the relations
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Multiport Networks
using
where
using
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Equivalent and Dual NetworksTwo networks are said to be equivalent if the matrices of their corresponding network parameters are equal,
irrespective of the fact that the networks may differ greatly in their configurations and in the number of
elements possessed by each.
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
Equivalent and Dual Networks
In accordance with this definition, an inductance of x henries is dual to a capacitance of x
farads, a resistance of x ohms is dual to a conductance of x mhos, a short circuit is the
dual of an open circuit, a series connection is the dual of parallel connection, and so on.
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Microstrip Filters for RF Microwave Application Prof. T. L. Wu
T parameter
−
−
=
−
−
=
⋅
=
11
12
11
11
122122
11
21
2221
1211
21
221112
21
11
21
22
21
2221
1211
2
2
2221
1211
1
1
1,
1
T
T
T
T
T T T
T
T
S S
S S
S
S S S
S
S
S
S
S
T T
T T
a
b
T T
T T
b
a
Microstrip Filters for RF Microwave Application Prof. T. L. Wu
T parameter
⋅
⋅
=
⋅
=
⋅
=
y
y
y y
y y
x x
x x
x
x
y
y
y y
y y
y
y
x
x
x x
x x
x
x
a
b
T T
T T
T T
T T
b
a
a
b
T T
T T
b
a
a
b
T T
T T
b
a
2
2
2221
1211
2221
1211
1
1
2
2
2221
1211
1
1
2
2
2221
1211
1
1,
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