# Cartesian Saleh Model

In the quadrature representation, the output of the quasi-memoryless nonlinear system is represented by Equations 4.5-4.9. The in-phase and quadrature nonlinearities, *Gj(A)* and Gq(A), respectively, are given by:

As with the polar case, the coefficients in Equations 4.34 and 4.35 are also determined by a least-squares fit; and, it has been shown [10] that the resulting functions provide excellent agreement with several sets of measured data from TWTAs.

Similarly, the model can be made frequency-dependent by adding filters that mirror how the coefficients change with frequency leading to the frequency-dependent model coefficients *aj(f), p!*(f), Uq(f), and Pq(f).

**Figure 4.9 **Saleh model with parameters: *a _{a}* = 2.1587, = 1.1517,

*а*= 4.033, and

_{ф}*?*9.1040

_{ф}=**Figure 4.10 **Complex gain profile for Saleh model with parameters: *a _{a} =* 2.1587,

*fi*1.1517,

_{a}=*а*4.033, and

_{ф}=*р*9.1040

_{ф}=# Frequency-Dependent Saleh Model

Until this point of the chapter, the models discussed consider the characteristics of TWT amplifier as frequency independent. However, for broadband input signals driving limited bandwidth TWTA and/or other components of the transmission chain, a frequency-dependent model is required. In such case, the power and frequency-dependent in-phase and quadrature nonlinearities, *G*_{i}*(A,*f) and *G*q*(A,f)**, *respectively, are given by:

where *a _{j}*(

*f*), fa(

*f*),

*aQ( f)*

*,*and

*Q f)*are determined by curve fitting at each frequency while sweeping the amplitude of the input signal.