Four-Terminal Networks

Author: Leonard Krugman

In all types of engineering circuit design, it is frequently convenient to represent a device by an electrical equivalent. This invariably eases the task of optimizing the design, since the device is, in effect, reduced to a simpler equivalent form. One of the most useful methods of equivalent representations is by means of the four-terminal network.

The four-terminal network (also called a coupling network, or two-terminal pair network) is shown in Fig. 3-1. Terminals a and b represent the input to the network and terminals c and d the output. The network itself, which represents the equivalent of a device or any combination of devices, is located between the input and output terminals, and is considered sealed, so that electrical measurements can be made only at the input and output terminals.

The sealed network may be, and often is, very complex. As an example, consider the case of relating the acoustical input to a microphone in a multi-link transmission circuit to the acoustical output of a receiver. This system involves transmission lines, electronic circuts, acoustical, electrical, and mechanical power and transducers. In the four-terminal method of analysis, however, the complete intermediate system between the microphone input and the receiver output is represented by the sealed box.

Fig. 3-1. Four-terminal network, conventional designation.

The advantage of this type of representation is that only one basic analysis of a particular device or system is required. Once accomplished, problems involving the same system or device are a matter of routine and become simple substitutions of numbers. For electronic devices, other advantages are that the basic equivalent circuit can be modified to include the effects of high-frequency operation, and that the equivalent circuit invariably contains a minimum number of parameters which can be directly related to external measurements.

Four-terminal networks are divided into two general classifications: active and passive. Passive networks are those that contain no source of energy within the sealed box; currents and voltages within the box are a result of the application of energy to the external terminals. Examples of passive networks include filters, attenuators, and transmission lines. Active networks, on the other hand, do contain internal sources of energy. Examples of these, therefore, include all types of amplifying devices, including the transistor. Although the conventional transistor has but three external connections, four-terminal network analysis is applicable because one of the electrodes is common to both the input and output circuits.

The performance of the transistor can be completely defined by the voltage and current measured at the input and output terminals. Actually only two of the four values are independent, because if any two are specified, the other two values are automatically determined. This situation is exactly the same as that in the conventional triode electron tube, where the four values are the grid current, grid voltage, plate current, and plate voltage. The grid and plate voltages of a tube are usually considered the independent variables, and their respective currents then become the dependent variables.