Two Port Network - 1 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE) PDF Download

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

  ....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

 .....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)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 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

 
Z₁₁ = Z₂₂

Y- PARAMETERS

  .............(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)

...(o utput driv in g po in t admittance)

Equivalent Circuit Y-parameter

• 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

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
 V₂ = A'V₁ + B' (–I₁)

The inverse transmission parameter can be defined as

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

 ...(transfer admittance with sending end open circuited)

 ....(transfer impedance with sending end short circuited)

  ...(forward current ratio with sending end short circuited)

Condition of Reciprocity

Condition for Symmetry

 A' = D'