(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.
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.)
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.
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.
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.
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.
[measured spectrum] 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.
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.
[Schematic of the FS30's output stage] 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.
[Tentative build of a balanced amplifier] 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.
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.