EE2003
Circuit Theory
Chapter 19
Two-Port Networks
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1
Two Port Networks
Chapter 19
19.1
19.2
19.3
19.4
19.5
Introduction
Impedance parameters z
Admittance parameters y
Hybrid parameters h
Transmission parameters T
2
19.1 Introduction (1)
What is a port?
It is a pair of terminals through
which a current may enter or
leave a network.
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19.1 Introduction (2)
One port or two
terminal circuit
Two port or four
terminal circuit
• It is an electrical
network with two
separate ports for
input and output.
• No independent
sources.
4
19.2 Impedance parameters (1)
Assume no independent source in the network
V1  z11I1  z12I 2
V2  z 21I1  z 22I 2
V1   z11 z12   I1 
V    z z   I   z 
 2   21 22   2 
 I1 
I 
 2
where the z terms are called the impedance parameters,
or simply z parameters, and have units of ohms.
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19.2 Impedance parameters (2)
z11 
V1
I1
and
z 21 
I 2 0
V2
I1
I 2 0
z11 = Open-circuit input
impedance
z21 = Open-circuit transfer
impedance from port 1 to
port 2
z12 
V1
I2
and
I1  0
z 22 
V2
I2
z12 = Open-circuit transfer
impedance from port 2 to
port 1
z22 = Open-circuit output
impedance
I1  0
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19.2 Impedance parameters (2a)
z11 
z12 
V1
I1
V1
I2
and
z 21 
I 2 0
and
I1  0
z 22 
V2
I1
I 2 0
V2
I2
I1  0
•When z11 = z22, the two-port
network is said to be symmetrical.
•When the two-port network is
linear and has no dependent
sources, the transfer impedances
are equal (z12 = z21), and the twoport is said to be reciprocal.
7
19.2 Impedance parameters (3)
Example 1
Determine the Z-parameters of the following circuit.
I1
V1
60 40
Answer: z  


40 70
I2
z11 
V2
z12 
V1
I1
V1
I2
and
z 21 
I 2 0
and
I1  0
z 22 
V2
I1
I 2 0
V2
I2
I1  0
 z11 z12 
z


z 21 z 22 
8
19.3 Admittance parameters (1)
Assume no independent source in the network
I1  y11V1  y12V2
I 2  y 21V1  y 22V2
I1   y11 y12  V1 
V1 
I    y y  V   y V 
 2   21 22   2 
 2
where the y terms are called the admittance parameters,
or simply y parameters, and they have units of Siemens.
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19.3 Admittance parameters (2)
y11 
I1
V1
and
y 21 
V2  0
I2
V1
V2  0
y11 = Short-circuit input
admittance
y21 = Short-circuit transfer
admittance from port 1 to
port 2
y12 
I1
V2
and
V1  0
y 22 
I2
V2
y12 = Short-circuit transfer
admittance from port 2 to
port 1
y22 = Short-circuit output
admittance
V1  0
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19.3 Admittance parameters (3)
Example 2
Determine the y-parameters of the following circuit.
I2
I1
y11 
V1
I1
V1
and
y 21 
V2  0
I2
V1
V2  0
I2
V2
V1  0
V2
y12 
0.75  0.5 
S

 0.5 0.625
Answer: y  

I1
V2
and
V1  0
y 22 
 y11 y12 
y
S

 y 21 y 22 
11
19.3 Admittance parameters (4)
Example 3
Determine the y-parameters of the following circuit.
I1  y11V1  y12V2
I1=i
V1
 0.15  0.05
y

Answer:
 0.25 0.25  S


I 2  y 21V1  y 22V2
I2
Apply KVL
V2
V1  8I1  2(I1  I 2 )
V2  4(2i  I 2 )  2(I1  I 2 )
I1  0.15V1  0.05V2
I 2  0.25V1  0.25V2
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19.4 Hybrid parameters (1)
Assume no independent source in the network
V1  h11I1  h12V2
I 2  h 21I1  h 22V2
V1   h11 h12  I1 
I1 
 h   
I   h



 2   21 h 22  V2 
V2 
where the h terms are called the impedance parameters, or
simply h parameters, and each parameter has different units,
refer above.
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19.4 Hybrid parameters (2)
Assume no independent source in the network
V
h 11  1
I1
I
h 21  2
I1
V2  0
V2  0
h11= short-circuit
input impedance ()
V1
h12 
V2
H2 = short-circuit
forward current gain
h 22 
I2
V2
I1  0
I1  0
H12 = open-circuit
reverse voltage-gain
H22 = open-circuit
output admittance (S)
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19.4 Hybrid parameters (3)
Example 4
Determine the h-parameters of the following circuit.
I1
I2
V1
I1
h11 
V1
V2
h12 
4Ω  23 

Answer: h 
 2
1 
9 S
 3
V1
V2
and
h 21 
V2  0
and
I1  0
h 22 
I2
I1
V2  0
I2
V2
I1  0
h11Ω h12 
h

h
h
S
22 
 21
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19.5 Transmission parameters (1)
Assume no
independent source in
the network
V1  AV2  BI 2
I1  CV2  DI 2
V1  A B V2 
V2 
I    C D  I   T  I 
  2
1 
 2
where the T terms are called the transmission parameters,
or simply T or ABCD parameters, and each parameter has
different units.
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19.5 Transmission parameters (2)
V
A 1
V2
I
C 1
V2
A=open-circuit
voltage ratio
I2 0
I 2 0
C= open-circuit
transfer admittance
(S)
V1
B
I2
D
I1
I2
V2  0
B= negative shortcircuit transfer
impedance ()
V2  0
D=negative shortcircuit current ratio
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19.5 Transmission parameters (3)
Example 5
Determine the T-parameters of the following circuit.
V1  AV2  BI 2
I1  CV2  DI 2
V1
V2
Apply KVL
V1  10I1  20(I1  I 2 )
V2  3I1  20(I1  I 2 )
Answer:
 1.765 15.294Ω 
T

0.059S 1.176 
30
260
V2 
I2
17
17
1
20
I1  V2  I 2
17
17
V1 
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19.5 Transmission parameters (4)
Example 6
The ABCD parameters of the two-port network below are
 4
T= 
0.1S
20Ω 
2 

The output port is connected to
a variable load for maximum
power transfer. Find RL and the
maximum power transferred.
I1
V1
Answer: VTH = 10V V; RL = 8; Pm = 3.125W.
I2
V2
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