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Harmonic spurs (harmonics of the transmitter frequency, as seen by a wide-band receiver or SDR) in the RF spectrum might be caused by an imperfectly sinusoidal or badly filtered transmitter carrier frequency oscillator, non-linearities in the transmitter amplifier, or non-linearities somewhere in the receiver before or inside the 1st mixer.

What might be some tests or other means for helping determine where (most of) this harmonic spur problem might be located? Are there any ways to test this without needing to acquire extremely expensive lab equipment? Basically, are the spurs a transmitter or receiver problem? (assuming neither comes with manufacturer specs, e.g. home-built or kit, etc.)

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    $\begingroup$ One easy test is to attenuate the input to the receiver: if a 3dB attenuator attenuates a suspect spur by more (say, 6dB) then this is a sure sign the spur originates in the receiver. The same technique is useful for verifying test equipment. Perhaps you are measuring IMD with a spectrum analyzer (or another radio being used as one) and you want to know if the intermod you are measuring is from the DUT or the analyzer. $\endgroup$ – Phil Frost - W8II Apr 1 '17 at 18:27
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You've nailed this!

So, I'm sometimes involved in these kinds of investigations. It all gets easier when you have control over the transmitter – when some spurs disappear as soon as you turn it off, but others remain, you've ruled out the transmitter as the source of these.

Then, digital receivers typically, as you notice, have different sources of spurs. As I'm usually not at the receiver that is being "debugged", the only way to work with this is really an elimination approach; in no particular order, Problems, the way I'd approach detecting them and some mitigation hints:

Problem sources

Harmonics all over the place: clipping?

Reduce receiver gain. Add attenuator. Can usually (often, depending on the receiver DSP chain) be seen by looking at the numerical values of samples coming from device; it should be $|z| < 1$. If not: Looks like $(1)$

Spurs due to intermodulation of receive signals due to receive (typically: LN) amplifier saturation

Add attenuation in-line to receive antenna. If spurs significantly reduce, we've got this.

LO leakage & DC offset

Typical artifact of all direct conversion receivers. Can (on some SDR peripherals) completely be mitigated by letting the built-in DSP functionality digitally shift the receive signal in frequency prior to decimation, see $(2)$. For a "relatively good" mitigation: a notch HPF directly after the ADC is often part of SDR receivers, too.

Sampling clock spurs

Mixing products of receiver LO and ADC clock. Tune the LO a few Hertz to either side. Do they move, but keep the same distance from LO leakage?

Unwanted LO synth side products

Oscillator synthesizers are impressive devices, which are able to produce a huge number of tones from a single reference oscillator (example: MAX2871). They do that by elegantly multiplying frequencies, and having non-integer multiples through cleverly "jumping" PLLs (keyword: fractional-N PLL). That inherently, however, might produce some frequencies that are not even multiples or integer divisions of the target clock. If you can, try a configuration where you use integer-N tuning only. If that helps, there's your problem. Often, when using a wideband receiver especially if it supports $(2)$, you can choose from a whole range of physical LO frequencies without affecting what part of the spectrum you see. Experiment!

Digital Operating Clocks

SDR devices are digital devices, thus have a lot of square wave clocks... If you see something that happens to be relatively strong, and research shows it's one of $1\cdot f_{clock},\, 3\cdot f_{clock},\, 5\cdot f_{clock},\ldots$, there you go. You'll have an easier time figuring out $f_{clock}$s that appear in your device if you have a schematic, and knowledge of Firmware/FPGA images used.

Supply Noise

A classic. If the SDR has an external power supply, try a different one, ask the manufacturer about known spurs, and use ferrites where applicable.

Digital Interface Noise

Your SDR device is a USB1/2 device and you see a $N\cdot11$ MHz signal, spread around with some rather "sinc"-y shape: USB's to blame, typically. Applies to other buses with other baud rates, too. Hard to mitigate if hardware's fixed.

Phase noise of LO

The aforementioned synthesizers are typically pretty good; this often stems from phase noise of the reference oscillator. If possible with yout device: try a "less accurate" (read: you got lying around) one, and compare.

Reference oscillator overtones, noise through ref oscillator input

Yeah, not all things that seem to be a good idea actually are. I've seen it more than once that people, thinking their external high-accuracy, long-time stable oscillator would significantly improve operation, only to find out later, that the reference signal not only contains the wanted (e.g. 10 MHz) tone, but also other components, partly from supplies etc. Make sure your reference is clean! If in doubt, try the internal one, too!

Illustrations

(1)

Clipping

By twitter user "da Swede", https://twitter.com/uber_security/status/844116167870627841

(2)

Offset tuning in an USRP

*Offset tuning with the DSP chain of an Ettus USRP". By myself, copyright Marcus Müller/Ettus Research.

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Harmonic spurs as detected in a receiver could be generated in the transmitter, the receiver, or the transmission lines or antennas in between. Usually of course the antennas and transmission lines aren't the problem, which leaves the transmitter and receiver as potential culprits.

The most accurate way to test a transmitter is to connect it to a calibrated spectrum analyzer, through an attenuator of course, and directly measure the power of the harmonics relative to the output at the primary frequency, and see how clean the signal is in general. If you don't have a spectrum analyzer, you might try asking at your local ham club to see if someone there does who could help you. (My club has someone who owns several spectrum analyzers, who is always willing to help troubleshoot a transmitter or amplifier.)

Failing that, you could always ask another ham to listen to your signal at the primary frequency, and also the harmonics, to estimate whether your transmitter is up to the standards of good amateur radio practice. Of course hardly anyone has antennas with identical gain from one band to the next, so that method is generally only good for a rough guess.

The problem of course could be in the receiver, especially if it's being overloaded. Some good ways to determine if the problem is overloading in the receiver are to turn down the RF gain, switch on the internal attenuator, or insert an external attenuator in the signal path. If attenuating the signal makes harmonics or other distortion go away, then it's safe to say that the problem was in the receiver.

Naturally, if spurs are detected in one receiver, then a simple way to determine if the problems come from the receiver is to listen to the signal with a different receiver.

By the way, it should be mentioned that the builder of any transmitter is responsible for ensuring that the transmitter meets regulatory specifications. Designers of reputable kit transmitters ensure that their designs meet specifications when the kits are built correctly.

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I believe you have described the situation very well. It is caused by the generation of impure signals, usually in the transmitter.

Other causes could include using a transmitting antenna that resonates at or near a harmonic, such as using 40 meters on a dipole and finding harmonics around the 15 meter band.

It is rare for harmonics to be caused by the receiver, although you might find artifacts like "birdies" caused by the receiver's internal oscillator. The cheaper the receiver the more this possibility exists. But these would not be harmonic to the receive frequency - they are generally at fixed frequencies that may be harmonic to the oscillator's frequency.

Then consider the mixer that brings the received frequency down to the IF. It will take the input frequency and IF oscillator, and produce the sum and difference frequencies. Bandpass filtering is supposed to remove the spurious outputs from the mixer. But these would not be harmonic to the receive frequency in any case.

As for testing, I don't really understand from the OP what exactly you are trying to test for.

In the rules there are specified limits to the amount of spurious signals that are allowed to be transmitted by amateur equipment, whether type-accepted or homebrew. As long as you are below those limits (and more importantly, as long as you are not interfering with another licensed service), they don't present an immediate problem that needs to be fixed.

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    $\begingroup$ Artifacts caused by the receiver are quite common in my experience, during big contests at least, where someone nearby might be transmitting 1.5+ kW through a directional antenna that happens to point my way. Received signal strengths of -10 dBm (aka "S9 +40") are not uncommon. $\endgroup$ – rclocher3 Mar 31 '17 at 1:11

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