TABLE OF CONTENTS In this chapter we describe methods for simulating the nonlinear behavior of RF amplifiers. We include the traveling wave tube (TWT) amplifier commonly used on communication satellites, and model a mixer spur chart.
The simplest model of a nonlinear amplifier is given by the transfer function
where a is the linear gain term. The standard specification of the nonlinearity is called the third order two-tone intercept point, IP 3. To see what this means, we take the input signal x as the sum of two equal amplitude sinusoids (tones)
and see what y looks like. The result is
Now we substitute the three standard trigonometric identities:
then gather terms of the same frequency. The result is summarized in Table 11.1. The following notation applies: x=2 ?f 1 t, and y=2 ?f 2 t. In addition, we used frequencies f 1=10 Hz and f 2=11 Hz to make things more specific.
| Coefficient | Harmonic Term | Value (Hz) |
|---|---|---|
| aA+3cA 3/4 | sin( x) | 10 |
| aA+3cA 3/4 | sin( y) | 11 |
| ?3cA 3/4 | sin(3 x) | 30 |
| 3cA 3/4 | sin(3 y) | 33 |
| 3cA 3/2 | cos(2 x y) | 9 |
| 3cA 3/2 | cos(2 y x) | 12 |
| ?3cA 3/2 | cos(2 x+ y) | 31 |
| ?3cA 3/2 | cos(2 y+y) | 32 |
In the general case with higher order nonlinearities, the procedure shown above...
