TWO PORT NETWORKS

SUMMARY
Properties of Two Port Network
Some important properties exhibited by two port networks are:
 Linear and Lumped: A two port network demonstrates linear behavior meaning superposition holds. It
also follows lumped element approximation.
 Reciprocal: If the network is linear and passive, it satisfies the condition of reciprocity where its mixed
partial parameters are equal (Z12=Z21, Y12=Y21, and so on).
 Causal: The output cannot precede the input. It simply describes input-output relationships.
 Time-invariant: Network behavior does not change over time for a fixed set of inputs.
 Deterministic: Specific inputs will always produce the same outputs.
Two Port Network Parameters
The input-output relationships in a two port network can be described through various parameter sets. Based on
which variables are considered dependent/independent, different parameter representations are possible.
Some common two port network parameters include:
Z parameters
z parameters of two port network:The Z parameters, also known as impedance parameters, represent the
relationship between the voltage and current at each port of the network. They are defined by the voltage and
current ratios at the input and output ports.
With voltages dependent and currents independent, this gives impedance parameters Z11, Z12, Z21, and Z22.

The Z parameters are

 Z parameters are called as impedance parameters because these

are simply the ratios of voltages and currents. The units of Z parameters are Ohm (Ω).
 We can calculate two Z parameters, Z11 and Z21, by doing open circuit of port2. Similarly, we can
calculate the other two Z parameters, Z12 and Z22 by doing open circuit of port1. Hence, the Z
parameters are also called open-circuit impedance parameters.
  Y parameters
 y parameters of two port network:
 The Y parameters, or admittance parameters, describe the conductance and susceptance of the network
at each port. They are the reciprocal of Z parameters and are useful for analyzing networks in terms of
current rather than voltage.
 Taking currents dependent and voltages independent yields admittance parameters Y11, Y12, Y21, and
Y22.
 When considering the variables I1 and I2 as dependent and V1 and V2
 as independent, we can derive a set of two equations representing the behavior of the two port networks.
 These equations are typically written in matrix form as:

 The Y parameters represent the two port network when the

currents are considered as the dependent variables and voltages as the independent ones.

 The Y parameters are defined as:

 Y11 is the input admittance seen when port 2 is short circuited.
Y12 is the transfer admittance with port 1 short circuited.
Y21 is the reverse transfer admittance with port 2 short circuited.
Y22 is the output admittance with port 1 short circuited.
 In simpler terms -
 Y11 = Current I1/Voltage V1 when V2 is zero
Y12 = Current I1 /Voltage V2 when V1 is zero

 And so on for Y21 and Y22

 Since they represent ratios of currents to voltages, the units of Y parameters are Siemens (S).
 We can measure the Y parameters by doing a short circuit (connecting the terminals) at one port while
measuring the other. So Y parameters describe the two port network under short circuit conditions

ABCD or T parameters

abcd parameters of two port network:

Using voltages and currents as dependent-independent defines transmission parameters A, B, C, and D.

We will get the following set of two equations by considering the variables V1 & I1 as dependent and V2 & I2
as independent.
The coefficients of V2 and -I2 are called T parameters.

The T parameters are:

The parameters commonly known as T parameters in a two-port

network are also referred to as transmission parameters or ABCD parameters. Among these parameters, A and
D are dimensionless, lacking any units. However, the units of parameters B and C are ohms and mhos,
respectively.

To determine the values of parameters A and C, an open circuit is implemented at port 2, allowing for the
calculation of the resulting parameters. Conversely, parameters B and D can be obtained by performing a short
circuit at port 2, facilitating the determination of their values.

g parameters

g parameters of two port network:

Considering inverse hybrid representation leads to inverse hybrid parameters g11, g12, g21, g22.

When considering the variables I1 and V2 as dependent and V1 and I2

as independent, we can derive a set of two equations representing the behavior of the two-port network. These
equations are typically expressed in matrix form as:

The g-parameters are:

 g-parameters are called inverse hybrid parameters. The
parameters, g12, and g21 are dimensionless, since they are unitless. The units of parameters, g11, and g22 are
mho and ohm respectively.

By doing an open circuit of port2, we can calculate two parameters, g11, and g21. Similarly, we can calculate
the other two parameters, g12 and g22 by doing a short circuit of port1.

h parameters(hybrid parameters)

h parameters of two port network:

Considering the variables V1 and I2 as dependent and I1 and V2 as independent, we can formulate a set of two
equations describing the behavior of the two-port network. These equations can be represented in matrix form
as:

The h-parameters are:

h-parameters are called hybrid parameters. The parameters, h12 and h21, do not have any units, since those are
dimension-less. The units of parameters, h11, and h22, are Ohm and Mho respectively.
We can calculate two parameters, h11 and h21 by doing a short circuit of port2. Similarly, we can calculate the
other two parameters, h12, and h22 by doing an open circuit of port1.

The h-parameters or hybrid parameters are useful in transistor modeling circuits (networks).

Two port network parameters conversion table

It is often necessary to convert between different two port network parameter representations based on analysis
requirements. The following table lists the transformations between common parameter sets:

Where ⇌ indicates the conversion relationships between the given parameter sets. This provides a handy
reference to convert between representations as needed for solving network problems.

Application of two port network

Two port networks serve as basic but useful models with wide-ranging applications across different domains:

 Circuit analysis: Used to represent circuits involving resistors, capacitors, coils, and basic electronic
components.
 Transmission lines: Characterize voltage and current propagation along transmission lines.
 Antennas: Employed to model radiation properties and matching networks of antennas.
 Amplifiers: Describes small signal behavior of transistors in amplifiers.
 Networks: Model communication systems, control systems, mechanical and acoustic systems.
 Acoustics: Analogous to electric circuits in modeling acoustical/mechanical systems.
 Electrical machines: Represent transformers, motors, and generators through suitable parameter
models.