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TWO-PORT NETWORK
TKT 419/3Sem 1 Sidang Akademik 2010/2011
Lecturer: Pn. Wan Nur Suryani Firuz Bt Wan Ariffin (012-4820815)
TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships among two-port
parametersAnalysis of terminated two-port
circuitInterconnected two-port circuits
TERMINAL EQUATIONS
s -d o m ain
c ir c u it
1V
2V
1I2I
s-domain two-port basic building block
Terminal equations relationships1st Relationship:
2221212
2121111
IzIzVIzIzV
2nd Relationship:
2221212
2121111
VyVyIVyVyI
3rd Relationship:
2222211
2122111
IaVaIIaVaV
4th Relationship:
1221212
1121112
IbVbIIbVbV
5th Relationship:
2221212
2121111
VhIhIVhIhV
6th Relationship:
2221212
2121111
IgVgVIgVgI
TWO PORT NETWORK:
Terminal equationsTwo-port parametersRelationships between
parametersAnalysis of terminated two-port
circuitInterconnected two-port circuits
IMPEDANCE PARAMETERS
z parameters
02
222
01
221
02
112
01
111
12
12
II
II
IVz
IVz
IVz
IVz
2221212
2121111
IzIzVIzIzV
ADMITTANCE PARAMETERSy parameters
SVIyS
VIy
SVIyS
VIy
VV
VV
02
222
01
221
02
112
01
111
12
12
2221212
2121111
VyVyIVyVyI
a parameters
02
122
02
121
02
112
02
111
22
22
VI
VI
IIaS
VIa
IVa
VVa
b parameters
01
222
01
221
01
212
01
211
21
11
VI
VI
IIbS
VIb
IVb
VVb
a and b parameters are called transmission parameters
HYBRID PARAMETERSh parameters
SVIh
IIh
VVh
IVh
IV
IV
02
222
01
221
02
112
01
111
12
12
INVERSE HYBRID PARAMETERSg parameters
02
222
01
221
02
112
01
111
12
12
VI
VI
IVg
VVg
IIgS
VIg
Example 1Find z parameter for the
below circuit:
1V
2V
1I 2I
20
5
15
Solutions:
When port 2 open-circuit, I2=0 so,
1040
)20(20
01
111
2IIVz
When I2=0, thus V2
112 75.0515
15 VVV
5.710/
75.0
1
1
01
221
2V
VIVz
I
Now, when I1=0,so
375.940
)25(15
02
222
1IIVz
When port 1 open-circuit, I1=0, so:
221 8.0205
20 VVV
375.9
22
VI
5.7375.9/
8.0
2
2
02
112
1V
VIVz
I
TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships between parameters
Analysis of terminated two-port circuit
Interconnected two-port circuits
RELATIONSHIPS BETWEEN PARAMETERS
yIy
yIy
yyyyyIyI
V
212122
2221
1211
222
121
1
yIy
yIy
yyyyIyIy
V
121211
2221
1211
221
111
2
Compare these two above equations:
yyz
yyz
yyz
yyz
1122
2121
1212
2211
Find z parameters as functions of a parameters
221
221
212
1 IaaI
aV
21221
22111
21
111 Ia
aaaI
aaV
Therefore,
21
2222
2121
2112
21
1111
1aaz
az
aaz
aaz
RECIPROCAL TWO-PORT CIRCUITS
If a two-port circuit is reciprocal, the following relationships exist among port parameters:
21122112
21122211
21122211
21122112
11
gghhbbbbbaaaaayyzz
Symmetric of a reciprocal two-port circuitsFollowing relationships exist among
port parameters:
11
21122211
21122211
22112211
22112211
ggggghhhhhbbaayyzz
Example of symmetric two-port circuits
Z a
Z b
Z a
1V
2V
1I 2ISymmetric tee
Symmetric pi
Z b
1V
2V
1I 2I
Z a Z a
Symmetric bridge tee
Z b
1V
2V
1I2I
Z a Z a
Z c
Symmetric lattice
Z b
1V
2V
1I2I
Z a
Z a
Z b
TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships between
parametersAnalysis of terminated two-port circuit
Interconnected two-port circuits
ANALYSIS OF TERMINATED TWO-PORT CIRCUITS
T w o - p o r t m o d elo f a
n e tw o r k
1V
2V
1I2I
Z L
Z g
gV
6 characteristics of terminated two-port circuitInput impedance (Zin=V1/I1) or
admittance (Yin=I1/V1)Output current, I2
Thevenin voltage and impedance (ZTh, VTh) with respect to port 2
Current gain I2/I1
Voltage gain V2/V1
Voltage gain V2/Vg
6 characteristics in term of z parameters
4 parameter equations that describe the circuit:
L
gg
ZIV
ZIVVIzIzVIzIzV
22
11
2221212
2121111
1st characteristic (input impedance)
22
1212 zZ
IzIL
Lin Zz
zzzZ
22
211211
2nd characteristic (output current, I2)
g
g
ZzIzV
I
11
2121
21122211
212 ))(( zzZzZz
VzI
Lg
g
3rd characteristic (Thevenin voltage @ impedance)
11
12112102
2 zVzIzV
I
11
2102
2 zZzVVVg
gThI
Impedance Thevenin
gZzIzI
11
2121
gTh
VZzzzzZ
IV
g
11
211222
02
2
4th characteristic (current gain)
22
21
1
2
zZz
II
L
5th characteristic (voltage gain V2/V1)
LZVzIzV 2
221212
L
L
ZzVz
zVI
ZVzVIz
11
212
11
11
2121111
zZzZz
zzzzZzZz
VV
L
L
L
L
11
21
2112221111
21
1
2
6th characteristic (voltage gain V2/Vg)
222
11
21
11
212212 )(
VZz
ZzVz
ZzZVzzV
Lg
g
gL
g
g
gL ZzV
ZzZVzI
1111
2121 )(
21122211
212
))(( zzZzZzZz
VV
Lg
L
g
TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships between parametersAnalysis of terminated two-port
circuitInterconnected two-port circuits
INTERCONNECTED TWO-PORT CIRCUITS
Cascade connection
Two-port parameters
2222211
2122111
IaVaIIaVaV
2222211
2122111
IaVaIIaVaV
Interconnection (V’2=V’1 and I’2= -I’1)
1221211
1121111
IaVaIIaVaV
Relationship V’1 and I’1 with V2 and I2 in second circuit :
2222211
2122111
IaVaIIaVaV
2222212212212211211
2221212112211211111
)()()()(IaaaaVaaaaIIaaaaVaaaaV
2222122122
2122112121
2212121112
2112111111
aaaaaaaaaaaaaaaaaaaa
Reference book
Electric Circuits, James W. Nilsson and Susan A. Riedel, Prentice Hall