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; xsat and ysat 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 ysat is the output saturation value, xsat 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.
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. yx, y2, a1, and a2 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, a1 = 2.2689, and a2 = 0.8234.