# Rapp Model

The general form of the Rapp input-output relationship can be used for memoryless nonlinearity and it is described by [14]:

where *x(t)* and *y(t)* are the model’s input and output signals, respectively. *a* is a positive smoothing factor, *x _{sat}* is the input saturation value, and

*G*is the small-signal gain. Note than when

_{ss}*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

# White Model

The White model has been proposed for baseband modeling of complex gain nonlinearities [15]. 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.