Learning about oscillators in LTSpice

The weird artifacts come from excess Mike cleverness, and from not setting a maximum time step. Try this, switch to straight trapezoidal and the "alternate" solver, and use a 2097152-point FFT. Good behaviour results.

Cheers

Phil Hobbs

Version 4 SHEET 1 1656 900 WIRE -480 208 -512 208 WIRE -480 224 -480 208 WIRE -1040 240 -1056 240 WIRE -800 240 -816 240 WIRE -1056 288 -1056 240 WIRE -816 288 -816 240 WIRE 128 288 0 288 WIRE 144 288 128 288 WIRE 0 320 0 288 WIRE -480 336 -480 304 WIRE -160 336 -176 336 WIRE -48 336 -160 336 WIRE -160 384 -176 384 WIRE -48 384 -160 384 WIRE -1056 400 -1056 368 WIRE -816 400 -816 368 WIRE -496 416 -512 416 WIRE -496 432 -496 416 WIRE 0 432 0 400 WIRE -496 528 -496 512 FLAG -1056 400 0 FLAG -1040 240 n1 FLAG -816 400 0 FLAG -800 240 n2 FLAG -496 528 0 FLAG -480 336 0 FLAG -512 416 gn1 FLAG -512 208 gn2 FLAG 0 432 0 FLAG -160 336 gn2 FLAG -160 384 gn1 FLAG 128 288 out SYMBOL bv -1056 272 R0 SYMATTR InstName B2 SYMATTR Value V=random(50000*time) SYMBOL bv -816 272 R0 SYMATTR InstName B1 SYMATTR Value V=rand(101000*time+21000) SYMBOL bv -496 416 R0 SYMATTR InstName B3 SYMATTR Value V=sqrt(-2*ln(v(n2)))*cos(2*pi*v(n1)) SYMBOL bv -480 208 R0 WINDOW 3 60 49 Left 2 SYMATTR Value V=sqrt(-2*ln(v(n2)))*sin(2*pi*v(n1)) SYMATTR InstName B4 SYMBOL e 0 304 R0 SYMATTR InstName E1 SYMATTR Value {1/sqrt(2)} TEXT -1048 456 Left 2 !.tran 0 2.097152 0 1u TEXT -1256 496 Left 2 ;ARRRGGG! can't run for more than 8mS, else nulls out!!\ngn1,2's PDF appears to 'peak' somewhere near -0.12 in the range

TEXT -408 448 Left 2 !.options plotwinsize=0

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TEXT -408 448 Left 2 !.options plotwinsize=0

--
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

That method is appealingly simple, I agree. It generates independent samples much more slowly than the Box-Mueller approach, though, because you're relying on the central limit theorem to give you your Gaussian statistics, rather than applying the inverse function.

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

May be good, but don't see how to use it to analyze an MC1496, would you show us?

The RMS of the sum of N1+N2, over an adequately long observation, is almost exactly 1.41 times the values of N1 and N2.

I deliberately made the K values 100 and 101 to demonstrate correlation in the first second of a run. Don't do that in production.

This is noise; of course the measurements tend to be noisy.

The rand(K*time) function still has a uniform PDF, so it needs work to make it more gaussian: summing, lowpass filtering, hashing.

rand() is better than random(), for the better runtime.

--

John Larkin                  Highland Technology Inc 
www.highlandtechnology.com   jlarkin at highlandtechnology dot com    

Precision electronic instrumentation

Eternal September costs the same as aioe, and doesn't have the silly limitation.

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

Wouldn't you want to soften the sharp edges anyhow?

--

John Larkin                  Highland Technology Inc 
www.highlandtechnology.com   jlarkin at highlandtechnology dot com    

Precision electronic instrumentation

No thanks. Analyzing an MC1496 is a job for a historian, not an engineeer. Is it

50 years old yet?

Why not just measure it? It's probably noisier than a sim would predict.

Point is, rand(time) can be the basis of a pretty good time-domain noise source, and it's easy.

--

John Larkin                  Highland Technology Inc 
www.highlandtechnology.com   jlarkin at highlandtechnology dot com    

Precision electronic instrumentation

Yes, I am signed up for Eternal September and use it to receive every Usenet, but alt.home.repair

but alas some setting I haven't figured out won't let me post through it, keep getting an error about some setting is wrong.

So, when Aioe allowed me to instantly get going, was done.

Acutally white() is not a bad basis, but was 'difficult' to concquer the myriad of problems, thus the solution I posted to you.

This is your second email ADMITTING to not providing your offer of two noise sources. The other one you talked about 100 and 101 as some point of a flaw and this one you call it a basis. Still interested in a simple two resistor circuit with two sources

I'll post one here for you later, It has an interesting way to show the effects of that rounding in LTspice.

My N1 and N2 are independent noise sources. You're not making sense.

--

John Larkin                  Highland Technology Inc 
www.highlandtechnology.com   jlarkin at highlandtechnology dot com    

Precision electronic instrumentation

On Tue, 29 Jul 2014 07:26:15 -0700, John Larkin wrote:

No, they are not independent.

Again, Vrms for N1, N2, and sum are approximately the same value.

Check the spectrum of N1, N2 [which are the same], BUT the spectrum for the sum is off more than 8dB, signifying a fair bit of 'non-independency'.

you did look at my other reply?

named NoiseSources_JohnLarking_compared.asc

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I measured the sum as almost exactly 1.41 times the individual values. N1 and N2 only correlate for the first second, and that was deliberate. You don't have to do that.

You can break almost anything that you don't like. LT Spice will help you if you want.

--

John Larkin         Highland Technology, Inc 

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

APOLOGIES!

typo alert! left hand keeps adding a g and typing 'ing' instead of 'in'

Absolutely no insult intended. Again, apologies.

On Mon, 28 Jul 2014 21:00:57 -0700, John Larkin wrote:

As promised here is a simple resistor network with CALIBRATED noise sources. The schematic has comparison notes. It is interesting to note that the resistor networks do NOT even add a single node to the PSpice solution matrix, which maintains speed [and I'll bet accuracy]

some of the fonts may not transfer.

ResistorCompare.asc

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100uVp signal that is 52.258 uVrms\n.noise V(onoise) shows

at 3.2 nV/rtHz\n with no cap, approx -140dBV, estimate

3.2 nVrms/rtHz\n using V(out), peak arppox -86.0377dBV\n octave Post Processing:\n using V(compare_eq)\n time waveform, 2.04uVrms\n after conversion to spectrum using time2freq, starts with 3.64nV/rtHz\n using V(out_eq)\n after conversion to spectrum using time2freq, peak occurs at -85.639 dBV, 52.246uVrms TEXT 824 520 Left 2 ;NOTE: Usually the full formula of each PWL description are NOT shown,\n but are left shown here for review.

not trying to break, was examining it.

and the statment the same Vrms is BECAUSE when I summed I used 1/sqrt(2) to make them similar. Didn't you look at the schematic?

Barfs repeatedly for syntax errors. Probably you need to post with wrap turned off.

Also LTspice doesn't like "time_scale_factor={dt}" ...Jim Thompson

--
| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| San Tan Valley, AZ 85142     Skype: skypeanalog  |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 
              
I love to cook with wine.     Sometimes I even put it in the food.

Sure, but not by that large a factor, I shouldn't think. Modelling the edges of the distribution accurately out so some crest factor M requires integrating uniformly-distributed noise for some really long time (something like exp(M**2/2) samples), whereas with the Box-Mueller method, you get the Gaussian distribution to machine precision (or whatever your random generator can do) in one step.

Of course in LTspice, the rounded edges happen before the Box-Mueller transform, which will mess up the distribution a bit. One should really sample in the middle of the interval, transform, and then smooth again.

Whether any of that is worth the trouble depends on the situation. Shot noise and Johnson noise are really really Gaussian, so if one were trying to model the counting statistics of threshold crossings, for instance, you'd care quite a lot.

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

The alternative would be to sum a few (3-10 maybe) rand(K*time) terms and lowpass filter just enough to tame the edges. Crest factor would be OK for most uses... grows by square root of the number of summed sources, I think. I don't know if that would be faster or slower than Box-Mueller, and there's no way to tell but to try it.

I was impressed by random() being 6:1 slower than rand().

This discussion is interesting. I have no use for it right now, but I'm fairly sure I will one of these days. It is a break from writing Python test scripts.

I wonder if LT Spice pre-compiles or interprets math expressions. That could probably be determined by experiment.

--

John Larkin         Highland Technology, Inc 

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

No control over the wrap, have to straighten out by examination.

But, the LTspice version I have, 4.20x, May 2014, demands I put dt in {}

that's supposed to be all one line, not a single line by itself.

I'll send to you as .asc