Electrical Element - Two-port Elements

Two-port Elements

All the above are two-terminal, or one-port elements. There are two lossless, passive, linear two-port elements that are normally introduced into network analysis. Their constitutive relations in matrix notation are;

Transformer

Gyrator

The transformer maps a voltage at one port to a voltage at the other in a ratio of n. The current between the same two port is mapped by 1/n. The gyrator, on the other hand, maps a voltage at one port to a current at the other. Likewise, currents are mapped to voltages. The quantity r in the matrix is in units of resistance. The gyrator is a necessary element in analysis because it is not reciprocal. Networks built from the basic linear elements only are obliged to be reciprocal and so cannot be used by themselves to represent a non-reciprocal system. It is not essential, however, to have both the transformer and gyrator. Two gyrators in cascade are equivalent to a transformer but the transformer is usually retained for convenience. Introduction of the gyrator also makes either capacitance or inductance non-essential since a gyrator terminated with one of these at port 2 will be equivalent to the other at port 1. However, transformer, capacitance and inductance are normally retained in analysis because they are the ideal properties of the basic physical components transformer, inductor and capacitor whereas a practical gyrator must be constructed as an active circuit.