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Title: Two port
Description: For finding the parameters two port concept is used
Description: For finding the parameters two port concept is used
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Two-Port Networks
• Definitions
• Impedance Parameters
• Admittance Parameters
• Hybrid Parameters
• Transmission Parameters
• Cascaded Two-Port Networks
• Examples
• Applications
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McNames
Portland State University
ECE 222
Two-Port Networks
Ver
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11
2
Two-Port Networks: Definitions & Requirements
+
i1
i2
Two-Port
Network
v1
-
i'1
+
v2
i'2
-
• Two-port networks are used to describe the relationship between a
pair of terminals
• The analysis methods we will discuss require the following
conditions be met
1
...
No independent sources inside the network
3
...
i1 = i1 and i2 = i2
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McNames
Portland State University
ECE 222
Two-Port Networks
Ver
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4
Impedance Parameters
+
I1(s)
V1(s)
+
Two-Port
Network
-
V1 = z11 I1 + z12 I2
V2 = z21 I1 + z22 I2
V2(s)
I2(s)
-
V1
=
V2
z11
z21
z12
z22
I1
I2
• Suppose the currents and voltages can be measured
• Alternatively, if the circuit in the box is known, V1 and V2 can be
calculated based on circuit analysis
• Relationship can be written in terms of the impedance parameters
• We can also calculate the impedance parameters after making two
sets of measurements
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McNames
V1
I1
z21 =
I2 =0
Portland State University
ECE 222
V2
I1
I2 =0
Two-Port Networks
Ver
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11
6
Impedance Parameter Measurements Continued
+
+
Two-Port
Network
V1(s)
V2(s)
-
I2(s)
-
V1
V2
= z11 I1 + z12 I2
= z21 I1 + z22 I2
If the left port is an open circuit (I1 = 0), then we can easily solve for
the other two impedance parameters:
z12 =
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McNames
V1
=
I1
V2
=
I1
I2(s)
-
z12
I2 =0
ECE 222
V1
=
I2
I1 =0
z22
I2 =0
Portland State University
V2(s)
V2
=
I2
I1 =0
Two-Port Networks
Ver
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11
8
Impedance Parameter Equivalent
I1(s)
+
V1(s)
I2(s)
z11
z22
z12 I2
z21 I1
-
+
V2(s)
-
V1
V2
= z11 I1 + z12 I2
= z21 I1 + z22 I2
• Once we know what the impedance parameters are, we can model
the behavior of the two-port with an equivalent circuit
...
McNames
Portland State University
ECE 222
Two-Port Networks
Ver
...
11
9
Example 1: Impedance Parameters
200 Ω
+
40 Ω
I1
I2
800 Ω
+
500 Ω
V1
V2
1 kΩ
-
-
Find the z parameters of the circuit
...
McNames
Portland State University
ECE 222
Two-Port Networks
Ver
...
11
10
Example 1: Workspace
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For example, rewrite the defining equations in terms
of the voltages V1 and V2
...
McNames
Portland State University
ECE 222
Two-Port Networks
Ver
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11
12
Example 2: Workspace
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McNames
Portland State University
ECE 222
Two-Port Networks
Ver
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11
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Impedance & Admittance Parameters
I1(s)
I2(s)
+
V1(s)
+
Two-Port
Network
V2(s)
-
-
Impedance Parameters
V1 = z11 I1 + z12 I2
V2 = z21 I1 + z22 I2
V1
=
V2
z11
z21
z12
z22
I1
I2
Admittance Parameters
I1 = y11 V1 + y12 V2
I2 = y21 V1 + y22 V2
I1
=
I2
y11
y21
y12
y22
V1
V2
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McNames
Portland State University
ECE 222
Two-Port Networks
Ver
...
11
16
Transmission Parameters
I1(s)
I2(s)
+
+
Two-Port
Network
V1(s)
V2(s)
-
-
Transmission Parameters
V1 = a11 V2 − a12 I2
I1 = a21 V2 − a22 I2
V1
=
I1
a11
a21
b12
a22
b11
b21
b12
b22
V2
−I2
=A
V2
−I2
Inverse Transmission Parameters
V2 = b11 V1 − b12 I1
I2 = b21 V1 − b22 I1
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933)
• You should have a copy of this in your notes for the final
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1
...
Find the transmission parameters
...
5 cos(4000t + 30◦ ) A measured
I2
J
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25 cos(4000t + 150◦ ) A measured
Portland State University
ECE 222
Two-Port Networks
Ver
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11
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Example 3: Workspace
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2 v3
v2
-
Find the hybrid parameters for the circuit shown above
...
McNames
Portland State University
ECE 222
Two-Port Networks
Ver
...
11
21
Example 4: Workspace
800 Ω
i1
40 Ω
160 Ω
+
v3
-
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2 v3
v2
-
ECE 222
Two-Port Networks
Ver
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11
22
Example 4: Workspace Continued
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Find the transmission parameters
...
5 µA
= 10 V
I2
=
80 µA
I2
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b
b
Portland State University
b22
, a12 =
b
ECE 222
b12
, a21 =
b
b21
b
Two-Port Networks
, and
Ver
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Example 5: Workspace
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McNames
Portland State University
ECE 222
Two-Port Networks
Ver
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11
27
Example 6: Workspace Continued (1)
i1
v1(t)
R1
R3
v+(t)
R4
v-(t)
C1
i2
+
R2
v2(t)
-
C2
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McNames
Portland State University
ECE 222
Two-Port Networks
Ver
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11
29
Cascaded Two-Port Networks
I1(s)
+
V1(s)
-
I2A (s)
Two Port
Network
A
I1B (s)
+
+
V2A (s)
V1B (s)
-
-
I2(s)
Two Port
Network
B
+
V2(s)
-
• Two networks are cascaded when the output of one is the input
of the other
• Note that V2A = V1B and −I2A = I1B
• The transmission parameters take advantage of these properties
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McNames
I1B (s)
I2A (s)
a11
a21
=
a12
a22
V1B
I1B
A
+
+
V2A (s)
V1B (s)
-
I2(s)
-
V2A
−I2A
V1
=
I1
Portland State University
V1B
=
I1B
a11
a21
a11
a21
a12
a22
a12
a22
a11
a21
a12
a22
ECE 222
+
Two Port
Network
B
A
Two-Port Networks
V2(s)
-
B
V2
−I2
B
V2
−I2
Ver
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31
Cascaded Two-Port Networks Continued
I1(s)
+
V1(s)
-
I1B (s)
I2A (s)
Two Port
Network
A
+
+
V2A (s)
V1B (s)
-
I2(s)
-
+
Two Port
Network
B
V2(s)
-
The inverse transmission parameters are also convenient for cascaded
networks
...
McNames
A
V1B
−I1B
V2
=
I2
Portland State University
V2A
=
I2A
b11
b21
b12
b22
ECE 222
A
b11
b21
b12
b22
b11
b21
b12
b22
B
B
Two-Port Networks
V1
−I1
V1
−I1
Ver
...
11
32
Cascaded Systems: Two-Port Networks versus H(s)
I1(s)
+
V1(s)
-
I2A (s)
Two Port
Network
A
I1B (s)
+
+
V2A (s)
V1B (s)
-
I2(s)
-
Two Port
Network
B
+
V2(s)
-
• Two-ports and transfer functions H(s) are closely related
• H(s) only relates the input signal to the output signal
• Two-ports relate both voltages and currents at each port
• You cannot cascade H(s) unless the circuits are active
• Two-port networks have no such restriction
• Two-ports are used to design passive filters
• However, two-ports are more complicated than H(s)
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Title: Two port
Description: For finding the parameters two port concept is used
Description: For finding the parameters two port concept is used