# Four-terminal circuits Four-terminal is an abstract element of an electrical circuit, having four terminals – two-input and two-output. The four-terminals are shown in the scheme in Figure 1. If the four-terminals contain energy sources, it is called active for-terminal and marked with an A letter. If not it is called passive four-terminal.

As shown in the Figure 1, U1 and I1 are input voltage and current, U2 and I2 are output voltage and current. A four-terminal circuit is usually connected to load and source. The load and source parameters can be varied, but four-terminal characteristics do not vary. Parameters of passive four-terminals can be expressed with six equations, and every equation can be used in certain situations, depending on the four-terminal input data. These equations can be seen below: You can see that for the first equation, the positive direction of the current and voltage is depicted in Figure 2a; for equations 2, 3, 4 and 5 the positive direction of current and voltage is depicted in Figure 2b; for the last equation, the positive direction of current and voltage is depicted in Figure 2c. The four-terminal is symmetrical; if we change the source and load, the currents and voltages in four-terminal circuits won’t change direction. Figure 2. Positive directions of currents and voltages for different types of equations for four-terminal circuits

Passive four-terminals can also be replaced and simplified using the star or delta equivalent schemes, as shown in Figure 3. Figure 3. Delta and star types of equivalent schemes for four-terminals

The transformations between equation coefficients for four-terminals can be given without intermediate conclusions.

Different four-terminal equations can be used depending on the situation. For example, for the synthesis theory, Y and Z equations are usually used. For transistors Y, H and Z equations forms are good.

When the task is to find the input and output currents and voltages, we can use combinations of different forms of the equations. When four-terminals are connected, as shown in Figure 4a, its good to use Z-form of equations. When four-terminals are connected like in Figure 4b, it’s good to use Y-form. When the four-terminals are connected like in Figure 4c, it’s good to use H-form equations. When the four-terminals are connected like in Figure 4d, it’s good to use G-form. When the four-terminals are connected like in Figure 4e – it’s good to use the first form of equations.

The equations above also can help us to calculate attenuation or amplification of the four terminal circuit: $a=lg\frac{{S}_{1}}{{S}_{2}}=2lg\frac{{U}_{1}}{{U}_{2}}$ (Bells), if the load is coordinated across the four-terminal circuit.