# Limiter Model

The ideal limiter (clipping) model AM/AM relationship can be expressed as:

where *x(t)* and *y(t)* are the baseband input and output signals, respectively; *x _{sat}* and

*y*are the input and output saturation (clipping) levels, respectively.

_{sat}**Figure 4.13 **AM/AM and AM/PM characteristics for TWTA modeled using the Thomas-Weidner- Durrani model

The general limiter model baseband input-output relationship can be used for resistive memoryless nonlinearity that has no phase distortion and it can be described by:

where *y _{sat}* is the output saturation value,

*x*is the input saturation value and

_{sat}*s*is the compression shaping parameter. Note that s « 0 corresponds to a soft limiter and

*s*«то corresponds to a hard limiter. Figure 4.14 shows the limiter characteristics for different values of the parameter

*s*.

# ARCTAN Model

The general form of the ARCTAN (arctangent) bandpass input-output relationship can be used for memoryless nonlinearity and it is described by:

where *A* and *в* are the amplitude and phase of the input signal *x(t)* as defined in Equation 4.1, respectively. *y _{x}, y_{2}, a_{1},* and

*a*

*are the model coefficients. Figure 4.15*

_{2}Figure 4.14 Limiter characteristics

Figure 4.15 ARCTAN model characteristics depicts the AM/AM characteristics of the ARCTAN model for *y* = 8.0035 - j4.6116, * _{Yl} =* -3.7717 + j'12.0376,

*a*

*= 2.2689, and*

_{1}*a*

_{2}*=*0.8234.