Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Electrical Engineering SSC JE (Technical)

Electrical Engineering (EE) : Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

The document Chapter 7 (Part 1) 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

  • A pair of terminal through which a current may enter or leave a network is known as a port. Two-terminal 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 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev 

Chapter 7 (Part 1) 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 1) 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 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev.....the forward transfer impedance with the output port open

 Chapter 7 (Part 1) 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 I2 and Z21 I1 are current controlled voltage sources (CCVS) 
  • Rewriting equation (i),

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

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

 Chapter 7 (Part 1) 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 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Condition of Reciprocity and Symmetry 

Reciprocal Network 

  • A network must be reciprocal when ratio 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 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev
Z11 = Z22

Y- PARAMETERS

Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev 

 Chapter 7 (Part 1) 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 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev .....(reverse transfer admittance)

Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev....(forward transfer admittance)

Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev...(o utput driv in g po in t admittance)

 Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

Equivalent Circuit Y-parameter

Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev 

  • Rewriting equation of Y-parameters

 I1 = (y11 + Y12) V1 – Y12 (V1-V2)

I2 = (Y23 – Y12) V1 + (Y22 + Y12)V2 – Y12 (V2–V1)

For this equivalent II–network

 Chapter 7 (Part 1) 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 1) 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 1) 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 1) 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 1) 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 1) 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 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev 

Condition for Symmetry
 A=D

INVERSE TRANSMISSION PARAMETERS
 V2 = A'V+ B' (–I1)

 Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev

The inverse transmission parameter can be defined as

 Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev ...(forward voltage ratio with sending end open circuited)

 Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev...(transfer admittance with sending end open circuited)

 Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev....(transfer impedance with sending end short circuited)

 Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev ...(forward current ratio with sending end short circuited)

Condition of Reciprocity

  Chapter 7 (Part 1) Two Port network - Notes, Circuit Theory, Electrical Engineering Electrical Engineering (EE) Notes | EduRev 

Condition for Symmetry

 A' = D'

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