[time-nuts] practical details on generating artificial flicker noise

Jim Lux jimlux at earthlink.net
Sun Nov 23 09:05:01 EST 2014

I'm writing a short simulation program to generate samples from a analog 
system with some op amps, etc., and I'm wondering if anyone has some 
practical experience on picking parameters for the generator.

I'm generating minutes worth of data sampled at 1 kHz, and my opamps 
have their flicker/white knee at around 3-4 Hz (at least that's what the 
LT1679 data sheet claims.. we shall see if the model matches the data 
sheet matches what I measure on the actual hardware)

I'm using a Barnes-Jarvis (or Barnes-Greenhall) type generator for the 
flicker noise, which basically sums up a bunch of stages to create an 
arbitrarily smooth representation.  See threads:

The actual PTTI paper is

http://tycho.usno.navy.mil/ptti/1987papers/Vol%2019_19.pdf has the details
http://tycho.usno.navy.mil/ptti/1992papers/Vol 24_44.pdf has some 
corrections, but is a partial page..

You need to pick a few parameters:  how many stages to cover your 
frequency band of interest, how big the frequency steps are (e.g. 
octaves), and where's the "top band" filter cutoff (typically 0.3 to 0.5 
relative to the sample rate)

If you picked 4 stages, with a starting frequency of 0.4, and 
octaves(R=2), then the individual filter cutoffs would be

I'm interested in the behavior down in the 1 Hz and below range, say, to 
0.01 Hz.  So to cover 0.01 Hz to 1000Hz, one would need about 16-17 
octaves which is an enormous number of stages and I've got to believe 
you'd have all sorts of numerical problems

  And I think I don't need to do this
I can add white noise to establish the noise floor to match lab 
measurements (there's sources other than the op amps) for higher 
frequencies, say in the 20-1000 Hz area.

It would seem, then, that I can start the first filter at around 5 Hz 
and go down from there, if my assumption that most of the flicker noise 
is coming from the opamp and it's flicker noise comes above the thermal 
noise at 3-4 Hz.

Then, going in, say, octave jumps, I can get down to 0.01 Hz in about 8 
steps.  (this seems to match Figure 2 in the paper.. they used a 8 
stages with a frequency ratio of 2.4, and the spectrum looks pretty flat 
for a good 5 decades.

I suppose I could just write it and see what comes out, but if someone 
out there has worked with this kind of thing before, a bit of practical 
guidance would be useful.

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