The equivalent circuit of the z parameter model

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We are now almost in a position to draw an equivalent circuit for the black box

containing the transistor. But before attempting this, let's note that the term

z 12 I 2 is an input voltage source whose magnitude depends upon the output

current, and the term z 21 I 1 is an output voltage source which is dependent upon

the input current. The parameter z 12 represents a reverse trans-resistance

which connects output to input, whilst the term z 21 represents a forward transresistance connecting input to output. (It is, incidentally, the property of z 21 in

linking input to output which has given the transistor its name, i.e. from 'transresistance'.)

In fact, z 21 I 1 represents feedforward and z 12 I 2 feedback. The two

voltage sources are represented by voltage generator symbols in the equivalent

circuit, as shown below.

Having made this point, let's now try and draw an equivalent circuit. This can

be done by applying Kirchhoff's voltage law to the equations. Consider the

input equation

The voltage V 1 is equal to the sum of:

(i) a voltage derived from a current I 1, flowing through a resistance z 11

(ii) a voltage generated from the generator z 12 I 2.

Thus, the input circuit can be represented as shown below

Note that the circuit forms a Thévenin equivalent, and that z 11 represents the

input resistance to the black box with the output open circuit (so that I 2 is

zero).

Now consider the output equation:

The output voltage can be seen to be the sum of:

(i) a voltage generated by the voltage generator z 21 I 1

(ii) a voltage derived from a current I 2 flowing through a resistance z 22.

Thus, the output circuit can be represented as

Note that the circuit forms a Thévenin equivalent circuit and that

z 22 forms the output resistance of the box, with the input open circuit. Also

note again the direction of I 2. It is assumed to be flowing into the circuit.

The two circuits can now be combined to give a complete equivalent circuit:

This is the z equivalent circuit for our two port black box containing the

transistor.