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_{sat} are the input and output saturation (clipping) levels, respectively.

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_{sat} is the input saturation value and 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_{2} are the model coefficients. Figure 4.15

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_{1} = 2.2689, and a_{2} = 0.8234.