Chapter 1 - Two-port Circuits
Transcript of Chapter 1 - Two-port Circuits
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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)
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TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships among two-port
parametersAnalysis of terminated two-port
circuitInterconnected two-port circuits
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TERMINAL EQUATIONS
s -d o m ain
c ir c u it
1V
2V
1I2I
s-domain two-port basic building block
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Terminal equations relationships1st Relationship:
2221212
2121111
IzIzVIzIzV
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2nd Relationship:
2221212
2121111
VyVyIVyVyI
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3rd Relationship:
2222211
2122111
IaVaIIaVaV
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4th Relationship:
1221212
1121112
IbVbIIbVbV
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5th Relationship:
2221212
2121111
VhIhIVhIhV
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6th Relationship:
2221212
2121111
IgVgVIgVgI
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TWO PORT NETWORK:
Terminal equationsTwo-port parametersRelationships between
parametersAnalysis of terminated two-port
circuitInterconnected two-port circuits
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IMPEDANCE PARAMETERS
z parameters
02
222
01
221
02
112
01
111
12
12
II
II
IVz
IVz
IVz
IVz
2221212
2121111
IzIzVIzIzV
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ADMITTANCE PARAMETERSy parameters
SVIyS
VIy
SVIyS
VIy
VV
VV
02
222
01
221
02
112
01
111
12
12
2221212
2121111
VyVyIVyVyI
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a parameters
02
122
02
121
02
112
02
111
22
22
VI
VI
IIaS
VIa
IVa
VVa
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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
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HYBRID PARAMETERSh parameters
SVIh
IIh
VVh
IVh
IV
IV
02
222
01
221
02
112
01
111
12
12
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INVERSE HYBRID PARAMETERSg parameters
02
222
01
221
02
112
01
111
12
12
VI
VI
IVg
VVg
IIgS
VIg
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Example 1Find z parameter for the
below circuit:
1V
2V
1I 2I
20
5
15
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Solutions:
When port 2 open-circuit, I2=0 so,
1040
)20(20
01
111
2IIVz
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When I2=0, thus V2
112 75.0515
15 VVV
5.710/
75.0
1
1
01
221
2V
VIVz
I
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Now, when I1=0,so
375.940
)25(15
02
222
1IIVz
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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
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TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships between parameters
Analysis of terminated two-port circuit
Interconnected two-port circuits
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RELATIONSHIPS BETWEEN PARAMETERS
yIy
yIy
yyyyyIyI
V
212122
2221
1211
222
121
1
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yIy
yIy
yyyyIyIy
V
121211
2221
1211
221
111
2
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Compare these two above equations:
yyz
yyz
yyz
yyz
1122
2121
1212
2211
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Find z parameters as functions of a parameters
221
221
212
1 IaaI
aV
21221
22111
21
111 Ia
aaaI
aaV
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Therefore,
21
2222
2121
2112
21
1111
1aaz
az
aaz
aaz
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RECIPROCAL TWO-PORT CIRCUITS
If a two-port circuit is reciprocal, the following relationships exist among port parameters:
21122112
21122211
21122211
21122112
11
gghhbbbbbaaaaayyzz
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Symmetric of a reciprocal two-port circuitsFollowing relationships exist among
port parameters:
11
21122211
21122211
22112211
22112211
ggggghhhhhbbaayyzz
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Example of symmetric two-port circuits
Z a
Z b
Z a
1V
2V
1I 2ISymmetric tee
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Symmetric pi
Z b
1V
2V
1I 2I
Z a Z a
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Symmetric bridge tee
Z b
1V
2V
1I2I
Z a Z a
Z c
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Symmetric lattice
Z b
1V
2V
1I2I
Z a
Z a
Z b
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TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships between
parametersAnalysis of terminated two-port circuit
Interconnected two-port circuits
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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
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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
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6 characteristics in term of z parameters
4 parameter equations that describe the circuit:
L
gg
ZIV
ZIVVIzIzVIzIzV
22
11
2221212
2121111
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1st characteristic (input impedance)
22
1212 zZ
IzIL
Lin Zz
zzzZ
22
211211
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2nd characteristic (output current, I2)
g
g
ZzIzV
I
11
2121
21122211
212 ))(( zzZzZz
VzI
Lg
g
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3rd characteristic (Thevenin voltage @ impedance)
11
12112102
2 zVzIzV
I
11
2102
2 zZzVVVg
gThI
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Impedance Thevenin
gZzIzI
11
2121
gTh
VZzzzzZ
IV
g
11
211222
02
2
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4th characteristic (current gain)
22
21
1
2
zZz
II
L
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5th characteristic (voltage gain V2/V1)
LZVzIzV 2
221212
L
L
ZzVz
zVI
ZVzVIz
11
212
11
11
2121111
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zZzZz
zzzzZzZz
VV
L
L
L
L
11
21
2112221111
21
1
2
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6th characteristic (voltage gain V2/Vg)
222
11
21
11
212212 )(
VZz
ZzVz
ZzZVzzV
Lg
g
gL
g
g
gL ZzV
ZzZVzI
1111
2121 )(
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21122211
212
))(( zzZzZzZz
VV
Lg
L
g
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TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships between parametersAnalysis of terminated two-port
circuitInterconnected two-port circuits
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INTERCONNECTED TWO-PORT CIRCUITS
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Cascade connection
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Two-port parameters
2222211
2122111
IaVaIIaVaV
2222211
2122111
IaVaIIaVaV
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Interconnection (V’2=V’1 and I’2= -I’1)
1221211
1121111
IaVaIIaVaV
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Relationship V’1 and I’1 with V2 and I2 in second circuit :
2222211
2122111
IaVaIIaVaV
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2222212212212211211
2221212112211211111
)()()()(IaaaaVaaaaIIaaaaVaaaaV
2222122122
2122112121
2212121112
2112111111
aaaaaaaaaaaaaaaaaaaa
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Reference book
Electric Circuits, James W. Nilsson and Susan A. Riedel, Prentice Hall