The nonlinear voltage transfer characteristic for a TWT can be written as a power series

The third-order term gives rise to the intermodulation products. To illustrate this, let the input be two unmodulated carriers

and let the carrier spacing be ? ? as shown in Fig. E.1. The terms on the right-hand side of the transfer characteristic equation can be interpreted as follows:

Figure E.1

First term , ae _i . This gives the desired linear relationship between e _o and e _i.

Second term , . With e _i as shown, this term can be expanded into the following components: a dc component, a component at frequency ? ?, second harmonic components of the carriers, second harmonic + ? ? components. All these components can be removed by filtering and need not be considered further.

Third term , . This can be expanded as

The cubed terms in this can be expanded as

that is, a fundamental component plus a third harmonic component. The third harmonics can be removed by filtering.

The intermodulation products are contained in the cross-product terms 3 A ² B cos ² ? _A t cos ? _B t and 3 AB ² cos ? _A t cos ² ? _B t. On further expansion, the first of these will be seen to contain a cos(2 ? _A ? ? _B) t. With the carriers spaced equally by amount ?