Preamplifier and mixer non linearities

Pre-Amplifier and mixer non linearties:  Amplifier types other than the TWTA as well as the mixers used to translate the signal frequencies have nonlinear aspects as well.  Generally the transfer function of such devices is in terms of a polynomial


where the coefficients are chosen to satisfy common figures of merit such as the two tone third order intercept point , IP3.   The coefficient, a, is the linear gain term.  The problem arises when there are two or more input signals in the input x(t) of the form,


 This is common in shared transponder operation where several carriers occupy the usable bandwidth.  Substituting into the above and using standard trigonometric identities show that the output y(t) can have frequencies, intermod products (IM) with  frequency values,where m and n are integers.  Generally the power in the IM product decreases with increasing m and n.  The worst case generally occurs in the so-called third IM product when m = 2 and n = 1 and visa versa. Using figure 2, consider two wideband signals in the uplink to the satellite, one at f1 = 6105 MHz (channel 9 uplink), and one at f2  = 6065 MHz (channel 7 uplink).  The typical satellite employs a wideband frequency-translating receiver that provides about half of the 100 dB total repeater gain. Each pair of carriers creates two third order products: f3 = 2*6105 6065 MHz  = 6145 MHz (uplink channel 11 !!), and f3 = 2*6065 6105 MHz  = 6025 MHz (uplink channel 5).  Figure 4 shows the signal spectra just described.  Careful modeling of these third order and higher IM products is therefore essential. Another requirement is accurate accounting of all such products that can be produced within the transponder bandwidths. Even weak, high order IM products in the wrong place can be disastrous.  We want to insure that the satellite does not jam itself.  This mechanism also affects multiple signals within one channel as commonly employed by single channel per carrier (SCPC) systems.  The analysis above still applies and the IM from two SCPC channels within the transponder can fall into the same transponder.



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