## Monday, September 07, 2020

### An Intermodulation Primer

Even though you probably have not heard of Intermodulation distortion, you have already heard intermodulation distortion (IMD). But this is something you might not readily recognize in all it's multifaceted forms. Engineers work to minimize IMD because people find it significant more objectionable than harmonic distortion. (Be aware that this is a somewhat contention topic but explaining why is complicated because of semantics and physics.) This gets mathy but I'm going to steer away from the graphing calculator an try to keep this human-readable.

Let's start with the cause of intermodulation distortion. There is only one direct cause: the non-linear behavior of the signal processing equipment or algorithms. But indirectly it's the nonlinear input of that equipment or algorithm causes it to output that intermodulation distortion. That troublesome input is a "nonlinearity."  That definition is unfortunately very circular.  But in that nonlinear relationship, the output is not proportional to the input. This may be phrased that change in the input signal is not proportional to change in the output signal. That's semantics.  This is literally all that defines nonlinearity. That nonlinear input can just be a time variance, or multiple signal input. This may for example create a harmonic in the output audio to be filtered away like just another spurious signal.
 from Discogs.com
There are reasons why intermodulation distortion is more abrasive to the human ear than harmonic distortion. A nonlinearity (like nonlinear electrical loads) produces harmonic distortion when driven by a single sine wave with a single frequency ('pure' singe wave). That same nonlinearity produces IMD when driven by anything more complex than a single pure sine wave. But do you ever have a pure sine wave in the real world?  Nope. Pure Sine waves exist in hypothetical math to help people like me learn how to run functions on a graphing calculator. Intermodulation distortion is what harmonic distortion becomes when you leave the lab and enter the real world. In application there are many types of IMD, below are three types which you can readily identify with your car radio:

Cross Modulation
When you are listening to a distant FM station while driving past AM station's radio tower you can sometimes year both stations.  That is Cross Modulation, a fun form of IMD. An FM receiver is designed to receive one station at a time (See capture effect below). So if you get two FM signals it will only demodulate the stronger of the two. But in this example we have one AM and one FM.  The FM signal still enters the circuit through the front door. But with such close proximity the receivers RF amplifier acts as a rectifier varying its bias point. The amplifier's gain changes rapidly because of the two signals effectively modulating the distant FM station's signal at the rate of the AM signal. That mixed signal is then processed by the receivers demodulator as an FM signal having two audio messages superimposed one on the other.

Capture Effect
Remember that FM receivers are designed to receive one station at a time?  That's largely controlled with the Capture Effect In FM receivers.  When fed two FM signals, the Demodulator will only extract (capture) the strongest of competing signals. But some FM receivers have a weak point. When driving between two FM transmitters on the same frequency somewhere around the midpoint (depending on signal strength) the captured station will alternate sometimes so rapidly that it sounds as if they are both being demodulated.

Multi-Path Interference This type of IMD is most common in the downtown area. To a degree, radio signals reflect off of flat hard surfaces. So when you drive down a street and turn a corner at the intersection the Capture Effect is alternating between different reflected signals off of the buildings, changing in both amplitude and phase sometimes cancelling and sometimes combining as you navigate. This creates interesting audio artifacts, and noise.