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Suppose we have a spectrum analyzer whose range of frequencies goes from \$x \ \mathrm{Hz}\$ to \$y \ \mathrm{Hz}\$. Is there any problem that could arise from measuring signals that are near those frequencies? Any kind of "border effect", or something of that nature.

For instance, Keysight's N9320B states in the datasheet that the frequency range starts at 9 kHz. If I want to measure a sinusoid at 9 kHz, would there by any problem or uncertainty due to the fact that this frequency is at the limit of the SA operating range? (I'm not interested in just that SA, but I just put it here to show what I mean by 'frequency range'.)

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    \$\begingroup\$ Depends on the nature of the limit. If it's a filter roll-off (especially in the DC-block), might be okay for non-critical use. If it's an actual limit of what the instrument will display, then not being able to see both sides of the signal will leave you with questions about what you are looking at - in fact, even a slight frequency error might put it off the display entirely. Conversely if it's a limit of the center frequency you may well get half a normal display span below. Remember also that 9 KHz is audio frequency - there are other options there, including a quality sound card. \$\endgroup\$ – Chris Stratton Jul 28 '18 at 22:18
  • \$\begingroup\$ @ChrisStratton Thanks for your comments. Do you think that there is a way of knowing the nature of the limits? Also, what do you mean by "a filter roll-off"? I mean, I know what the roll-off of a filter is, but I didn't understand how that would put a limit on frequency range here. Doesn't it depend just on the oscillator and the range of frequencies it covers? (Sorry if this is too basic, I'm not too experienced with spectrum analyzers!) \$\endgroup\$ – Tendero Jul 28 '18 at 22:24
  • \$\begingroup\$ You might judge the quality of a SA's VCO stability by its lower-frequency spec (9 kHz for example). You can easily see drift and phase noise down there. You cannot tell from the display if your input signal is drifting, phase-noisy, or if the analyzer's VCO is drifting, phase-noisy. It is very easy to build a stable 9 kHz oscillator as a test signal. Any drift or phase noise you see displayed is the result of SA's VCO. A decent crystal oscillator test signal is OK too. \$\endgroup\$ – glen_geek Jul 28 '18 at 22:39
  • \$\begingroup\$ @glen_geek So would the border frequency present, in general, more phase noise than frequencies in the middle of the oscillating range? \$\endgroup\$ – Tendero Jul 28 '18 at 22:46
  • \$\begingroup\$ What's your actual goal? The instrument you link to is hugely expensive to buy or even rent, so much so that normally it would not be considered without project resources correlated to a far higher level of familiarity with these topics. If you are looking at low frequency signals, this is not the right choice, unless most of your need is elsewhere. \$\endgroup\$ – Chris Stratton Jul 28 '18 at 22:46
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There are several limits to the low frequency behaviour of spectrum analysers. Some are easy to intuit, some less so. Newer digital instruments are slightly different to the older analogue instruments in what they display.

One common limit is the high pass nature of the input DC blocking filter, which is generally no more than a series capacitor. That's quite simple. The filter might be -3dB at 9kHz, or it might be -1dB or even -0.1dB. It's fairly easy to see the level, and sort it out with calibration.

For the other limits, you need a block diagram for a typical spectrum analyser. This shows the simplified front end of a typical superheterodyne spectrum analyser.

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This one goes up to 1GHz, and you can see from the diagram down to nominally DC.

The bandpass filter at 2GHz provides the selectivity. This is the filter that is switched to the various bandwidths that the analyser will provide, the 10MHz, 1MHz, 100kHz, 10kHz settings. For the larger bandwidths, it's a real switchable LC bandpass filter. For the smaller bandwidths, it's a system that uses further mix-down to lower IFs. In the modern digital analysers, the last IF is left fairly high frequency and wideband, and is digitised with FFT used for the final filters.

For a 0.5GHz input, the VTLO is set to 2.5GHz, producing a 2GHz IF.
For a 1GHz input, it's set to 3GHz, producing the same 2GHz IF.
For a nominally DC input, it's set to 2GHz.

On old analogue instruments, the sweep controlling the LO frequency could be set to sweep 'below' DC, for an input frequency below 0Hz. What you'd see on the display is the negative frequency for the first part of the sweep, a 'DC pip' at DC, and then the normal positive frequency range above that. Digital synthesiser based spectrum analysers tend to limit the display so you don't see either.

The input mixer, while it provides isolation between all its ports in theory, in practice 'leaks' some of the LO signal out to the 2GHz IF. This is the origin of the 'DC pip' mentioned above, aka 'LO leak'. The leakage can be quite severe. A not uncommon specification for RF spectrum analysers was for -40dBm signal at the input mixer, which tended to mean -50dBm to the IF. With a typical LO drive of +13dBm to +17dBm, you can see that even 60dB LO to IF isolation would still mean the DC pip was more than the expected signal. This sort of isolation needs active balance in the first mixer, and is still a struggle to achieve stably.

The LO leak causes two problems

1) Phase noise on the LO signal lifts the noise floor for input frequencies close to it, it reduces the dynamic range from the bottom. That's why 9kHz is an often seen lower limit. Just low enough to sneak into the audio range, high enough to get away from the worst of the LO phase noise.

2) The LO leak gets into the 2GHz IF, as a signal of similar size to the wanted signal. Generally the first element in the 2GHz IF is an LC filter, wide enough for the widest expected IF, perhaps 40MHz width. This filters out the LO leak for input frequencies above 20MHz. The distortion of the analyser is now controlled by the single tuned signal getting into the IF's amplifiers. This is generally the distortion that's specified for the instrument.

At input frequencies less than 20MHz, the LO leak now appears full strength at the IF amplifiers, reducing the signal handling of the amplifiers and increasing their distortion. This reduces the dynamic range from above. As mentioned above, the 2GHz IF is actually a system, using progressively lower frequency IFs and smaller bandwidth filters. There will therefore be a progressive degradation in dynamic range as the smaller bandwidth means that filters can no longer protect the detector from seeing the LO leak signal. Finally at DC, the LO gets through to the detectors, and the spectrum analyser can no longer distinguish the input signal.

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