The impedance parameter is used to describe the behavior of linear electrical networks and the small-signal response of a non-linear network in electrical engineering.

The impedance parameter is also known as Z-parameter or open-circuit impedance parameter. Because the values of Z parameters are calculated under open-circuit conditions.

In a two-port network, the input current is I_{1 }and the output current is I_{2}. Then the Z parameter calculate by choose port-1 is open (I_{1}=0) in the first case and port-2 is open (I_{2}=0) in the second case. The below figure shows an electrical two-port network.

As we know the impedance is a ratio of voltage and current. If we write the equation of impedance in terms of a matrix, it is given as;

In this equation, V, Z, and I is in the form of matrix.

(1)

Where, Z_{11}, Z_{12}, Z_{21}, and Z_{22} are the impedance parameter.

This equation shows the matrix form of the impedance parameter. Now, separate both equations;

(2)

These equations are main equations of Z parameter and used to calculate other components.

## Calculation of Z Parameters

To calculate the Z parameter, perform two cases. In the first case, the port-1 is open-circuited. And hence, the current of port-1 that is I_{1} is zero. In the second case, the port-2 is open-circuited. And hence, the current of port-2 that is I_{2} is zero.

### First Case (Port-1 is open):

In this condition, the port-1 is open-circuited and the below figure shows this condition. Because of the open circuit, the current I_{1}=0.

Now put the value of I_{1}=0 in the eq-(2)

### Second Case (Port-2 is open):

In this condition, the port-2 is open-circuited and the below figure shows this condition. because of the open-circuit, the current I_{2}=0.

Now put the value of I_{2}=0 in the eq-(2)

As we can see, the value of the Z parameter is a ratio of voltage and current. Hence, this parameter is also known as the Impedance parameter. Hence, the unit of all Z parameter is ohm.

## Reciprocity Conditions for Z Parameter

A network is said to be reciprocal if the port-2 voltage is due to applied current at port-1 is the same as the port-1 voltage when the applied current is the same as port-2.

Generally, the network that consists of passive elements (resistor, inductor, and capacitor) only, that network are reciprocal networks and the network that consists of the active element (transistor or generator), that networks are not a reciprocal network.

Consider the below figure for the first condition,

From above figure,

Now, put these values in eq-(2),

Hence,

Now,

Consider the below figure for second condition,

From equation-2;

For condition of reciprocity,

This is the condition for reciprocity for Z parameter.

## Symmetry Conditions for Z Parameter

The electrical network is said to be symmetrical, if the input impedance is equal to the output impedance. It is not necessary that, this circuits are physically symmetrical.

Consider the below figure for the first Symmetry condition of Z parameter,

Put these values in the main equations of Z parameter.

Now, consider the below figure for the second Symmetry condition of Z parameter,

Put these values in the main equations of Z parameter.

The impedance of both ports must be equal to fulfil the condition of symmetry. Hence,

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