Image Impedances

The image impedances of a transducer are defined¹ as the "impedances which will simultaneously terminate each pair of terminals

Figure 17. Actual and equivalent circuits for a transformer.

of a transducer in such a way that at each pair of terminals the impedances in both directions are equal."

An unsymmetrical, unbalanced T network is shown in Fig. 18, the network being unsymmetrical because Z₁ does not equal Z₂. It is desired to find the two image impedances Z_I and Z_I' that

Figure 18. Circuit for studying image impedances.

will satisfy the definition previously given. If this is accomplished, then maximum power transfer would occur from the transducer to the impedance (or from the impedance to the transducer) at either set of terminals.

The equations for the image impedances can be written for the conditions specified in the definition. Thus, the input impedance at terminals 1-2, with image impedance Z_I' connected at terminals 3-4 (but with Z_I not connected), is

The input impedance at terminals 3-4, with image impedance Z_I connected at terminals 1-2 (but with Z_I' not connected), is

When these two equations are solved, the image impedances are found to be

and

It is also possible to write equations for the image impedances of a π section; or the π section can be transformed into a T section, and equations 43 and 44 then used. An investigation will disclose that unsymmetrical networks have impedance-transforming properties and that they can be used for impedance matching.