Measuring rise time with spectrum analyzer

Question

Is it possible to measure the rise time (range 100ps-1ns) of a square wave signal with a spectrum analyzer (my oscilloscope has 100MHz bandwidth only)? My model is Rigol 3030N (9kHz-3GHz).

My idea is that: since the Fourier transform is invertible, and what the analyzer reads is spectrum information, the inverse Fourier transform of the signal should show the signal in time domain.

Answer 1

So, hm, multi-layered answer:

Is it possible to measure the rise time (range 100ps-1ns) of a square wave signal

Rule of thumb for Gaussian systems is that bandwidth is roughly \$B\approx \frac{0.35}{t_{\text{rise}}}\$, so we're talking about, as an order of magnitudes, 3 GHz, with a good spectrum analyzer seeing components far higher than that.

since the Fourier transform is invertible, and what the analyzer reads is spectrum information, the inverse Fourier transform of the signal should show the signal in time domain.

A spectrum analyzer doesn't estimate the Fourier transform, it estimates the power spectrum. A power spectrum isn't the same as the Fourier transform – you lose the phase information on the way. Also, the spectrum analyzer doesn't just instantly get the PSD; it samples the spectrum with various filters. So, arguing directly throuh the inverse Fourier transform is possible, but it will require you to make some good assumptions on the filter shape.

Well, anyway, that kind of works. Take the PSD estimate that your spectrum analyzer gives you, realize it's not even a direct estimate of the PSD but of the PSD convolved with the analyzer's bandwidth filter shape, convert to linear terms (spectrum analyzers usually display powers in terms of decibel to some reference), take the square root (power isn't amplitude). Make a reasonable guess on the temporal nature of your bandwidth filter (i.e., observe a narrowband tone to get the spectral power density of that filter, do an inverse Fourier transform, find a physical model of that filter (probably a quartz or SAW filter), and fit that model, to get a best-fit time-domain estimate of your spectrum analyzer's filter's impulse response. Do the rest of the math (draw the rest of the owl). You should get a best-fit estimate of the actual shape of your pulse, from which you can read your rise time.

Or.

• Realize that rise time is a grand simplification, and in the 100ps range, chances are it isn't actually what you care about
• Chances are you actually do care about spectral shape wherever you use that nearly-square-wave signal
  • That's why the rule of thumb relating rise time to spectrum above isn't totally absurd
  • I'd recommend you ask a new question – namely,

Hi, I want to do {what it is that you want to do}. For that {thing you want to build}, I need to know whether the square wave ({frequency, rought rise time}) produced by {what it is that produces your square wave}) is sharp enough, because {explanation of why you need to know}. How can I determine that? The measurement equipment I have at hand are ({your oscilloscope, the actual model and frequency range of your spectrum analyzer}, other things like SDRs or FPGA boards you have at hand).

• Rise time is always a function of the load you're attaching; so, if whatever generates the squarish wave is already 50 Ω-matched, and you use 50 Ω cabling to an 50 Ω measurement device, all fine, you get sensible measurements, as long as all the involved cabling and devices don't have a cut-off that's reasonably close to say, 3× 3 GHz as estimated above, but:
  Is that really what you care about when you're measuring? This sounds like more of a job for an active high-impedance, high-speed probe quite close to whatever consumes the square wave, to get your systemic issues out of the way.

Answer 2

You can't.

Rise-time is a time-domain thing yet the spectrum analyser is specialised for frequency-domain things.

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Let's assume you could do it for a moment. There's one limitation here: Considering the fact that the rise time of a pulse can be approximated to one-third (0.33 ~ 0.35) of the period of a sinewave-component in Fourier series, the required bandwidth should be greater than 3 times (1/0.33 ~ 1/0.35) the inverse of the minimum rise time.

In your case the minimum rise time to-be-measured is 100 ps which makes the bandwidth requirement at least 3 / 100p = 30 GHz.

If you can calculate the amplitude of the Fourier series component with frequency of f = ~0.35/tr (tr: rise time) then this could be possible, barely.