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


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

h-parameter Equivalent Circuit

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

V2 = g21V1 + g22I2


The g-parameters can be defined as,

..... (i.e. input admittance with output open circuited)

...(i.e. forward voltage gain with output open circuited)

......(i.e. forward voltage gain with output open circuited)

  ....(i.e. output impedance with input short circuited)

Condition of Reciprocity 

g12 = - g21

Condition of Symmetry

 

g-parameter Equivalent Circuit

INTER RELATIONS IN NETWORK PARAMETERS

Y - parameter in terms of Z-parameters

ABCD-parameters in terms of Z- parameters

 V1 = Z11I1 + Z12I2
V2 = Z21I1 + Z22I2

from equation (ii),

 

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)

 

 

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

INTERCONNECTION OF TWO-PORT NETWORKS

1. Series Connection


I1a = I1b = I1  I2a = I2b = I2

V1 = V1a + V1b


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

2. Parallel Connection

 

3. Series Parallel Connection h-parameters


I1a = I1b = I1

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

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



 
Where

4. Parallel Series Connection

 




Where

5. Cascade Connection

 
I1 = I1a
V1 = V1a
I2 = I2b
I1b = –I2a
V1b = V2a

 

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

 

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

 


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.





  • 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

 

.........the input driving- point impedance with the output port open-circuited

 

....The reverse transfer impedance with the input port open-circuited

 

....the forward transfer impedance with the output port open-circuited

 

.....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,

 

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

 

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

 

Z11 = Z22

..............(Because in Y11 we have short circuit condition whereas in Z11 we have open cuicuit condition) input driving point admittance

 

.....(reverse transfer admittance)

 ....(forward transfer admittance)

 

...(output driving point admittance)

 

Equivalent Circuit Y-parameter

 

  • Rewriting equation of Y-parameters

 

For this equivalent II–network

 

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

 TRANSMISSION PARAMETERS (ABCD)

 

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

 

.....(i.e. the reverse voltage ratio with the receiving end open circuited)

 

....(i.e. the transfer admittance with the receiving end open-circuited)

...(i.e. the transfer impedance with the receiving end short-circuited )

....(i.e. the reverse  current ratio with the receiving end short circuited.)

Condition for Reciprocity

Condition for Symmetry

A = D
INVERSE TRANSMISSION PARAMETERS

The inverse transmission parameter can be defined as

.....(forward voltage ratio with sending end open circuited)

...( transfer a dmittance with sending end open circuited)

 

. .. (t ra ns fe r impeda nce wi th sending end short circuited)

 

....(forwar d current ratio with sending end short circuited)

Condition of Reciprocity

 

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

 

 

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

 

h-parameter Equivalent Circuit

 

g-PARAMETERS OR INVERSE HYBRID PARAMETERS


The g-parameters can be defined as,

...... (i.e. input admittance with output open circuited)

 

......(i.e. forward voltage gain with output open circuited)

 

......(i.e. forward voltage gain with output open circuited)

 

......(i.e. output impedance with input short circuited)

 Condition of Reciprocity
g12 = - g 21

Condition of Symmetry

 

g-parameter Equivalent Circuit

 

INTER RELATIONS IN NETWORK
 PARAMETERS

Y - parameter in terms of Z-parameters

 

ABCD-parameters in terms of Z- parameters

 V1 = Z11I1 + Z12I2
V2 = Z21I1 + Z22I2

from equation (ii),

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),

 



 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

INTERCONNECTION OF TWO-PORT NETWORKS
1 . Serie s Connection

 

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

V1 = V1a + V1b


Also

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

 

2 . Parallel Connection


I1 = I1a + 11b
I, = I2a + I2b
V1a = V1b = V1
V21 = V2b = V2

3 . Series Parallel Connection h-parameters

 




Where

4 . Parallel Series Connection




Where

5 . Cascade Connection

 

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


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


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.


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