The general form of the Rapp input-output relationship can be used for memoryless nonlinearity and it is described by :
where x(t) and y(t) are the model’s input and output signals, respectively. a is a positive smoothing factor, xsat is the input saturation value, and Gss is the small-signal gain. Note than when а к, 0, the model approaches the soft limiter’s behavior; and when а к to, it approaches the hard limiter behavior.
This model was found to be suitable for SSPAs. Figure 4.16 shows the characteristics of the Rapp model for different values of a.
Figure 4.16 Rapp model characteristics for different smoothing factor a
Figure 4.17 AM/AM and AM/PM characteristics of the White model
The White model has been proposed for baseband modeling of complex gain nonlinearities . The AM/AM and AM/PM functions of the model are shown in Equations 4.46 and 4.47, respectively:
where |y(t)| and A are the magnitudes of the output and input signals, respectively. a, b, c, d, f, g, and h are the model coefficients. Figure 4.17 depicts a sample of the output voltage and the phase shift predicted by the White model.