A mathematical model of the box

In order for our black box to be of any use as a model of an amplifier (or any

other type of system), we have to establish some mathematical relationship

between input and output. There are a number of ways of doing this. For

example, we could write:

where z 11, z 12, z 21 and z 22 are the circuit's parameters. A parameter is a

quantity upon which the characteristics of the circuit depend. In mathematical

jargon, the parameters are coefficients used in the pair of simultaneous

equations which relate the external voltages and currents. The subscripts

indicate if the parameter is a property of the input circuit (z 11), output circuit

(z 22) or if the parameter links input to output (z 21) or output to input (z 12).

The first equation of the pair is the input equation and shows how the input

voltage is related to the input and output currents.

The second equation is the output equation and shows how the output voltage

is related to the input and output currents.

Note that in the two equations, the left-hand term is voltage and will therefore have the units of volts.

Thus, the term z 11 I 1 which occurs in the right-hand side of the first equation must also have units of volts.

If the transistor is operated at 'low frequency' these impedances can be

regarded as being purely resistive. In this context 'low frequency' is up to a few

hundred kilohertz. W e shall assume such frequency limitation

applies so that all the z parameters are resistive.

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