TWO PORT NETWORKS

1
CHAPTER 6

• TWO PORT NETWORKS

2
Chapter 62 PORT NETWORKS - DEFINATION

• WHAT IS PORT NETWORK ?
• It is a pair of terminals through which
• current may enter or leave a network.
• 2 terminal devices or elements (resistors,
  inductors or capacitors) results in one network
• 4 terminal or 2-port circuit involves op-amps,
  transistor and transformer.
• 2-port network is an electrical network with 2
  separate ports for input and output as shown in
  the figure a b

3
Chapter 6 2 PORTS NETWORKS- DEFINATION

• 2-port network can be defined as voltage-driven
  or current driven as shown below
• V1 z11I1 z12I2
• V2 z21I1 z22I2
• In Matrix form
• V1 z11 z12 I2
  I1
• V2 z
• z21 z22 I1
  

I2
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Chapter 6 2-PORTS NETWORK DEFINATION

• Z are called IMPEDANCE PARAMETERS OR Z PARAMETERS
• The z parameters are determined as below
• z11 V1 / I1 I2 0
• z12 V1 / I2 I1 0
• z21 V2 / I1 I2 0
• z22 V2 / I2 I1 0

5
Chapter 62-PORTS NETWORK DEFINATION

• The determination of z-parameters are shown
  below
• z12 and z21 are called transfer impedance.
• If z11 z22 , the 2-port network is symmetrical.
• If z12 z21 , the 2-port network is reciprocal.

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Chapter 6 2-PORT NETWORKS DEFINATION

• The T-equivalent circuit for reciprocal case (a)
  and general equivalent circuit (b) is shown
  below

7
Chapter 6 2-PORT NETWORKS z-parameters

• EXAMPLE 1
• Determine the z-parameters for the following
  circuit

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Chapter 6 2-PORT NETWORKS z-parameters

• SOLUTION FOR EXAMPLE 1
• 1. Apply voltage source, V1 for the input
  port and leave output port open as shown
• 2. Calculate z11
• z11 V1 / I1 (2040)I1/I1
• 60 ?
• 3. Calculate z12
• z21 V2 / I1 40 ?
• 4. to calculate z12 z22, apply voltage
  source to output port and leave input port open
• z12 V1 / I2 40I2 / I2 40?
• z22 V2 / I2 (3040)I2 / I2 70?
• 5. Thus, z-parameters are
• z 60 ? 40 ?
• 40 ? 70 ?

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Chapter 6 2-PORT NEWTORKS z-parameters

• EXERCISE 2 (Exercise Problem 19.1)
• 1. Find the z-parameter for the circuit shown
  below

10
Chapter 6PORT NETWORKS z-parameters

• Solution for EXERCISE 2
• 1.Apply voltage source or current source at
  input

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Chapter 6 2-PORT NETWORKS

• EXERCISE 2 (CONTINUED)
• Apply voltage source at output and leave
  input voltage open

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Chapter 6 2-port networks z-parameters

• SOLUTION (continued)
• 1.

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Chapter 6 2-port networks z-parameters

• EXERCISE 3
• Find the z-parameters for the circuit below

14
Chapter 6 2-port networks z-parameters

• EXERCISE 4
• Calculate I1 I2 for the 2-port network
  shown below

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Chapter 6 2-port networks Y parameters

• ADMITTANCE PARAMETERS
• Admittance is a reciprocal of the Impedance
• Y 1/Z
• In 2-port network, it is defined as
• I1 y11 y12 V1 y V1
• I2 y21 y22 V2
  V2

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Chapter 6 2-port networks Y Parameters

• The value of y-parameters are determined by

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Chapter 6 2-port networks Y Parameters

• The y-parameters are also called short- circuit
  admittance parameters
• 1. y11 short-circuit input admittance
• 2. y12 short-circuit transfer admittance
• (port 2 to 1)
• 3. y21 short-circuit transfer admittance
• (port 1 to 2)
• 4. y22 short-circuit output admittance
• The unit for Admittance is S (Siemens)

18
Chapter 6 2-port networks Y Parameters

• A reciprocal network (when y12 y21) and a ?
  equivalent circuit general equivalent cct.

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Chapter 6 2-port networks Y Parameters

• EXAMPLE 2
• Determine the y-parameters for ? network
  shown below

20
Chapter 6 2-port networks Y Parameters

• SOLUTION FOR EXAMPLE 2
• 1. Short-circuit output port (V2 0V)
• V1 I1 (4//2) 4/3 I1
• y11 I1 / V1 I1 / 4/3 I1 0.75
  s
• -I2 (4/(42))I1 2/3 I1 (Use
  current Division )
• y21 I2 / V1 -0.5s
• 2. To get other y-parameters, short-circuit
  input port (V1 0V)
• and connect current source, I2 to output
  port.
• V2 I2 (8//2) 8/5 I2
• y22 I2 / V2 I2 / 8/5 I2 0.625 s
• -I1 (8/(82))I2 4/5 I2 (Use
  current Division )
• y12 I1 / V2 -0.5s
• 3. The y-parameters are
• y 0.75 -0.5
• -0.5 0.625

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Chapter 6 2-port networks Y Parameters

• EXERCISE 5
• Determine the y-parameters for the T Network
  shown below

22
Chapter 6 2-port networks Defination Hybrid
Parameters

• Z and y parameters in the 2-port network do not
  always exits. Thus , need to create another set
  of parameters which are called Hybrid parameters
  and defined as below
• V1 h11 h12 I1 h I1
• I1 h21 h22 V2
  V2

23
Chapter 6 2-port networks Defination Hybrid
Parameters

• The h-parameters are also called hybrid
  parameters defined as below
• 1. h11 short-circuit input impedance
• 2. h12 open-circuit reversed voltage gain
• 3. h21 short-circuit forward current gain
• 4. h22 open-circuit output impedance

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Chapter 6 2-port networks Hybrid Parameters

• For the reciprocal network,
• h12 -h21
• Hybrid model for 2-port network

25
Chapter 6 2-port networks Inverse Hybrid or g
Parameters

• The inverse or reciprocal of Hybrid parameter
  will produce g-parameter and defined as below
• g11 I1/V1 I2 0
• g12 I1/I2 v1 0
• g21 V2/V1 I2 0
• g22 V2/I2 v1 0
• I1 g11 g12 V1 g
  V1
• V2 g21 g22 I2
  V2

26
Chapter 6 2-port networks Inverse Hybrid or g
Parameters

• The model of g-parameters are shown below
• The h-parameters are also called inverse hybrid
  parameters defined as below
• 1. g11 Open-circuit input impedance
• 2. g12 Short-circuit reversed current gain
• 3. g21 Open-circuit forward voltage gain
• 4. g22 Short-circuit output impedance

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Chapter 6 2-port networks Defination Inverse
Hybrid or g Parameters

• EXAMPLE 3
• Determine the h-parameters for ? network
  shown below

28
Chapter 6 2-port networks Defination Inverse
Hybrid or g Parameters

• SOLUTION FOR EXAMPLE 3
• 1. Find h11 h21 by short-circuit the
  output port and connect input port to current
  source, I1
• V1 I1 (23 // 6) 4I1
• h11 V1 / I1 4?
• next, use current division to obtain h21
• h21 I2 / I1 -6/(63)I1
  -2/3 ?
• 2. Find h22 h12 by open-circuit the input
  port and connect output port to voltage source,
  V2

29
Chapter 6 2-port networks Inverse Hybrid or g
Parameters

• V1 V2 6 /(63) 2/3 V2
• h12 V1 / V2 2/3 ?
• next, use voltage division to find h22
• h22 I2 / V2 I2 /(63)I2
  -2/3 ?
• 3. The h-parameters are
• h 4 2/3
• -2/3 1/9

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Chapter 6 2-port networks Inverse Hybrid or g
Parameters

• The equivalent cct to compute h-parameters are
  shown below

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Chapter 6 2-port networks Inverse Hybrid or g
Parameters

• EXERCISE 6
• Determine the h-parameters for the T Network
  shown below

32
Chapter 6 2-port networks Inverse Hybrid or g
Parameters

• EXERCISE 7
• Determine the h-parameters for the ? Network
  shown below

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Chapter 6 2-port networks Inverse Hybrid or g
Parameters

• The g-parameters can be expressed in term of
  function of s (Laplace domain)
• For IH Inductor ? sL ? s
• For 1F Capacitor ? 1/sC ? 1/s
• To obtain g11 and g21 ? SC Output port Connect
  voltage source to Output port
• To obtain g22 and g12 ? SC Input port Connect
  current source to Output port

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Chapter 6 2-port networks Inverse Hybrid or g
Parameters

• EXAMPLE 4
• Determine the g-parameters in s-domain for
  T-network shown below

35
Chapter 6 2-port networks Inverse Hybrid or g
Parameters

• Solution for Example 4
• 1. Determine g11 g21
• Use Voltage Division to calculate I1
• V2
• I1 1 / (s 1) V1
• g11 I1 / V1 ? 1/(s1)
• V2 1 / (s 1) V1
• g21 V2 / V1 ? 1/(s1)

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Chapter 6 2-port networks Inverse Hybrid or g
Parameters

• Solution for Example 4 (Continued)
• 2. Determine g22 g12
• Use Voltage Division to calculate I1
• V2
• I1 -1 / (s 1) I2
• g12 I1 / I2 ? -1/(s1)
• V2 (1/s) (s//1) I2
• g22 V2 / I2 ? (s2 s 1)/ s(s1)

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Chapter 6 2-port networks Inverse Hybrid or g
Parameters

• The equivalent cct to
• determine g-parameters
• in the s-domain

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Chapter 6 2-port networks ABCD parameters

• ABCD is also called Transmission Parameters where
  the current I1 is entering the network while the
  current I2 is leaving the network.
• The input parameters are described in term of
  output parameters
• V1 A B V2 T V2
• I1 C D -I2
  -I2
• The ABCD parameters are used in the design of
  telephone systems, microwave networks radars.

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Chapter 6 2-port networks ABCD parameters

• The ABCD parameters are defined as below
• A V1 / V2 I2 0 B -V1 / I2
  V2 0
• C I1 / V2 I2 0 D -I1 / I2
  V2 0
• The transmission parameters are called as
• 1. A Open-circuit voltage ratio (unit
  less)
• 2. B Negative short-circuit transfer
  impedance (?)
• 3. C Open-circuit transfer admittance
  (Siemens)
• 4. D Negative short-circuit current ratio
  (unit less)
• It provides a direct relationship between input
  and output variables and very useful in cascaded
  network.
• Network is reciprocal if AD BC 1

40
Chapter 6 2-port networks abcd parameters
(inverse- transmission
parameters)

• For Inverse Transmission Parameters, Output
  parameters are described in term of Input
  parameters.
• V2 a b V1 t V1
• I2 c d -I1
  -I1
• The Inverse transmission parameters are
  reciprocal if AD BC 1, ad bc 1
• It is determined as below
• a V2 / V1 I1 0 b -V2 / I1
  V10
• c I2 / V1 I1 0 d -I2 / I1
  V10

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Chapter 6 2-port networks ABCD parameters

• EXAMPLE 5
• Find the ABCD parameters for the circuit shown
  below

42
Chapter 6 2-port networks ABCD parameters

• Solution for Example 5(Continued)
• 1. Connect Voltage source, V1 to the
• input port and let output port open.
• 2. Perform nodal analysis at node 1 2

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Chapter 6 2-port networks ABCD parameters

• Solution for Example 5(Continued)
• 3. Determine C,
• 4. Determine A
• 5. Determine B D by connecting input source
  to the input
• port and output port is short-circuit.

44
Chapter 6 2-port networks ABCD parameters

• Solution for Example 5(Continued)
• 6. Redraw the cct as below
• 7. Once again, perform nodal analysis

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Chapter 6 2-port networks ABCD parameters

• EXERCISE 8 (Practice Problem 19.36)
• Find I1 I2 if the transmission parameters
  for the 2 port networks in circuit below are
• 5 10 ?
• 0.4s 1

46
Chapter 6 2-port networks Interconnection

• The six parameters for 2-port networks are
• 1. z-parameters
• 2. y-parameters
• 3. h-parameters
• 4. g-parameters
• 5. ABCD-parameters
• 6. abcd-parameters
• All this parameters are interrelated.
• The relationship between y-parameters and
  z-parameters are shown below
• y11 z22 / ?z 2. y12 -z12 / ?z 3. y21
  -z21 / ?z
• 4. y22 z11 / ?z where ?z is determinant of z

47
Chapter 6 2-port networks Interconnection

• The relationship between h-parameters
  z-parameters are shown below
• 1. h11 ?z / z22 2. h12 z12 / z22
• 3. h21 -z21 / z22 4. h22 1 / z22
• where ?z is determinant of z
• The Conversion of 2-port parameters are shown in
  table 19.1

48
Chapter 6 2-port networks Interconnection

• EXAMPLE 6 (Practice problem 19.10)
• Determine y T of 2-port network where
  z-parameters are defined below
• z 6 4 ?
• 4 6

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Chapter 6 2-port networks Interconnection

• Solution for Example 6
• 1. Calculate determinant of z
• ?z (6)(6) (4)(4) 20
• 2. Use table 19.1, y 0.3 -0.2
• 
  -0.2 0.3
• y11 z22 / ?z 6/20 0.3
• y12 -z12 / ?z -4/20 -0.2
• y21 -z21 / ?z -4/20 -0.2
• y22 z11 / ?z 6/20 0.3
• 3. A z11 / z21 6/4 1.5
• B ?z / z21 20/4 5
• C 1/z21 1/4 0.25
• D z22 / z21 6/4 1.5

50
Chapter 6 2-port networks Interconnection

• The six parameters are used for the
  interconnection of 2-port networks for the
  following connection
• 1. Series Connection ? Use Impedance
• 
  Parameters
• 2. Parallel Connection ? Use Admittance
• 
  Parameters
• 3. Cascaded Connection ? Use Transmission
• 
  Parameters
• 4. Series Parallel Connection ? Use Hybrid
• 
  Parameters
• 5. Parallel-Series Connection ? Inverse
  Hybrid

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Chapter 6 2-port networks Interconnection

• Series Connection
• Z-parameter for series network
• z z11a z11b z12a z12b
• z21a z21b z22a
  z22b

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Chapter 6 2-port networks Interconnection

• Parallel Connection

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Chapter 6 2-port networks Interconnection

• Cascade Connection
• A B Aa Ba Ab Bb
• C D Ca Da Cb Db
• T Ta Tb

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Chapter 6 2-port networks Interconnection

• Series-Parallel Connection
• h ha hb
• Parallel-Series Connection
• g ga gb

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Chapter 6 2-port networks Interconnection

• EXAMPLE 7 (Exercise problem 19.67)
• Find the transmission parameters, T.

56
Chapter 6 2-port networks Interconnection

• SOLUTION FOR EXAMPLE 7
• 1. Obtain y-parameters then converted to z
• and then converted to T by using
• Conversion table.
• 2. The y-parameter for upper network are
• 3. Determine the determinant of y
• parameter
• ? (2)(2) (-1)(-1) 3
• 4. Convert to z-parameters, Za Zb
• Za y22 / ?y -y12 / ?y
  2/3 1/3
• -y21 / ?y -y12 / ?y
  1/3 2/3

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Chapter 6 2-port networks Interconnection

• SOLUTION FOR EXAMPLE 7
• 5. zb 1 1
• 1 1
• 6. z za zb 5/3 4/3
• 4/3
  5/3
• 7. now, calculate determinant of z, z
  25/9 16/9 1
• 8. From, the conversion table, determine
  transmission parameter, T
• T z11/z21 ?z / z21
  1.25 0.75
• 1/z21 z22 / z21
  0.75 1.25

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Chapter 6 2-port networks Interconnection

• EXERCISE 9 (Exercise Problem 19.70)
• For the parallel-series connection of 2-port
  network, find g-parameters.