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Scope FFT funnies

So I'm taking some performance data on the first articles of the shot-noise

-limited nanoamp photoreceiver that the hunchbacks and I are planning to se ll. (It works very well--more details soon.)

Because noise measurements don't need a whole lot of dynamic range, I'm usi ng my TDS 784A scope's FFTs, which work fine if you have a good antialiasin g filter, which isn't hard with a 4 Gs scope and a 1 MHz DUT.

Measurements of the noise at various photocurrents demonstrate its performa nce OK, but I was initially puzzled that the measured low frequency noise f loor was 2-3 dB below the value calculated from first principles (shot and Johnson noise).

I was using a rectangular window, so the frequency bin width is 1/(measurem ent time) with no funnies. After searching pretty diligently for pilot erro r (the usual source of such problems) I discover that the problem is the sc ope. The main clue was that the error is just about exactly 2.5 dB. Why i s that, you ask?

It's well known that analogue spectrum analyzers read 2.5 dB low on Gaussia n noise (see the classic HP/Agilent app note AN150, "Spectrum Analyzer Basi cs"). The effect is due to taking the logarithm (via a DLVA) and then avera ging afterwards using a slow filter. That's why there are separate resoluti on and video bandwidth settings.

The log amp applies less gain to the peaks, which shifts the average lower by 2.5 dB. You can correct for this if you know the problem exists, just th e way you add 1 dB to noise measurements taken on an average-reading voltme ter such as an HP400EL.

But surely a digital scope must be doing a proper RMS average and so gettin g the right answer?

Apparently not!

Cheers

Phil Hobbs

Reply to
pcdhobbs
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se-limited nanoamp photoreceiver that the hunchbacks and I are planning to sell. (It works very well--more details soon.)

sing my TDS 784A scope's FFTs, which work fine if you have a good antialias ing filter, which isn't hard with a 4 Gs scope and a 1 MHz DUT.

mance OK, but I was initially puzzled that the measured low frequency noise floor was 2-3 dB below the value calculated from first principles (shot an d Johnson noise).

ement time) with no funnies. After searching pretty diligently for pilot er ror (the usual source of such problems) I discover that the problem is the scope. The main clue was that the error is just about exactly 2.5 dB. Why is that, you ask?

ian noise (see the classic HP/Agilent app note AN150, "Spectrum Analyzer Ba sics"). The effect is due to taking the logarithm (via a DLVA) and then ave raging afterwards using a slow filter. That's why there are separate resolu tion and video bandwidth settings.

r by 2.5 dB. You can correct for this if you know the problem exists, just the way you add 1 dB to noise measurements taken on an average-reading volt meter such as an HP400EL.

ing the right answer?

Phil, I always learn stuff from your questions! Here's the (88 page) app note. (for others)

formatting link

I've always found the units displayed on our SRS spectrum analyzer to be co nfusing. (And mostly just use them as a relative gauge.)

How are you getting a "good" FFT from the noise with the 'scope? Are you taking the average of several single shot FFT's? or averaging before the FFT? (which is what I do.)

George H.

Reply to
George Herold

It ought to be power per frequency bin, usually quoted in dBV. The bin width equals the sampling frequency divided by the number of samples, or equivalently it's the reciprocal of the measurement interval. If you use non-rectangular windows, the interval is effectively shorter, so the bins get wider by an amount you can calculate. That helps a lot when there are strong signals present, but just gets in the way when measuring fairly smooth noise floors.

For instance, I was taking 5000 samples at 100 Ms/s, so the interval was

100 us and the bin width 10 kHz. With noise, you just divide the measured value by sqrt(10,000) to get per-hertz units.

Averaging before the FFT suppresses the noise, so because the noise is what I want to measure, I'm averaging afterwards. For a single run, the variance of the power spectrum equals the mean, so to get a decent estimate of the power spectrum you have to either average M runs or sum M adjacent bins. It takes a pretty large M to get a smooth curve--I was averaging 400-500 runs per plot.

The 784A is a pretty nice scope, but it's not in its first youth, so I expect they had to trade off a fair amount for speed--maybe using 16 bit words in the transform and using a 10-bit lookup table to take the log, then averaging that.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net
Reply to
Phil Hobbs

50 Ms/s, doh.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net
Reply to
Phil Hobbs

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