# Two Port Network | Two Port Network Parameters

By Mohit Uniyal|Updated : May 17th, 2022

We can use two-port networks to represent any complex electrical network into a simple equivalent model. The electrical components like transmission lines and transformers can be modeled in two-port network models. Similarly, electronic components like transistors and op-amps can also be modeled in two-port network models.

In this article, get an overview of two-port network parameters and how to calculate them. In this article, we also provided the condition for symmetry and reciprocal for the given network with respect to two-port network parameters. These conditions will be helpful for checking the given network whether it is symmetrical or not and similarly reciprocal or not.

## What is Two Port Network

Pair of terminals is known as a port. Here, current enters through one terminal and leaves from the other terminal. So, the electrical components like resistor, inductor and capacitor are examples of one port network.

If the network has two such ports, then it is known as a two-port network. In the following two-port network, there are two ports namely port 1 and port 2. Here, V1 and V2 are the voltages across port 1 and port 2 respectively. Similarly, I1 and I2 are the currents flowing through port 1 and port 2 respectively.

## Two Port Network Parameters

In the two-port network, we can give the input to any port and similarly we can take the output from any port. Since we are having two electrical quantities voltage and current, obviously the input and output also will be among those two forms.

The parameters that we will use in two port networks are known as two port network parameters. Since there are four variables V1, V2, I1 and I2 we will get a total six sets of parameters regarding the two port networks. Now, let’s see the following two port network parameters one by one.

• Z Parameters
• Y Parameters
• T Parameters
• T’ Parameters
• h Parameters
• g Parameters

## Z Parameters

Among the four variables V1, V2, I1 and I2 of two-port network, let’s consider I1 and I2 as independent variables and V1 and V2 as dependent variables. That means, I1 and I2 are the inputs whereas V1 and V2 are the outputs of the two-port network. The two equations of this two-port network and the corresponding Z parameters are mentioned below.

• V1=Z11I1+Z12I2
• V2=Z21I1+Z22I2
• Z11=V1/I1, when I2=0
• Z12=V1/I2, when I1=0
• Z21=V2/I1, when I2=0
• Z22=V2/I2, when I1=0

Here, the ratio of output (voltage) and input (current) gives the value of impedance, and the units are Ohm (Ω). Hence, these two-port network parameters are called impedance parameters or Z parameters. We can find two Z parameters Z11 and Z21 by making port 2 as an open circuit. Similarly, we can find other two Z parameters Z12 and Z22 by making port 1 as an open circuit.  Hence, we can call Z parameters as open circuit impedance parameters.

• A two-port network is said to be symmetrical network, if Z11=Z22.
• A two-port network is said to be reciprocal, if Z12=Z21.

## Y Parameters

Among the four variables V1, V2, I1 and I2 of two-port network, let’s consider V1 and V2 as independent variables and I1 and I2 as dependent variables. That means, V1 and V2 are the inputs whereas I1 and I2 are the outputs of the two-port network. The two equations of this two-port network and the corresponding Y parameters are mentioned below.

• I1=Y11V1+Y12V2
• I2=Y21/V2+Y22V2
• Y11=I1/V1, when V2=0
• Y12=I1/V2, when V1=0
• Y21=I2/V1, when V2=0
• Y22=I2/V2, when V12=0

Here, the ratio of output (current) and input (voltage) gives the value of admittance, and the units are mho (). Hence, these two-port network parameters are called admittance parameters or Y parameters. We can find two Y parameters Y11 and Y21 by making port 2 as a short circuit. Similarly, we can find other two Y parameters Y12 and Y22 by making port 1 as a short circuit.  Hence, we can call Y parameters as short circuit admittance parameters.

• A two-port network is said to be symmetrical network, if Y11=Y22.
• A two-port network is said to be reciprocal, if Y12=Y21.

## T Parameters

Among the four variables V1, V2, I1 and I2 of two-port network, let’s consider V2 and I2 as independent variables and V1 and I1 as dependent variables. That means, V2 and I2 are the inputs whereas V1 and I1 are the outputs of the two-port network. The two equations of this two-port network and the corresponding T parameters are mentioned below.

• V1=AV2-BI2
• I1=CV2-DI2
• A=V1V2, when I2=0
• B=-V1I2, when V2=0
• C=I1V2, when I2=0
• D=-I1I2, when V2=0

Here, A and D are not having any units. Whereas the units of B and D are ohm (Ω) and mho () respectively. ABCD parameters are also called Transmission parameters or T parameters in short. We can find two T parameters A and C by making port 2 as open circuit. Similarly, we can find the other two T parameters B and D by making port 2 as a short circuit.

• A two-port network is said to be a symmetrical network, if A=D.
• A two-port network is said to be reciprocal, if AD-BC=1.

## T’ Parameters

Among the four variables V1, V2, I1 and I2 of two-port network, let’s consider V1 and I1 as independent variables and V2 and I2 as dependent variables. That means, V1 and I1 are the inputs whereas V2 and I2 are the outputs of the two-port network. The two equations of this two-port network and the corresponding T’ parameters are mentioned below.

• V2=A'V1-B'I1
• I2=C'V1-D'I1
• A'=V2V1, when I1=0
• B'=-V2I1, when V1=0
• C'=I2V1, when I1=0
• D'=-I2I1, when V1=0

Here, A’ and D’ are not having any units. Whereas the units of B’ and D’ are ohm (Ω) and mho () respectively. A’B’C’D’ parameters are also called Inverse Transmission parameters or T’ parameters in short. We can find two T’ parameters A’ and C’ by making port 1 as open circuit. Similarly, we can find the other two T’ parameters B’ and D’ by making port 1 as a short circuit.

• A two-port network is said to be a symmetrical network if A’=D’.
• A two-port network is said to be reciprocal if A'D'-B'C'=1.

## h Parameters

Among the four variables V1, V2, I1 and I2 of two-port network, let’s consider I1 and V2 as independent variables and V1 and I2 as dependent variables. That means, I1 and V2 are the inputs whereas V1 and I2 are the outputs of the two-port network. The two equations of this two-port network and the corresponding h parameters are mentioned below.

• V1=h11I1+h12V2
• I2=h21I1+h22V2
• h11=V1/I1, when V2=0
• h12=V1/V2, when I1=0
• h21=I2/I1, when V2=0
• h22=I2/V2, when I1=0

Here, h12 and h21 are not having any units. Whereas the units of h11 and h22 are ohm (Ω) and mho () respectively. The h parameters are also called Hybrid parameters. We can find two h parameters h11 and h21 by making port 2 as a short circuit. Similarly, we can find other two h parameters h12 and h22 by making port 1 as an open circuit.

• A two-port network is said to be symmetrical network, if h=1, i.e., h11h22-h21h21=1.
• A two-port network is said to be reciprocal, if h12=-h21.

## g Parameters

Among the four variables V1, V2, I1 and I2  of two-port network, let’s consider V1 and Ias independent variables and I1 and V2 as dependent variables. That means, V1 and I2 are the inputs whereas Iand V2 are the outputs of the two-port network. The two equations of this two-port network and the corresponding g parameters are mentioned below.

• I1=g11V1+g1I2
• V2=g21V1+g22I2
• g11=I1/V1, when I2=0
• g12=I1/I2, when V1=0
• g21=V2/V1, when I2=0
• g22=V2/I2, when V1=0

Here, g12 and g21 are not having any units. Whereas the units of g11 and g22 are mho () and ohm () respectively. The g parameters are also called Inverse Hybrid parameters. We can find two g parameters g11 and g21 by making port 2 as an open circuit. Similarly, we can find other two g parameters g12 and g22 by making port 1 as a short circuit.

• A two-port network is said to be symmetrical network, if g=1, i.e., g11g22-g12g21=1.
• A two-port network is said to be reciprocal, if g12=-g21.

In this article, we discussed the two port network parameters and how to calculate them. We also mentioned the condition for symmetry and reciprocal for the given network with respect to two port network parameters. Whenever we want to check whether the given network is symmetrical or not and similarly reciprocal or not that time, we can use those conditions.

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## FAQs on Two Port Network.

• Cascade means the output of one stage we will give as the input for the next stage. If multiple blocks are connected in cascaded form, then we will get the equivalent block transfer function by multiplying the transfer function of each block. Similarly, if the two-port networks are connected in cascaded form, then we can multiply the respective T parameters or Transmission parameters of those networks.

• A two-port network consists of two ports. So, there are four variables V1, V2, I1, and I2. At any time by choosing two of them as independent variables, we will get a total of six sets of parameters regarding the two port networks. The two-port network parameters are Z, Y, T, T’, h, and g parameters.

• We are having a total of six sets of two-port network parameters Z, Y, T, T’, h and g. Among which the pair of matrices of two port network parameters, which are inverse to each other are (Z, Y), (T, T’), and (h, g). That is the matrices [Z] and [Y] are inverse to each other. Similarly, the matrices [T] & [T’], [h] & [g] are inverse to each other.

• If multiple resistors are connected in series, then we will get the equivalent resistance value by adding all those resistances. Similarly, if the two port networks are connected in series, then we can add the respective Z parameters or impedance parameters of those networks.

• If multiple resistors are connected in parallel, then we will get the equivalent conductance value by adding all those conductance. Conductance is nothing but reciprocal resistance. Similarly, if the two-port networks are connected in parallel, then we can add the respective Y parameters or admittance parameters of those networks.

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