## Wednesday, March 18, 2009

### Intermodulation Distortion by Lee Bond, N7KC

For the 43rd session of the Educational Radio Net, I have chosen to continue a review of basic and important concepts that cannot be avoided when dealing with radio equipment. Earlier sessions dealt with the relationship of energy, power, time, voltage, current, and resistance. The 13 parts of the Impedance series is a good starting point for individual review. Check the blog if you are interested in rehashing earlier material. This week I will delve into the subject of intermodulation distortion.

The 38th session looked at harmonic distortion in detail. I think it will be useful to review a bit of that material so that we can contrast harmonic distortion and intermodulation distortion. First, harmonic distortion is a single frequency process in contrast with IMD which is a multiple frequency process. An amplifier designed for high fidelity is expected to be completely linear in the sense that output signals are expected to be simply larger versions of the input signals. For example, an amplifier with a gain of 3 is expected to treat all input signals… regardless of frequency or phase… in the same manner. The output signal should match the shape of the input signal except for size.

There are two approaches to understanding harmonic distortion. The most elegant and more difficult is the mathematical process to analyze the effect. The second and less difficult is the empirical look at what happens when non linear amplifier processes distort the input signal. Initially lets take the empirical path and assemble on our bench an amplifier, either audio or RF… it makes no difference in what we will see... , a signal source, and a spectrum analyzer. First we look at our signal source with the analyzer and notice that it is a perfect sine wave of frequency f. The analyzer shows a single vertical line at frequency f and looking around we see no energy at multiples of frequency f over the expected range of frequencies and amplitudes that we plan to use in the demonstration.

Now connect the spectrum analyzer to the amplifier output along with a suitable load. Adjust the signal generator output level about mid range and connect it to the amplifier under test. The good news is that the spectrum analyzer shows a single vertical line in response to the input signal. Now, lets slowly increase the amplitude of the input signal within its known ‘perfect’ range while observing the analyzer. All of a sudden a second line appears to the right of the input signal… in fact at exactly twice the frequency of the input signal. This is not good news. Continuing on with increasing the input signal amplitude we notice a third signal pop up and this one is exactly three times the frequency of the input signal.

What we are observing is the practical ramifications of an amplifier being driven into some non linear region. Engineers describe the relationship between output signal and input signal as a ‘transfer function’. If the transfer function is a straight line… as in linear amplifier… then the signal, or multiple signals, will not mutually interact within the amplifier and the output will appear as distinct output signals on the analyzer. Departures from linear move toward a ‘square law’ transfer function and the amplifier output takes on the non linear character of y = x squared. If the single input signal is of the form A sin wt then a linear response would produce 3(A sin wt) if the amplifier gain were 3. When the amplifier is driven into the early square law region then the response becomes (A sin wt) squared and the mathematical result is a frequency doubling function. This is harmonic distortion… a single input signal producing output signals that are integer multiples of the input frequency.

Ok, enough of this harmonic distortion business. Lets do another demonstration with the same amplifier and input signal source but include a second signal source that is independent of the first. Lets assert that both of these ‘generators’ will produce a very clean signal on a spectrum analyzer. First we will drive the amplifier with source ‘A’ and notice that the amplifier output is well behaved and clearly in the linear region since no 2nd harmonic distortion products show up on the analyzer. Now lets add the higher frequency ‘B’ source to the amplifier input and, again, we see a very nice linear amplifier output signature on the spectrum analyzer. Outputs from A and B are clearly independent since we can vary the frequency of each signal and see the corresponding output signal change frequency in response. So far so good.

Now increase the amplitude of signal A to the point where the amplifier just starts to enter the square law region for signal A. At this point something interesting starts to happen on the analyzer attached to the amplifier output. Multiple output signals show up and they are both harmonically and non harmonically related to each other. The amplifier is now producing harmonic products plus linear combinations of the two input signals so if m and n are integers ranging from zero to two then the output signals will be generally represented by mA +/- nB where n or m can each range from 0 to higher values in integer steps. Given that we only have two signals then m or n cannot both be zero since that would mean that no input signal is present. So, assume m=1 and n=0 or m=0 and n=1 which gives us the first order products of the non linear mix and which are the fundamental input frequencies. Plugging the integer values m=1 and n=1 into the defining relationship gives B-A and B+A or the so called second order products.

Continuing in this manner let m=1 and n=2 (and vice versa) then 4 products of the form A+2B, 2A+b, 2B-A, and 2A+B are produced and which are called the 3rd order products. Notice that the order is the sum of the absolute values of the coefficients. Even order products become very large and are, generally, out of the pass band of interest but odd order products are very near to the fundamental frequencies and can wreck havoc on any desired signal. We are experiencing intermodulation distortion or IMD simply by overdriving the test amplifier with at least two signals present. If the two signals are complex such as speech then the output becomes hopelessly garbled.

How well any particular radio receiver handles large signals in or near the passband is a measure of receiver quality. Receiver manufacturers will quote the third order intercept point to illustrate the receiver dynamic range where more db is better. Receiver dynamic range is the difference between the noise floor performance at a desired frequency and the noise floor measured by tuning to a 3rd intercept point. The bigger the difference the better the receiver can handle large in band or near band signals without overloading.

Of particular interest is the fact that any rectifying junction is, by definition, nonlinear so dissimilar metals, corroding junctions, etc. can produce IMD in the presence of at least two strong RF signals. Repeaters without circulators can be a source of IMD since many repeaters live in the vicinity of powerful commercial transmitters and RF energy near the cavity passband can enter the final amplifier and mix with the repeater frequency to produce very nasty distortion products. Modern broadband receivers are particularly prone to IMD since they freely pass energy to the input stages that would never make it through highly selective circuitry as found in narrow band equipment.

This concludes the set up discussion for intermodulation distortion. Are there any questions or comments with regard to tonight's discussion?

This is N7KC for the Wednesday night Educational Radio Net

#### 1 comment:

Michelle said...

Hi Lee, Looking for your email or phone # to talk about Dave's birthday present (computer program to communicate with his ICOM for inputting settings????).
Thanks! Michelle - KE7HVG