Transcript Chap: 6 TWO PORT NETWORK

CHAPTER 6
TWO PORT NETWORKS
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OBJECTIVES
• To understand about two – port networks
and its functions.
• To understand the different between zparameter, y-parameter, ABCD- parameter
and terminated two port networks.
• To investigate and analysis the behavior of
two – port networks.
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SUB - TOPICS
 6-1 Z – PARAMETER
 6-2 Y – PARAMETER
 6-3 ABCD – PARAMETER
 6-4 TERMINATED TWO PORT
NETWORKS
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TWO – PORT NETWORKS
• A pair of terminals through which a current may enter
or leave a network is known as a port.
• Two terminal devices or elements (such as resistors,
capacitors, and inductors) results in one – port
network.
• Most of the circuits we have dealt with so far are two
– terminal or one – port circuits. (Fig. a)
• A two – port network is an electrical network with two
separate ports for input and output.
• It has two terminal pairs acting as access points. The
current entering one terminal of a pair leaves the
other terminal in the pair. (Fig. b)
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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.
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6-1 Z – PARAMETER
• Z – parameter also called as impedance parameter and
the units is ohm (Ω)
• The “black box” is replace with Z-parameter is as
shown below.
I
I1
+
V1
-
V1  z11I1  z12I 2
V2  z 21I1  z 22I 2
2
Z11
Z12
Z21
Z22
+
V2
-
V1   z11 z12   I1 
V    z z   I   z 
 2   21 22   2 
where the z terms are called the impedance parameters, or
simply z parameters, and have units of ohms.
 I1 
I 
 2
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V1
z11 
I1
and
I 2 0
V2
z 21 
I1
I 2 0
z11 = Open-circuit input impedance
z21 = Open-circuit transfer
impedance from port 1 to port 2
V1
z12 
I2
and
I1  0
V2
z 22 
I2
I1  0
z12 = Open-circuit transfer
impedance from port 2 to port 1
z22 = Open-circuit output
impedance
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Example 1
Find the Z – parameter of the circuit below.
+
V1
I2
I1
+
240Ω
120Ω
_
V2
_
40Ω
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Solution
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Example 2
Find the Z – parameter of the circuit below
I1
+
V1
_
2Ω
10Ω
j4Ω
+
_
I2
+
10I2
-j20Ω
V2
_
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Solution
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6-2 Y - PARAMETER
• Y – parameter also called admittance parameter and
the units is siemens (S).
• The “black box” that we want to replace with the Yparameter is shown below.
I2
I1
+
V1
-
I1  y11V1  y12V2
I 2  y 21V1  y 22V2
Y11
Y12
Y21
Y22
+
V2
-
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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I1
y11 
V1
and
V2  0
I2
y 21 
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
V1  0
y12 = Short-circuit transfer
admittance from port 2 to port 1
y22 = Short-circuit output
admittance
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Example 3
Find the Y – parameter of the circuit shown
below.
+
V1
_
I1
5Ω
I2
+
20Ω
15Ω
V2
_
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Solution
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Example 4
Find the Y – parameters of the circuit
shown.
I1
+
V1
_
2Ω
10Ω
j4Ω
+
_
I2
+
10I2
-j20Ω
V2
_
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Solution
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6-3 T (ABCD) PARAMETER
• T – parameter or also ABCD – parameter is a another
set of parameters relates the variables at the input
port to those at the output port.
• T – parameter also called transmission parameters
because this parameter are useful in the analysis of
transmission lines because they express sending – end
variables (V1 and I1) in terms of the receiving – end
variables (V2 and -I2).
• The “black box” that we want to replace with T –
parameter is as shown below.
I2
I1
+
V1
-
A11
B12
C21
D22
+
V2
-
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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.
V
A 1
V2
I1
C
V2
A=open-circuit
voltage ratio
I2 0
I 2 0
C= open-circuit
transfer admittance
(S)
V
B 1
I2
D
I1
I2
V2  0
B= negative shortcircuit transfer
impedance ()
V2  0
D=negative shortcircuit current ratio
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Example 5
Find the ABCD – parameter of the circuit
shown below.
I1
2Ω
4Ω
+
V1
_
I2
+
10Ω
V2
_
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Solution
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6-4 TERMINATED TWO –
PORT NETWORKS
• In typical application of two port network, the circuit
is driven at port 1 and loaded at port 2.
• Figure below shows the typical terminated 2 port
model.
Zg
Vg
+

I2
I1
+
V1
-
Two – port
network
+
V2
-
ZL
Terminated two-port parameter can be implement to Z-parameter,
Y-parameter and ABCD-parameter.
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• Zg represents the internal impedance of the source and
Vg is the internal voltage of the source and ZL is the
load impedance.
• There are a few characteristics of the terminated twoport network and some of them are;
V1

I1
i)
input impedance, Zi 
ii)
output impedance, Zo 
V2

I2
I2
iii) current gain, A i 
I1
iv) voltage gain, A v 
V2
V1
v) overall voltage gain, A g 
V2
Vg
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•The derivation of any one of the desired expression
involves the algebraic manipulation of the two – port
equation. The equation are:
1) the two-port parameter equation either Z or Y or ABCD.
For example, Z-parameter, V1  Z11I1  Z12I 2 .......(1)
V2  Z 21I1  Z 22I 2 .......(2)
2) KVL at input,
V1  Vg  I1Zg .......(3)
3) KVL at the output, V  I Z .......(4)
2
2 L
•From these equations, all the characteristic can be obtained.
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Example 6
For the two-port shown below, obtain the suitable value of
Rs such that maximum power is available at the input
terminal. The Z-parameter of the two-port network is given
as
 Z11
Z
 21
Z12  6


Z 22  4
2
4
With Rs = 5Ω,what would be the value of
Rs
Vs
+

I2
I1
+
V1
-
V2
Vs
Z
+
V2
-
4Ω
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Solution
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Example 7
The ABCD parameter of two – port network shown below
are.
 4
0.1S

20 
2 
The output port is connected to a variable load for a
maximum power transfer. Find RL and the maximum power
transferred.
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Solution
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