Microstrip Filters for RF Microwave Application - ntuemc.twntuemc.tw/upload/file/201102171627422f589.pdf · Microstrip Filters for RF Microwave ... It is the purpose of this chapter

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.


� Network Variables

� Scattering Parameters

� Impedance and Admittance Parameters

� ABCD Parameters

� Transmission Line Networks

� Network Connections

� Symmetrical Network Analysis

� Equivalent and Dual Networks


Network Variables

)(1

)(1

)(

)(

)(

nn

on

nn

on

n

nnonnnn

on

nn

on

nn

baZ

VVZ

I

baZVVV

wavereflectedZ

Vb

waveincidentZ

Va

−=−=

+=+=

=

=

−+

−+

−

+

[ ] [ ]***

2

1Re2

1

)(2

1

)(2

1

nnnnnnn

non

on

nn

non

on

nn

bbaaIVP

IZZ

Vb

IZZ

Va

−=⋅=

−=

+=

Note that the voltage and current variables are complex

amplitudes when we consider sinusoidal quantities.


Scattering Parameters

n

n

on

on

a

b

ZV

ZV

V

VS === +

−

+

−


Scattering ParametersFor filter characterization, we may define two parameters:

where LA denotes the insertion loss between ports n and m and LR represents the

return loss at port n.

The definition of VSWR is

phase delay, defined by

group delay, defined by

express the reflection parameter

S11 in terms of the terminal impedance

Z01 and the so-called input impedance

power conservation condition


Scattering Parameters


Example


Impedance & Admittance

Parameters

j

iij

I

VZ =

j

iijV

IY =



Parameters


Example



Parameters


Example


ABCD Parameters

22

22

DC

BA

11

11

DC

BA

×

=

×

×

=

×

=

3

3

3

3

22

22

11

11

2

2

11

11

1

1

I

V

DC

BA

I

V

DC

BA

DC

BA

I

V

DC

BA

I

V


Some useful two-port networks

and their ABCD parameters


TRANSMISSION LINE

NETWORKS

Z02

lossless

an open circuit or a short circuit at one terminal of a two-port transmission line network


Network Connections

� Parallel

� Series


Network Connections

� Cascade


Network Parameter Conversion


Symmetrical Network Analysis






Example


Even and Odd Mode


4-port S-parameters


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


Multiport Networks

� Assume that an M1-port network N’ and an M2-port network N’’ connect each other at c

pairs of ports.

where

all the connections satisfy the relations


Multiport Networks

using

where

using


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.


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.


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

TTT

T

T

SS

SS

S

SSS

S

S

S

S

S

TT

TT

a

b

TT

TT

b

a


T parameter

⋅

⋅

=

⋅

=

⋅

=

y

y

yy

yy

xx

xx

x

x

y

y

yy

yy

y

y

x

x

xx

xx

x

x

a

b

TT

TT

TT

TT

b

a

a

b

TT

TT

b

a

a

b

TT

TT

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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Microstrip Filters for RF Microwave Application - ntuemc.twntuemc.tw/upload/file/201102171627422f589.pdf · Microstrip Filters for RF Microwave ... It is the purpose of this chapter