# Simulate power of intermodulation products

I would like to predict if in- and out-of-band interference will hurt my ability to read signals in the 902-928MHz spectrum.

I recorded the maximum received interference power from 10MHz to 3GHz with a spectrum analyzer connected to my antenna. I think if I model the input to my system as a two-tone signal made of the $i^{th}$ interferer and my desired signal, I will be able to predict the power of each of the intermodulation products and harmonics in my spectrum.

For example, with an uneven two-tone input to a non-linear system, the second-order IM products will be:

$$V_{in} = Acos(\omega_1 t) + Bcos(\omega_2 t) \\ V_{out}(x) \approx a_0 + a_1 x + a_2 x^2 + a_3x^3 \\ V_{out, 2nd}(x) = (1/2~a_2A^2)cos(3\omega_1 t) + (1/2~a_2B^2)cos(3\omega_2 t)$$

However, I am not sure how to translate the last formula to "real life". The spec sheet for an LNA has measures like the IIP3 point, not the non-linear coefficients $a_0, a_1$. I did find a formula to estimate the power of the 3rd order IM products, using the IIP3:

$$P_{out} = 3 P_{in} - 2 IIP3$$

Is there an IIP formula for predicting the power of other IM products and harmonics? Failing that, is there a way to simulate the power of all the products and harmonics with Matlab's RF Toolbox or Excel?

For context, I am an intern helping design the RF front end for a wireless networking startup. I don't have much experience with RF, but I've been doing some reading on interference and LNA design.

• $a_1$ is related to the linear gain of the amplifier, and $a_3$ can be determined from the IIP3 figure. If I can figure out $a_2$, I think I can model the intermodulation products. Jul 11, 2017 at 1:23

• That would be useful for the second order IM products, and with IIP2 I can derive the $a_2$ coefficient to estimate the other products and harmonics. It looks like amplifier data sheets do not include IIP2, so the most accurate way to find IIP2 would be to measure it. I'm currently simulating the amplifier's response using S-parameters in Simulink. Jul 11, 2017 at 23:22