# How should I scale intermodulation products?

I'm trying to automatically measure the amount of intermodulation based on a broadband spectrum capture(which is averaged over time). There is a given set of reasonably narrowband carrier waves, which are always present. If there's a non-linearity in the RF-path, such as a rusty bolt(which is basically a point contact diode) or an amplifier that's over/under driven, these will produce a set of intermodulation products.

So far, I've managed to automatically calculate the composite second order(CSO) and composite trible beat(CTB) frequencies. The thing is: a lot of CSO/CTB frequencies are exactly the same. So there are e.g. 10 CSO products at 622.25 MHz and 2 CTB products at 623 MHz. But that means they scale differently.

My idea to detect intermodulation is to numerically integrate the received power in a very narrow bandwidth around the precalculated CSO/CTB frequencies and try to find some thresholds for the result of that integral.

My question is: how should I scale n CSO/CTB-products that come together in a single point? Should I just subtract 10*log_10(n) dB from that datapoint? Should I also include scaling for the binomial coefficients of the CSO/CTB products?

Side question: are typical nonlinear distortions very frequency dependent? If yes, I would imagine that scaling for the number of products won't be very significant.

• Are you aware that CSO and CTB are just ways of describing 2nd and 3rd order distortion ? You're unlucky that the frequencies are the same, this can be the result of your narrow band input signal. CSO/2nd order components scale 2dB per dB of input signal, CTO/3rd order scale 3dB per dB. Nonlinear distortions are not frequency dependent assuming the system by itself is not frequency sensitive (i.e. has a small bandwidth). Commented Aug 28, 2017 at 14:28
• The frequencies are the same because the set of known carriers occur in a fairly regular pattern. Other question: what exactly do you mean by 2 dB per dB of input signal? Also: the system is definitely not narrow band, the measured band can go from 40 MHz to 1 GHz at a resolution of 10 kHz. Commented Aug 28, 2017 at 14:36
• Then you should space those carriers differently so that they and up at different frequencies. 2dB per dB for 2nd order means that if you increase the input signal by 1 dB the 2nd order frequency components will increase in power by 2 dB (assuming you're not close to compression yet). Commented Aug 28, 2017 at 14:38
• The carriers cannot be spaced differently, the spectrum plan is very much set in stone. Commented Aug 28, 2017 at 14:41
• OK, but just as a test, would you be able to input just one carrier into the system and observe the resulting output. The response to all those combined carriers should be the same as the sum of the individual responses. Commented Aug 28, 2017 at 14:50

What you can do -----reduce the power levels by 6dB or 10dB or 20dB.

If the spur drops exactly double the amount of power reduction --- the spur is 2nd order.

If the spur drops exactly triple the amount of power reduction --- the spur is 3rd order.

The spurs generated by overlapping 2nd + 3rd (or higher) are the challenge.

• Altering the incoming signal is out of the question, all my program is allowed to do is observate and analyse, completely non-invasive. Commented Aug 28, 2017 at 20:09
• Then supply an external 600MHz tone (your frequency of choice, power level of your convenience), inject into the input pin. Commented Aug 30, 2017 at 3:49

So I contacted my professor and he mentioned the key aspect which renders this "scaling" useless: the different intermodulation products that coincide at a specific frequency don't necessarily have the same phase.(Simpson's rule affects the frequency as well as the phase). That means the power at a certain CSO/CTB frequency isn't just a simple addition of the power of all individual IM products. They interfere with one another, producing a rather unpredictable end result depending on the phases.

My take-away from this was just to take an average of the power at all CSO/CTB-frequencies. I'll have to do a lot more field testing to see if my method is effective at detecting non-linear distorsions.