"Random" Circuit Needed.

--
Sorry, loose lips sink ships... 

John Fields

--
And what, exactly, would be wrong with that?

--
To a mind which is closed, probably not.

--
Omigod, Heckle and Jeckle are at it again...

Oh, if it's a matter of national security, by all means keep it secret.

--

John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com

--
If it had anything to do with national security I would have made no 
comment at all.  But of course you know that - or at least you 
should - so, other than being your usual nasty little self, what's 
the reason for your gratuitous snarkiness? 

John Fields 
Professional Circuit Designer

--
Well, of course you don't and, your perception of being at the very 
pinnacle of the food chain makes everything you don't understand 
unimportant.

Define "truly random output", and I'll tell you if my board meets your standards.

This is an electronics discussion group. We need things to discuss. And I do a *lot* of electronics!

--

John Larkin         Highland Technology, Inc 
picosecond timing   laser drivers and controllers 

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com

--
They're not _my_ standards, John, we all live by them. 

Most of us understand the concept, and you could too if Google were 
your friend.

OK, you have no definition of "truly random."

I post goofy ideas, and outright blunders, too. Circuits that work, and circuits that don't.

"Loose lips sink ships" is back-patting in a far less honest way.

--

John Larkin         Highland Technology, Inc 
picosecond timing   laser drivers and controllers 

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com

--
And a lot of off-topic garbage that has no place in a technical 
discussion group.

Did you know that Shannon and Nyquist were late to lunch? The basic sampling theorem was already stated in much the same way 35 years earlier by E.T. Whittaker. I found traces of older references, but haven't been able to get my hands on any.

Jeroen Belleman

On Wed, 01 Apr 2015 11:00:25 -0700, Jim Thompson wrote:

Only vaguely on-topic, here is a noise generator experiment. The mess on the left makes 1-bit digital noise clocked at 1 MHz, like a linear shift register, just easier to draw. The issue at hand is what kind of lowpass filter to use to get approximately Gaussian noise.

The 200 KHz filter is right out of AoE3 p 559. It looks fine in the audio frequency domain, but it's nothing like Gaussian.

The 3-pole filter is a lot nicer.

We're actually going to use a LFSR in an FPGA and do the serious filtering digitally, and drive a DAC with a little analog filtering afterwards.

Version 4 SHEET 1 1316 680 WIRE 912 -64 848 -64 WIRE 1056 -64 912 -64 WIRE 1200 -64 1136 -64 WIRE 1248 -64 1200 -64 WIRE 1312 -64 1248 -64 WIRE 1200 -16 1200 -64 WIRE 368 64 208 64 WIRE 480 64 368 64 WIRE 208 96 208 64 WIRE 1200 96 1200 48 WIRE 720 112 656 112 WIRE 752 112 720 112 WIRE 432 128 400 128 WIRE 480 128 432 128 WIRE 208 208 208 176 WIRE 848 208 848 -64 WIRE 912 208 848 208 WIRE 1056 208 992 208 WIRE 1200 208 1136 208 WIRE 1248 208 1200 208 WIRE 1312 208 1248 208 WIRE 848 240 848 208 WIRE 400 256 400 128 WIRE 1200 256 1200 208 WIRE 400 368 400 336 WIRE 848 368 848 320 WIRE 1200 368 1200 320 FLAG 208 208 0 FLAG 368 64 NOISE FLAG 400 368 0 FLAG 720 112 SH FLAG 848 368 0 FLAG 912 -64 COMP FLAG 1200 368 0 FLAG 1248 208 LPF2 FLAG 432 128 CLK FLAG 1200 96 0 FLAG 1248 -64 LPF1 SYMBOL bv 208 80 R0 WINDOW 0 -63 105 Left 2 WINDOW 3 -131 174 Left 2 SYMATTR InstName B1 SYMATTR Value V=random(1.83e7*time) - 0.5 SYMBOL SpecialFunctions\\sample 560 96 R0 SYMATTR InstName A1 SYMBOL voltage 400 240 R0 WINDOW 0 -85 76 Left 2 WINDOW 3 -323 114 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value PULSE(0 1 0 0 0 500n 1u) SYMBOL bv 848 224 R0 WINDOW 0 -120 42 Left 2 WINDOW 3 -187 87 Left 2 SYMATTR InstName B2 SYMATTR Value V=sgn(v(sh)) SYMBOL res 1152 192 R90 WINDOW 0 69 58 VBottom 2 WINDOW 3 75 56 VTop 2 SYMATTR InstName R2 SYMATTR Value 1K SYMBOL cap 1184 256 R0 WINDOW 0 51 15 Left 2 WINDOW 3 50 51 Left 2 SYMATTR InstName C1 SYMATTR Value 5n SYMBOL res 1152 -80 R90 WINDOW 0 69 58 VBottom 2 WINDOW 3 75 56 VTop 2 SYMATTR InstName R1 SYMATTR Value 5K SYMBOL cap 1184 -16 R0 WINDOW 0 51 15 Left 2 WINDOW 3 50 51 Left 2 SYMATTR InstName C2 SYMATTR Value 150p SYMBOL ind 896 224 R270 WINDOW 0 -33 54 VTop 2 WINDOW 3 -39 51 VBottom 2 SYMATTR InstName L1 SYMATTR Value 17m TEXT 552 -48 Left 2 !.tran 25m TEXT 216 -72 Left 2 ;Noise Generator Test TEXT 208 -32 Left 2 ;J Larkin April 28, 2015 TEXT 432 240 Left 2 ;1 MHz CLOCK TEXT 640 352 Left 2 ;COMPARATOR TEXT 1056 48 Left 2 ;200 KHz TEXT 1056 312 Left 2 ;20 KHz TEXT 864 56 Left 2 ;DIGITAL TEXT 864 88 Left 2 ;NOISE

--

John Larkin         Highland Technology, Inc 
picosecond timing   laser drivers and controllers 

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com

Den onsdag den 29. april 2015 kl. 06.39.25 UTC+2 skrev John Larkin:

-Lasse

Er, well.. surely an LFSR will be flat, not Gaussian, no?

Fortunately, there is an app\\\ transform for that:

shouldn't be too bad to implement on FPGA. Log can be very crudely obtained as the highest active ('1') bit position, and can be improved iteratively (by repeated squarings and bit-shifts, or Taylor series polynomial approximation methods).

Obviously, to shoot it out of a DAC, the bounds must be strictly limited, so part of your spec will be how many sigma of Gaussian it's good for (usually 3 or so?).

Which, in turn, implies that the argument of the log can't be near zero (which is what produces the peaky outliers), and certainly can't be zero exactly (which would be undefined), so perhaps the LFSR's inherent bias could be tuned to match the dynamic range of the desired output? Nah, probably not, not for any reasonable sequence length. So you'll have to do something ugly (and hopefully not badly behaved), like RND * scale + offset.

There are also methods for that -- ensuring that an output of truncated, arbitrary range is calculated correctly from an even distribution in some other range.

The geometric form is interesting, too; a random time delay could trigger a S&H of complementary (90 degree phase shifted) sine waves, and the other random number could feed a suitable arrangement of matched diode junctions or OTAs which computes the sqrt(ln(x)) function, and simultaneously controls the gain on the S&H buffers.

The "random" time delay has a strictly bounded range, so it could be triggered on a fixed clock, 'computed', then 'registered' with a second S&H on the following clock pulse, to give regularly sampled outputs (same as you'd use extra D-flops to neaten up the transitions in a digital logic circuit). Who even needs a DAC? ;)

Or you could randomly sample a sin/cos table and vary the VREF into an MDAC, or...

Tim

-- Seven Transistor Labs, LLC Electrical Engineering Consultation and Contract Design Website:

I have a Daqarta "mini-app" for converting a uniform to an arbitrary distribution. I use Gaussian as the example. The Help page is at . It includes a "Theory" section, plus the complete macro script (it's in Daqarta's own macro language, but I've added lots of comments).

The basic method uses the inverse Cumulative Distribution Function (iCDF) with a lookup table. The trick is to create the proper table.

Best regards,

Bob Masta DAQARTA v7.60 Data AcQuisition And Real-Time Analysis

Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, Pitch Track, Pitch-to-MIDI FREE Signal Generator, DaqMusiq generator Science with your sound card!

Single bit digital noise has a PDF with two big impulses, about the worst approximation to Gaussian (or flat) imaginable. So you need to sum a LOT of them to get something sort of Gaussian... the Central Limit Theorem thing. Hence the 20 KHz filter. Higher-order filters work way better than single-pole ones.

If you nab 16-bit words from the shift register, and not the single bit, you start with a basically flat histogram. Summing a modest number of them gets Gaussian pretty fast. That's harder to Spice.

We have a +-10 volt DAC range, and we figure that 1 volt RMS is a good number, and our 15-tap FIR filter will give us a crest factor of about

5.5. That sounds OK; I don't think our customers would want truly Gaussian noise with infinite voltage spikes.

A tapped analog delay line is easy to Spice. If you poke in random values and evenly sum the taps, that amounts to summing a sucession of samples, so it does the Central Limit thing for you. And it's also a finite-impulse-response filter. Everything turns out the be the same thing, just looked at from different angles.

I really need a histogram back end for LT Spice. Snarl, snap, I guess I'll have to make one.

--

John Larkin         Highland Technology, Inc 
picosecond timing   laser drivers and controllers 

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com

Den onsdag den 29. april 2015 kl. 17.27.05 UTC+2 skrev John Larkin:

run LTSpice, plot your wave, click on waveform window, then File-> export

install octave these lines

x=textread('exportedfilename.txt','%f','delimiter',' '); hist(x(2:2:end),1000);

-Lasse

Cool, I'll try that. Thanks.

--

John Larkin         Highland Technology, Inc 
picosecond timing   laser drivers and controllers 

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com