Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Electrical Engineering SSC JE (Technical)

Electrical Engineering (EE) : Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

The document Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev is a part of the Electrical Engineering (EE) Course Electrical Engineering SSC JE (Technical).
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Two Port network

h - PARAMETERS OR HYBRID PARAMETERS

  • The hybrid parameters (h- parameters) would find wide usage in electronic circuit, especially in constructing models for transistors. 
  • The par ameters of a transistor cannot be measured either by short-circuit admittance parameter measurement or open circuit impedance parameter measurement alone.

Because of the forward bias of the base-emitter junction, the device has a very low input resistance. For open-circuit impedance measurement of Z12 and Z22, it is very difficult to make the input open circuited. Z11 and Z12 can be measured by open circuit impedance measurements, since the collector-emitter junction is reversed biased.

  • By making a short-circuit admittance parameter measurement, Y12 and Y22 can be measured by short-circuiting the input port, but Y11 and Y21 cannot be measured since the collector emitter junction is reverse biased. 
  • By making a short-circuit admittance parameter measurement. Y12 and Y22 can be measured by short circuiting the input port, but Y11 and Y21 cannot be measured since the collector-emitter junction is reverse biased. 
  • Some kind of parameter representation is required by which some parameters are measured by open circuiting the input ort, while the rest of the parameters can be measured by short-citcuiting the output port. This is the socalled hybrid parameter representation.
  • This parameter representation is a hybrid of shortcircuit admittance and open-circuit impedance measurement. 
  • One set of equations result when the voltage o the input port and the current of the output por are expressed in terms of the current of the input port and the voltage of the output port, in the form

V1 = h11I1 + h12V2

I2 = h21I+h22V2

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

where,hi : input impedance with the output short-circuited.

hr : reverse voltage gain with the input open-circuited.

hf : Forward current gain with the output short-circuited.

ho : Output admittance with the input open-circuited

Condition of Reciprocity

h12 = - h 21 

Condition of Symmetry

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

h-parameter Equivalent Circuit

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

g-PARAMETERS OR INVERSE HYBRID PARAMETERS
I1 = g11 V1 + g12I2

V2 = g21V1 + g22I2

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
The g-parameters can be defined as,

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev..... (i.e. input admittance with output open circuited)

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev...(i.e. forward voltage gain with output open circuited)

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev......(i.e. forward voltage gain with output open circuited)

  Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev....(i.e. output impedance with input short circuited)

Condition of Reciprocity 

g12 = - g21

Condition of Symmetry

  Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

g-parameter Equivalent Circuit
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

INTER RELATIONS IN NETWORK PARAMETERS

Y - parameter in terms of Z-parameters

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

ABCD-parameters in terms of Z- parameters

 V1 = Z11I1 + Z12I2
V2 = Z21I1 + Z22I2

from equation (ii),

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

from equation (i) and (ii),

NOTE: ABCD parameters relate voltage and current in the primary to the voltage and current in the secondary

Z-parameters in terms of h-parameters

 V1 = h11I1 + h12V2 ..................... (i)

I2 = h21I1 + h22V2 .....................(ii)

from equation (ii)

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

  Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Similarly 

  • Find out Y parameters in terms of ABCD parameters. 
  • h-parameters in terms of ABCD parameters.

Condition Under which passive Two-port Network is reciporcal and Symmeterical

Parameters   condition for Reciprocity   Condition for Symmetry

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRevChapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

INTERCONNECTION OF TWO-PORT NETWORKS

1. Series Connection

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev


I1a = I1b = I1  I2a = I2b = I2

V1 = V1a + V1b

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

so, in matrix form the Z-parameters of the seriesconnected combined network can be written as
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

2. Parallel Connection

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

3. Series Parallel Connection h-parameters

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
I1a = I1b = I1

V1 = V1a + V1b ........................(i)

I= I2a + I2b ........................(ii)

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev 
Where
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

4. Parallel Series Connection

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Where
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

5. Cascade Connection

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
I1 = I1a
V1 = V1a
I2 = I2b
I1b = –I2a
V1b = V2a

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev 

BARLETTS BISECTION THEOREM

  • This theorem is applicable for symmetrical network. 
  • A symmetrical network can be split into two half then the Z= parameters of the network are given by

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Network is symmetrical as well as reciprocal ZOC – Open circuited driving point impedances for half of section.
ZSCH – Short circuited driving point impedances for half of section.

SYMMETRICAL LATTICE NETWORK

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Zb ~ ZOCH
Za ~ ZSCH

IMAGE IMPEDANCE

  • If Zi1 is the impedance seen at pot 1 with Zi2 connected at port 2 and Zi2 is impedance seenm at port 2 with Zi1 connected at port 1. Then Zi1 and Zi2 are called image impedance at port 1 and 2 respectively.

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

  • A pair of terminal through which a current may enter or leave a network is known as a port. Twoterminal devices or element (such as resistors, capacitors, and inductors) result in one-port networks.
  • Here, we are mainly concerned with the twoport networks. A two-port network is an electrical network with two separate ports for input and output. Thus, a two-port network has two terminal pairs acting as access points. The current entering in the pair leaves the other terminal in the pair. Three-terminal devices such as transistors can be configured into two-port networks.
  • Armed only with the knowledge that the circuit is linear, and the ability to measure the voltage and currents, we will shortly see that it is possible to characterize such a network with a set of parameters that allows us to predict how the network will interact with other networks.

Network parameters 

  • Z– parameters
  • Y= parameters
  • ABCD parameters (Transmission parameter)
  • A' B' C' D ' parameters (Inverse transmission parameter)
  • h-parameters
  • g-parameters

Z – PARAMETERS

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev.........the input driving- point impedance with the output port open-circuited

 

.Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev...The reverse transfer impedance with the input port open-circuited

 

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev....the forward transfer impedance with the output port open-circuited

 

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev.....the output driving point impedance with input port opencircuited

  • The equivalent circuit representation of equation (i) is in figure below, where Z12 Iand Z21 I1 are current controlled voltage sources (CCVS)
  • Rewriting equation (i),

 V1 = (Z11 –Z12)I1+ Z12 (I1 + I2)
V2 = (Z21 – Z12) I1 + (Z22 –Z12)I2
+ Z12 (I1 + I2) ...........(ii)

  • The equivalent circuit for equation (i) is given as,

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

  • The equivalent circuit for equation (ii) is given as,

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Condition of Reciprocity and Symmetry Reciprocal Network

  • A network must be r eciproca l when r atio of response at port 2 to the excitation at port '1' is same as ratio of response at port 1 to the excitation at port 2

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Z11 = Z22

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

.Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev.............(Because in Y11 we have short circuit condition whereas in Z11 we have open cuicuit condition) input driving point admittance

 

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev.....(reverse transfer admittance)

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev....(forward transfer admittance)

 

...(output driving point admittance)

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Equivalent Circuit Y-parameter

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

  • Rewriting equation of Y-parameters

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

For this equivalent II–network

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

For reciprocal network Y12 = Y21
For sysmmetrical network Y11  = Y22

 TRANSMISSION PARAMETERS (ABCD)

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

V1 = AV2 + B (–12)
I1 = CV2 + D (–I2)
The transmission parameters are

 

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev.....(i.e. the reverse voltage ratio with the receiving end open circuited)

 

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev....(i.e. the transfer admittance with the receiving end open-circuited)

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev...(i.e. the transfer impedance with the receiving end short-circuited )

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev....(i.e. the reverse  current ratio with the receiving end short circuited.)

Condition for Reciprocity

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Condition for Symmetry

A = D
INVERSE TRANSMISSION PARAMETERS

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

The inverse transmission parameter can be defined as

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev.....(forward voltage ratio with sending end open circuited)

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev...( transfer a dmittance with sending end open circuited)

 

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev. .. (t ra ns fe r impeda nce wi th sending end short circuited)

 

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev....(forwar d current ratio with sending end short circuited)

Condition of Reciprocity

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Condition for Symmetry

A'=D'

h–PARAMETERS OR HYBRID PARAMETERS

  • The hybrid parameters (h- parameters) would find wide usage in electronic circuit, especially in constructing models for transistors.
  • The parameters of a transistor cannot be measured either by short-circuit admittance parameter measurement or open circuit impedance parameter measurement alone. Because of the forward bias of the base-emitter junction, the device has a very low input resistance. For open-circuit impedance measurement of Z12 and Z22, it is very difficult to make the input open circuited. Z11 and Z12 can be measured by open circuit impedance measurements, since the collector-emitter junction is reversed biased.
  • By making a short-circuit admittance parameter measurement, Y12 and Y22 can be measured by short-circuiting the input port, but Y11 and Y21 cannot be measured since the collector emitter junction is reverse biased.
  • By making a short-circuit admittance parameter measurement. Y12 and Y22 can be measured by short circuiting the input port, but Y11 and Y21 cannot be measured since the collector-emitter junction is reverse biased.
  • Some kind of parameter representation is required by which some parameters are measured by open circuiting the input ort, while the rest of the parameters can be measured by short-citcuiting the output port. This is the so-called hybrid parameter representation.
  • This parameter representation is a hybrid of short-circuit admittance and open-circuit impedance measurement.
  • One set of equations result when the voltage o the input port and the current of the output por are expressed in terms of the current of the input port and the voltage of the output port, in the form

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev 

where,
hi : input impedance with the output short-circuited.
hr : reverse voltage ga in with the input open-circuited.
hf : Forward cur rent gain with the output short-circuited.
ho : Output admittance with the input open-circuited.

Condition of Reciprocity
h12 = - h21

Condition of Symmetry

  Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

h-parameter Equivalent Circuit

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

g-PARAMETERS OR INVERSE HYBRID PARAMETERS

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

The g-parameters can be defined as,

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev...... (i.e. input admittance with output open circuited)

 

.Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev.....(i.e. forward voltage gain with output open circuited)

 

.Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev.....(i.e. forward voltage gain with output open circuited)

 

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev......(i.e. output impedance with input short circuited)

 Condition of Reciprocity
g12 = - g 21

Condition of Symmetry

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

g-parameter Equivalent Circuit

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

INTER RELATIONS IN NETWORK
 PARAMETERS

Y - parameter in terms of Z-parameters

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

ABCD-parameters in terms of Z- parameters

 V1 = Z11I1 + Z12I2
V2 = Z21I1 + Z22I2

from equation (ii),

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

from equation (i) and (ii),

NOTE: ABCD parameters relate voltage and current in the primary to the voltage and current in the secondary Z-parameters in terms of h-parameters

V1 = h11I1 + h12V2 ..................... (i)
I2 = h21I1 + h22V2 .....................(ii)

 from equation (ii),

  Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

 Similarly

  • Find out Y parameters in terms of ABC D parameters.
  • h-parameters in terms of ABCD parameters.

Condition Under which passive Two-port Network is reciporcal and Symmeterical 

Parameters   Condition for Reciprocity    Condition for Symmetry

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRevChapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRevChapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

INTERCONNECTION OF TWO-PORT NETWORKS
1 . Serie s Connection

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

From diagram,
I1a = I1b = I1   I2a = I2b = I2

V1 = V1a + V1b

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Also
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

so, in matrix form the Z-parameters of the seriesconnected combined network can be written as

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

2 . Parallel Connection

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
I1 = I1a + 11b
I, = I2a + I2b
V1a = V1b = V1
V21 = V2b = V2

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

3 . Series Parallel Connection h-parameters

 Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Where
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

4 . Parallel Series Connection

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Where
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

5 . Cascade Connection

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

 

BARLETTS BISECTION THEOREM

  • This t heor em is a pplicab le for symmetr ica l network.
  • A symmetrical network can be split into two half then the Z= parameters of the network are given by

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Network is symmetrical as well as reciprocal ZOC – Open circuited driving point impedances for half of section.
ZSCH – Short circuited driving point impedances for half of section.
 

SYMMETRICAL LATTICE NETWORK

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Zb » ZOCH 
Za » ZSCH

IMAGE IMPEDANCE

  • If Zi1 is the impedance seen at pot 1 with Zi2 connected at port 2 and Zi2 is impedance seenm at port 2 with Zi1 connected at port 1. Then Zi1 and Zi2 are called image impedance at port 1 and 2 respectively.

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev


Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Chapter 7 (Part 2) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

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