Impedance Matching

The principle use of transformers is in the transmission and distribution of commercially generated electricity. However, a second, very important use of transformers is as impedance matching devices. Recall, from Sect. 7.9, that for maximum power delivery from a source to a load, the load must have the same resistance as the internal resistance of the source. This can be accomplished by using a transformer to match the two resistances. Suppose that the power source is connected to the primary circuit, and the load to the secondary. If the resistance of the load is $R$, then $R= V_2/I_2$. However, from the transformer equation, (299), we have

$$V_1 = \frac{N_1}{N_2}\,V_2,$$ (301)

and

$$I_1 =\frac{N_2}{N_1}\,I_2.$$ (302)

Now the effective resistance $R'$ of the load in the primary circuit is given by

$$R' = \frac{V_1}{I_1} = \left(\frac{N_1}{N_2}\right)^2\,\frac{V_2}{I_2},$$ (303)

which easily reduces to

$$R' = \left(\frac{N_1}{N_2}\right)^2\,R.$$ (304)

Thus, by choosing the appropriate turns ratio, the effective load resistance $R'$ can be made equal to the internal resistance of the source, no matter what value the actual load resistance $R$ takes. This process is called impedance matching.