Lecture 27Two-port Network

Hung-yi Lee

Reference• Chapter 14.1, 14.2, 14.3 (out of the scope)

Two and Three Terminal Networks

Chapter 4.6 Chapter 2

Two-TerminalNetwork

i

Circuit

i

v

+

-Three-Terminal

Network

Circuit

Four Terminal Network

Input port

i1 = i3

Output port

i2 = i4

4 parameters: i1, v2, i2, v2 (E.g. Filter)

Two-Port Network

Is it a two-port network?

Is it a two-port network?

i1

i1

i2

i2

i11

i12

Note

Two-port network can be expressed by the phasor notation.

A two-port network contains no independent sources, although it may contain controlled sources.

i-v characteristics

2221212

2121111

IIV

IIV

zz

zz

2

1

2

1

II

VV

z

2221

1211

zzzz

z

Z parameters:

Z parameters2221212

2121111

IIV

IIV

zz

zz

Superposition Principle:Any current (or voltage) for an element is the weighted sum of the voltage (or current) of the sources.

Z parameters• How to find the Z parameters?

2221212

2121111

IIV

IIV

zz

zz

Set 0I1 2112 IVz

1111 IVz

2222 IVz

1221 IVz0I2 Set

Z parameters – Example 14.1

2221212

2121111

IIV

IIV

zz

zz

Set 0I1

2112 IVz

2222 IVz sCR 1R||

sCsC

12R1RR

12sCRRsCR 2

21 I

12RR

RV

sC

sC12RR 2

1R2R 2

sCsC

Z parameters – Example 14.1

2221212

2121111

IIV

IIV

zz

zz

Set 0I2

22z 12sCRRsCR 2

21z12z 1R2R 2

sCsC

11z

Find z11 and z21……

symmetric

Equivalent Two Port Network

2221212

2121111

IIV

IIV

zz

zz

Two Impedances, Two controlled sources

Three Impedances, One controlled source

Equivalent Two Port Network• Tee Network

Set 0I1 2112 IVz

1111 IVz

2222 IVz

1221 IVz0I2 Set

2221

1211

zzzz

z

cZ

cZca ZZ

cb ZZ

cbc

cca

ZZZ

zZ

ZZ ReciprocalNetwork

Equivalent Two Port Network• Tee Network

• Reciprocal Network

cbc

cca

ZZZ

zZ

ZZ

22

11

zzzz

zzz 11

z

zz 22

Equivalent Two Port Network

2221212

2121111

IIV

IIV

zz

zz

112212221122

2121111

IIIV

IIV

zzzz

zz

12z

1211 zz 1222 zz

11221 Izz

Other kinds of Parameters

2

1

2

1

II

VV

z

Z parameters:

2

1

2

1

VV

II

y

y parameters:

1 zy

The y parameters does not always exist.

[z] is not always invertible.

6 kinds of Parameters

2

1

2

1

II

VV

z

z parameters:

2

1

2

1

VV

II

y

y parameters:

2

1

2

1

VI

IV

h

h parameters:

2

1

2

1

IV

VI

g

g parameters:

2

2

1

1

IV

IV

T

T parameters:

1

1

2

2

IV

IV

t

t parameters:

42C

Be careful!

T/t Parameters• T/t for transmission

For T Parameters

For t Parameters

2

2

1

1

IV

IV

T

1

1

2

2

IV

IV

t

2I 1I

Connecting the Two-port Networks• Parallel Connection:

• Series Connection:

• Cascade Connection:

Parallel Connection

2

1

2

1

VV

yII

aa

a ay1V

2V

1aI 2aI

2

1

2

1

VV

yII

bb

b by1V

2V

1bI 2bI

Parallel Connection

ay

1V

2V

1aI 2aI

by

1bI 2bI

2

1

2

1

VV

yII

aa

a

2

1

2

1

VV

yII

bb

b

b

b

a

a

II

II

II

2

1

2

1

2

1

bapar yyy

2

1

2

1 VV

yII

par

1I 2I

2

1

VV

yy ba

Parallel Connection - Note

bapar yyy

V10

5V

A0

5.2

5.2

10

5

5.2

Parallel two two-port network can break the port condition

1V

1V

2V

2V

A0

A2 A2

Series Connection

2

1

2

1

II

VV

aa

a z az1aV

2aV

1I 2I

2

1

2

1

II

bb

b zVV bz1bV

2bV

1I 2I

Series Connection

2

1

2

1

II

VV

aa

a z

az1aV

2aV

1I 2I

2

1

2

1

II

bb

b zVV

bz1bV

2bV

1I 2I1V

2V

baser zzz

2

1

II

zz ba

b

b

a

a

VV

VV

VV

2

1

2

1

2

1

Not always true because parallel connection may also break the port condition

Cascade connection

The overall T parameters equals the product of the individual T parameters.

2

2

1

1

IV

TTIV

ba

2

2

1

1

IV

TIV

bb

b

a

aa IV

TIV

2

2

1

1

2

2

IV

T cas

Cascade connection

inV outV

11

1

1

1

V

V

sCR

sC

in

x

22

2

1

1

VsC

R

sCV

x

out

xV

x

out

in

x

in

out

VV

VV

VV

21212

212211 RRR11

V

V

RCCsCRCCsin

out

Cascade connection

inV outV

aT

out

outba

in

in

IV

TTIV

bT

inI 0I out

0DCBA

DCBA outV

out

out

VV

CA

DCBA

out

out

VDCVBA

CACA

CBAAin

out

1VV

21212

212211 RRR11

VV

RCCsCRCCsin

out

Cascade connection

1V

2V

1I 2I

2

2

1

1

IV

IV

T

2

2

IV

DCBA

221

221

IVI

IVV

DC

BA

0I2 2

1

VV

A1

11

11RsCsC

1R11 sC 12

1

VI

C sC

0V2

2

1

IV

B 1R2

1

II

D 1

Cascade connection

inV outV

aT bT

inI 0I out

CBAAin

out

1VV

21212

212211 RRR11

VV

RCCsCRCCsin

out

11R

DCBA

1

111

sCRsC

T a

1

1RDCBA

2

222

sCRsC

T b

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Acknowledgement• 感謝 張桓誠 (b02)• 上課時指出投影片的錯誤

Three Terminal to Two Port