Appendix 3A. Intermodulation Distortion Formulas

In the weak and memoryless nonlinear case, we can use power series to model the nonlinearity of a device such as an amplifier or a mixer. If the input signal and output signal power of the device is P _i and P _o, respectively, then the output of the nonlinear device can be represented by its input as follows:

(3A.1)

where g _m ( m = 1, 2, , n) is the power gain when m =1, and the nonlinear gain coefficients when m ? l, and P _m, is the m-th order distortion power of the total output power P _o, and it is related to the input signal power P _i as

(3A.2)

The power P _i, P _o, and P _m ( m = 1, 2, , n) all are in natural scale. In the output terms of (3A.2), let us to look at two special cases i.e., the fundamental term and the mth order term as follows:

(3A.3)

and

(3A.4)

In fact, (3A.3) describes the linear relationship between the output and input, and (3A.4) is a generic high-order distortion representative. Converting (3A.3) and (3A.4) into dB scale, we obtain

(3A.5)

and

(3A.6)

where

Equation (3A.5) and (3A.6) represent two straight lines in the output power vs. input power plan as shown in Fig. 3A.1.

Figure 3A.1: Fundamental and mth order intermodulation distortion response