# How Do Intermodulation Products Manifest in Transmitting Equipment?

1. Intermodulation products manifest in receiving equipment as a result of several near-by transmitters, each operating at different carrier frequencies, mixing at the receiving antenna.
2. The signal sensed at the receiving antenna produces an alternating current that contains a mix of each carrier frequency (plus harmonics thereof, for each carrier).
3. Presuming that frequency selective components before the RF amplifier don't attenuate the power at each carrier too much, non-linearities in the RF amplifier will produce intermodulation products at frequencies which are linear combinations of each input carrier.
4. Some of these intermodulation products fall near the receiver's tuned bandwidth, creating undesired power in the side-band (which is why it's worth modeling intermodulation effects).

# But...

However, I've learned that transmitter intermodulation products can be important to model as well. How do these intermodulation products manifest themselves in a victim transmitter?

Let's consider a two-carrier mix at the input of the RF amplifier (block diagram shown below).

The first carrier is easy to explain: it is passed through the IF-stage into the RF-stage, to the input of the RF amplifier. However, there are only two possible routes for the second carrier to be passed to this victim transmitter's RF amplifier:

• The second carrier penetrates the victim transmitter's casing (seems nearly impossible, saying that a Faraday cage sole purpose is to attenuate external radio signals)
• The second carrier impinges on the victim transmitter's antenna, producing an alternating current that is passed through the output of the amplifier into its input (seems more likely, since there wouldn't be any protective casing over an antenna)

producing an alternating current that is passed through the output of the amplifier into its input

So far, I've accepted this as an explanation for how these IMPs manifest themselves in a victim transmitter. But, I realize that it's very hand-wavy. Can some provide a more technical explanation of this, if my understanding is even correct?

There are essentially two mechanisms:

1. Internal nonlinearities, arising from non-ideal behaviour of mixers and amplifiers.

When passed through a nonlinear device, a modulating signal containing F_1 & F_2 can produce an output signal with side bands located at: $$\{F_1, F_2,\\ (F_1+F_2), (F_1-F_2),\\ 2*F_1, 2*F_2,\\ 2*F_1+F_2, 2*F_2+F_1,\\ 2*F_1-F_2, 2*F_2-F_1,\\ 3*F_1, 3*F_2\\ ...\}$$ Even though we want mixers that are multipliers they're often closer to Taylor series, and only approach being multipliers for a given signal domain. We also want linear amplifiers, but we also want them to be efficient and cheap... that is a tricky, tricky mix.

1. Effects due to externally applied RF.

Power amplifiers are sensitive to energy applied to the output and particularly when operated close to or in saturation, they can look an awful lot like a switching mixer if you squint just right, so again you can get sum and difference series produced. This is an especially good party trick on a shared mast with multiple co-located services where adding a transmitter can cause one that YOU do NOT own, to interfere with another receiver that you ALSO do not own... That can get amusingly political. I have had LOTS of fun with this when co-locating low band VHF kit.

Power amplifiers are sensitive to energy applied to the output.

To expand on this detail (from discussion in comments): It all boils down to the non-linear curve that describes the input-output relationship of an amplifier. When a voltage is introduced at the output, you're modifying that relationship. Thus, the resulting inter-modulation products observed at the output contain the sum & difference of every multiple of the frequencies introduced at either the input or output.

• I appreciate your reply, #2 contained some useful information! "Power amplifiers are sensitive to energy applied to the output"; that's an interesting statement. Do you mean that regardless whether energy is applied at the input or the output of the amplifier, a different Taylor series is observed at the output of the amplifier? In your words, does "externally applied RF" equate to what I said about an interfering transmitted signal impinging on a victim transmitter's antenna? – Vladislav Martin Jun 14 '17 at 2:55
• Yea, usually it takes quite a lot of third party signal at the antenna for this to be significant, but if you have multiple transmitter antennas on the same mast, along with repeater receivers it can become a real issue. – Dan Mills Jun 14 '17 at 8:54
• If what I said sounds right, then - first, YAY! - and second, would you mind if I edited that bit into your answer so that I can accept it? – Vladislav Martin Jun 14 '17 at 20:38
• Not just the frequencies introduced at the input and output, but all the IM products of all those frequencies! The levels are low but if you get unlucky you can swamp a nearby receiver. And yea, go ahead and edit if you like. – Dan Mills Jun 14 '17 at 22:21

Consider a broadband signal, say 5MHz wide, centred around a frequency of fc. Consider some energy at at fc-2.5, and some energy at fc-1.5. These two components will intermodulate to produce products at fc-4 (carrier spread) and fc-1 (which will interfere with the energy that should be there).

You do not need two explicit carriers for intermodulation to take place, you only need energy at different frequencies. Obviously both transmitter and receiver need to pass wideband signals like this, so both will suffer.

For economy, modern transmitters tend to produce several carriers through the same signal chain, usig for instance a 20MHz wide bandwidth to generate 4 adjacent 5 MHz bands. This maks the problem worse at transmitters.

• Thanks for the concise reply! Right, modulated carriers can have fairly complex spectra (definitely more than just a tone), with power concentrated in a main band and several prominent side bands that are all adjacent and within the transmitter's bandwidth. I guess it's fair to say this is the more likely case, but, that doesn't satisfy the particular case I described. Is that because what I described is so rarely considered & "transmitter intermodulation" almost never refers to my described case? – Vladislav Martin Jun 13 '17 at 20:38