Note: I’m contemplating designing a spectrum analyzer. The following are a compilation of my own notes that I’m making public. They might not make a lot of sense as a coherent treatise but take the pieces for what they are.

The classical way of performing RF spectrum analysis is to mix the input with a local oscillator (FLO1) that ramps between two higher frequencies, producing IF1.

IF1 is sent through a narrow band filter which leaves you with a narrow piece of the input spectrum that has been shifted up. The ramping action gives you a sliding window of the input spectrum, shifted up to the center frequency of the narrow bandpass filter.

Stepping back, remember that the IF1 frequency is the result of nonlinear mixing of the input with the local oscillator.
Let’s make some assumptions:

– the input (Fin) is any signal between zero and 1000 MHz.
– the local oscillator (FLO1) ramps between 1050 and 2050 MHz
– the narrow bandpass filter (FBP) is 1050 MHz

Mixing the local oscillator and the input with a non-ideal mixer gives you:

IF1 = N*input +- M*LO

The strongest output spectra will be where N=1 and M=1. This gives you spectra centered at:

(a) Fin + FLO1
and
(b) Fin – FLO1

Since FLO1 is always greater than Fin, we get a nice strong first image (a) between 1050 and 2050 MHz.
The first negative image (b) is wrapped into the range of 0 to 1050 MHz. Subsequent energies are present at higher orders, however their amplitude is orders of magnitude lower than the main images.

FILTERING
After mixing, IF1 is filtered using a high-Q filter. Q, of course, is a measure of how wide the pass-band is.
Q = Fc/Fbw where Fbw is the -3dB bandwidth.

Common hobbyist spectrum analyzers[1][2] use cavity or helical filters.

A cavity filter has radiative elements (I’ll liberally call antennae) in a conductive can along with a resonator whose length can be changed. They can and often contain multiple cavities

Here’s a paper from M/A COM on cavity and helical filter design.

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References

[1] Scotty’s Modularized Spectrum Analyzer
[2] Andrew Holme – Homebrew spectrum analyser