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Title: Two port
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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11

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
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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

14

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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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

19

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

-

J
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2 v3

v2
-

ECE 222

Two-Port Networks

Ver
...
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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11

24

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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1
...
McNames

Portland State University

ECE 222

Two-Port Networks

Ver
...
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