Intermodulation measurement

Pieter-Tjerk de Boer, PA3FWM web@pa3fwm.nl

(This is an adapted version of part of an article I wrote for the Dutch amateur radio magazine Electron, July 2024.)

When two or more strong signals arrive at a non-linear circuit, such as the amplifier in broadband active antenna, undesired mixing products are generated: that's called intermodulation. This article is about measuring intermodulation, with particular emphasis on the complication that intermodulation can also occur in the signal generators being used.

Measurement method

The figure shows the principle of intermodulation measurement. At left we start with two signal generators, generating frequencies f₁ and f₂ output signals are fed to a combiner, and the joint signal goes to the Device Under Test (DUT). The DUT's output signal goes to a spectrum analyzer, for which nowadays a good SDR can also be used. Ideally, at the output of the DUT we only see the two input signals, but in practice signals on other frequencies appear as well : those are the intermodulation products.

Intermodulatieproducten

Intermodulation products arise on frequencies that are sums and/or differences of the input frequencies. They are of various 'orders': how 'often' the input signals 'occur' in them. An example of such an intermodulation product is f₁+f₁−f₂, that is, 2f₁−f₂. In this example, f₁ occurs twice and f₂ occurs once, for a total of three, making it an intermodulation product of third order. In practice, products of second and third order are most important.

How often a frequency 'occurs' in a frequency formula like 2f₁−f₂ has another important meaning: it tells us something about how the strength of the intermodulation product varies when the input signal of that particular frequency is made stronger or weaker. If we attenuate one input signal by 1 dB, then the intermodulation product is attenuated by as many dB as the number (without minus sign) that's in front of that frequency. So in case of 2f₁−f₂, the intermodulation product increases by 2 dB if we make the f₁ signal 1 dB stronger, but only by 1 dB if we do the same to the f₂ signal. If we make both signals 1 dB stronger, the intermodulation product will become a total of 3 dB stronger, equally much as its order.

(This isn't a coincidence, but follows directly from the math that describes the intermodulation. In the end, every step in the generation of the intermodulation is a multiplication of the voltages involved; so if one of the two input voltages is doubled (6 dB more), and that signal 'occurs' twice in the intermodulation product, then we have a quadrupling (12 dB) of the output voltage.)

Where are the intermodulation products generated?

Unfortunately, intermodulation cannot only be generated in the DUT, but also at other places in the setup, such as in the generators, the combiner, or the spectrum analyzer. In order to still be able to draw conclusions about the DUT itself, it is important to find out where the measured intermodulation comes from. For this, variable attenuators are useful, indicated as V1 through V4 in the figure.

Suppose the intermodulation indeed happens in the DUT. Then if we introduce an extra dB of attenuation at V3, i.e, before the signals reach the DUT, then the intermodulation products will be come 2 or 3 or more dB weaker, as explained above. But after the DUT the intermodulation products are just signals like any other; so if we increase the attenuation at V4 by 1 dB, the intermodulation products will also become just 1 dB weaker. This allows us to verify if the intermodulation indeed happens in the DUT. If the IM products indeed decrease by 2 or more dB when increasing V4 by 1 dB, then apparently the intermodulation happens after V4, so in the analyzer. And if they decay by only 1 dB when changing V3, then they must have arisen before the DUT, for example in the combiner.

The combiner

Of course, one could just use a simple T adapter as the combiner: just connect both generators and the DUT directly. But then less than half of each generator's output power will end up in the DUT: the rest is partially reflected due to the impedance mismatch, and partially ends up in the other generator. That's a pity, since it makes the signal unnecessarily weaker, while we were trying to study how our DUT behaves with strong signals. Even worse, if the signal of one generator reaches the other generator, intermodulation products could be generated in that generator. A good combiner makes sure that the signal from each generator reaches the DUT, but not (or heavily attenuated) the other generator.

But even with an ideal combiner, the signal from one generator can still reach the other. The DUT's input most likely does not have a perfect 50 ohm impedance, so part of the incoming power is reflected by it. For that reflected power the combiner inevitably acts as a splitter: it is divided fifty-fifty between the two generators. Thus, intermodulation can still occur in the generators.

One could prevent this by putting filters between the generators and the combiner, which only pass the respective generator's frequency. But then one could only do measurements at frequencies for which one has suitable filters.

Misleading

Suppose we increase V3's attenuation by 1 dB. The f₁ signal will then arrive 2 dB weaker at the second generator, as it must go through V3 twice, once on its way to the DUT and once again after reflection. Now consider the intermodulation product 2f₂−f₁ arising in the second generator. The f₂ signal is still as strong as before (since it doesn't go through V3), but the f₁ signal became 2 dB weaker. Since f₁ is included once in 2f₂−f₁, this intermodulation product will become 2 dB weaker. On its way to the DUT and the spectrum analyzer it has to pass through V3 once more, and loses another 1 dB there. So in total the intermodulation product as seen by the analyzer became 3 dB weaker.

By our previous argument, we should conclude from this that it arises after V3, even though in fact it arises in the generator, so before V3. So in this case we cannot distinguish between the intermodulation arising in the DUT or in the generator.

Comparing generators experimentally

In view of the above, it's very important to be sure that generators do not produce too much intermodulation when the signal from another generator is fed into their output. Surprisingly though, in the documentation of even professional signal generators this performance is not specified. So we have to try it out ourselves.

In the course of time I've "collected" several signal generators at amateur radio fleamarkets etc. They are all rather older models, from the late 1960s to the early 1980s. That is an interesting time though: in that time, frequency synthesis gradually replaced free-running oscillators, and manufacturers increasingly paid attention to spectral purity. Furthermore, while on the one hand they are already transistorized, on the other hand they can usually be repaired easily, with the detailed service documentation often being available. And they don't need to be bad; the most recent one of them, a Rohde&Schwarz SMPC, in the HF range performs almost as well as current products.

The picture shows my intermodulation measurement setup. At the bottom is the (already 30 years old) spectrum analyzer, in the middle the R&S SMPC, and on top the Marconi TF2002b. That Marconi is still a classical free-running oscillator, not a synthesizer. To study how much intermodulation arises in the generators themselves, they are connected by a simple T-adapter, and there's no DUT.

The next figure shows the measured spectrum, with the Marconi on 6000 kHz and the R&S on 6100 kHz. We clearly see the third-order intermodulation: 2 × 6000 − 6100 = 5900 kHz, and 2 × 6100 − 6000 = 6200 kHz, and also a fifth-order product on 5800 kHz.

These products arise in the generator and not later on in the system. I know this because they become a lot weaker if I use a real coupler instead of the T-adaptor. Also the fact that they are not equally strong hints at this. At later stages, in the DUT or the analyzer, there is nothing which would treat one frequency differently from the other, unless the DUT is or contains a filter. But such a difference is there if the product arises in the generator's final amplifier: it is to be expected that such an amplifier responds differently to a signal injected into its output than into its input, and also the levels are different.

The spectrum picture clearly shows that the third-order product on 6200 kHz is much weaker than on 5900 kHz; so if we use this combination of generators and frequencies, we better measure the DUT's third-order intermodulation on 6200 kHz to be least disturbed by intermodulation that may arise in the generator.

Where exactly does the intermodulation arise?

The spectrum figure also tells us that the R&S itself produces less intermodulation than the Marconi, so is better in this respect. Intermodulation products in a final amplifier are strongest for those products which is of "lower order" in the "foreign" signal. After all, the "foreign" signal arrives at the amplifier via attenuators; an intermodulation product which is of higher order in this signal will get weaker more quickly. In my example, the 5900 kHz product will arise mostly in the Marconi final stage (because 5900 = 2 × 6000 − 6100, so is first order in the (from the Marconi's viewpoint) "foreign" signal).

By the same argument one would expect the 6200 kHz product to arise in the R&S, but also this product turns out to come from the Marconi. I could ascertain this by increasing the Marconi's output attenuator by 1 dB. If the 6200 kHz would arise in the R&S, its level should have decreased by only 1 dB: the "foreign" 6000 kHz signal arrives there 1 dB weaker and the 6200 kHz product is first order in this signal. However, if the product arises in the Marconi, that 1 dB of extra attenuation makes the "foreign" 6100 kHz 1 dB weaker in the Marconi's final stage; the 6200 kHz product is of second order in the 6100 kHz, so should become 2 dB weaker, and then has to pass once more through the output attenuator, for a total reduction of 3 dB. And indeed, I measure 3 dB.

Different final amplifier stages

The next figure shows two more generators from my collection: synthesizers made by Schlumberger, the FS-30 and the FSO-30/100. This gives me more combinations of generators to try, and in these tests it turns out that the SMPC and the Schlumberger FS30 produce much less intermodulation than the other two. Furthermore, above 21.25 the SMPC suddenly becomes much worse. Apparently, from all of these generators, the FS30 is the best, at least in terms of intermodulation. That's not bad, given that's it's also the oldest, designed way back in 1967!

What causes this large difference, and why does the SMPC become so much worse above 21.25 MHz? To start with the latter: the SMPC has two final amplifiers. Below 21.25 MHz it uses a balanced amplifier stage, and above that a stage with a single transistor. The Marconi also has a single-transistor output stage, while the FS30 has a balanced amplifier, of which the schematic is shown in the next figure. The conclusion seems clear: a balanced output stage gives much less intermodulation.

And that's explicable by the balanced amplifier's symmetry. Suppose the externally applied signal somehow influences the stage's amplification. Because of symmetry, that influence must be the same in the positive and negative peaks. As a consequence, the amplification varies at double the frequency of the external signal; or, stated differently, intermodulation products which are of odd order in this signal are suppressed extra by the symmetry.

I tentatively built a copy of the FS30's output stage, albeit with modern transistors: BC546 and BC557 in the first stage, and 2N2219 and 2N2905 in the final stage. Connecting this after the Marconi, it hardly gives any intermodulation, confirming the hypothesis.

B.t.w., the combination of transistors in the FS30's schematic is odd: both PNP transistors are germanium types, and both NPN transistors are silicon. Usually in such a balanced circuit one tries to use complementary transistors, but that didn't happen here. The 2N2219's complementary PNP partner is the 2N2905, and that transistor already existed at the time this apparatus was designed; still, the designers chose not to use it. Also the rest of the generator contains mostly germanium transistors; apparently in 1967 that was still the most suitable (cheapest?) choice.

Automatic level control

Intermodulation can arise in the generator not just directly in the final stage, but also indirectly via the automatic level control. Signal generators often feature a diode detector which measures the signal amplitude at the output, and use this to control the amplification of an earlier stage to stabilize the output amplitude. When a "foreign" signal arrives at the output, it will also contribute to the measured amplitude. The total amplitude will go up and down at the beat frequency, i.e., the frequency difference between both signals. If the control system tries to correct for this amplitude variation, it will effectively modulate the generators own signal at that beat frequency: that's also a form of intermodulation. On the other hand, the control loop has a limited bandwidth: very fast amplitude variations cannot be corrected. So the problem will only occur if the frequencies of both generators are close.

This is very noticeable when using the R&S above 21.25 MHz: its intermodulation reduces stubstantially (but remains worse than the FS30's) if I separate the generators by a MHz instead of a few kHz. For the Marconi, this makes only a few dB of difference, so there apparently the control loop doesn't contribute much to the intermodulation. Below 21.25 MHz the R&S measures the level before the final amplifier, and is therefore not affected by the the "foreign" signal; and the Schlumberger FS30 simply doesn't have an an automatic level control at all.

Conclusions

1. For intermodulation measurements it's important two use generators of which at least one produces little intermodulation, even if using a good combiner (because of reflections against the DUT).
2. It can be handy to use two different types of generator, as asymmetry immediately reveals that the intermodulation arises in the generators rather than the DUT.
3. Manufacturers do not tell how good their generators are in this respect; one has to try oneself.
4. Balanced final stages seem to be much better than single-ended stages, and can easily be built for use after a not-so-good generator.

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Text on this page is copyright 2024, P.T. de Boer, web@pa3fwm.nl .
Republication is only allowed with my explicit permission.