Help Given phase noise in a source, what is the effect?

Not simple. The phase noise can be of various bandwidth.

--

John Larkin         Highland Technology, Inc 

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

Dear RobertMacy,

I searched but didn't see your post on the LT1115 circuit. Maybe it didn't go through. For your current question, there is not enough information to provide a good answer.

Think of your system as a communications transmitter. The carrier is your 1 kHz signal and the noise is the message which modulates the phase of the carrier. Intuitively, the bandwidth of the modulated signal depends on the bandwidth of the message. You gave info on the max deviation, but not the rate of deviation.

If you want to develop an understanding I can think of three ways for you to proceed.

First and best is analytical. Look at books on signals-and-systems and communications. Write the equation for the carrier and modify it to add your phase modulation. Do the Fourier transform and plot the results. If you don't want to manually do the math, then use an analytical package or a fancy calculator. The TI-nspire is pretty good.

The second best way is to use numerical simulation. Matlab is good, Scilab is good and free. You need to understand the effect of windowing when using the FFT or you'll be fooled by artifacts.

The third and most difficult way is to build a circuit and make measurements in the lab. The pitfalls here are artifacts due to the circuit operating in unexpected ways and generalizing from the specific circuit response to the principle involved.

ChesterW

+1

Doing the math longhand generates understanding faster than anything else.

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

Thank you for your thoughtful response.

Didn't see the posting? That explains the lack of responses, however I got a copy back?! Perhaps, gmail accounts are blocked.

I didn't think that was 'max' deviation at all! That was 1 degree RMS with a gaussian distribution.

Yes I have modeled the system in octave [free Matlab clone] as stated in my question, but the answers I got didn't believe, for example, I could tell NO spectral difference between broadband additive noise (johnson noise) and broadband phase noise! They BOTH produce a flat spectrum. The only difference shows up *IF* you modify something and look again, or examine the distribution. The additive noise preserves the gaussian shape, but the phase noise comes out looking very 'spikey' three times higher peak and quite sharp. Thus, I posted the question here.

I'm going to post my other question again, but as a 'reply' to your question. Maybe that will get it through.

HERE WAS THE ORIGINAL POSTING: watch for wrap

The following is a simple [absolutely made up, stupid topology, but simulation predicts it oscillates] RC oscillator that seems to want to run slightly under 400Hz. Because it is an RC oscillator, how does one determine the phase noise, or jitter, or however one specs this thing by using LTspice?

I used a simple .tranoise model and it shows/predicts in a spectral plot the sidebands for this oscillator, but how would I find the expected value using only .tran and .noise? Or is there some calculation one uses?

Version 4 SHEET 1 27404 860 WIRE 2304 -1072 1920 -1072 WIRE 2416 -1072 2368 -1072 WIRE 1920 -864 1920 -1072 WIRE 2176 -864 1920 -864 WIRE 2416 -864 2416 -1072 WIRE 2416 -864 2256 -864 WIRE 2240 -800 2192 -800 WIRE 2192 -768 2192 -800 WIRE 1696 -752 1440 -752 WIRE 1792 -752 1760 -752 WIRE 1920 -752 1920 -864 WIRE 1920 -752 1872 -752 WIRE 2160 -752 1920 -752 WIRE 1440 -736 1440 -752 WIRE 2416 -736 2416 -864 WIRE 2416 -736 2224 -736 WIRE 2528 -736 2416 -736 WIRE 2624 -736 2528 -736 WIRE 2688 -736 2624 -736 WIRE 2704 -736 2688 -736 WIRE 2160 -720 2112 -720 WIRE 2528 -704 2528 -736 WIRE 2624 -704 2624 -736 WIRE 2192 -672 2192 -704 WIRE 2240 -672 2192 -672 WIRE 1440 -624 1440 -656 WIRE 2528 -592 2528 -640 WIRE 2624 -592 2624 -624 WIRE 2112 -512 2112 -720 WIRE 2112 -512 1952 -512 WIRE 2160 -512 2112 -512 WIRE 2288 -512 2224 -512 WIRE 2416 -512 2416 -736 WIRE 2416 -512 2368 -512 WIRE 1952 -496 1952 -512 WIRE 1376 -464 1360 -464 WIRE 1424 -464 1376 -464 WIRE 1520 -464 1504 -464 WIRE 1552 -464 1520 -464 WIRE 1680 -464 1632 -464 WIRE 1696 -464 1680 -464 WIRE 1520 -400 1520 -464 WIRE 1952 -352 1952 -416 FLAG 1376 -464 Vcc FLAG 2240 -800 Vcc FLAG 1680 -464 Vss FLAG 2240 -672 Vss FLAG 2624 -592 0 FLAG 2528 -592 0 FLAG 1520 -400 0 FLAG 2688 -736 out FLAG 1440 -624 0 FLAG 1952 -352 0 SYMBOL Opamps\\LT1115 2192 -800 R0 SYMATTR InstName U1 SYMBOL Misc\\battery 1408 -464 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 -32 56 VBottom 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName Vpos SYMATTR Value 9Vdc SYMBOL Misc\\battery 1536 -464 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 -32 56 VBottom 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName Vneg SYMATTR Value 9Vdc SYMBOL res 1936 -512 R0 SYMATTR InstName Rbias SYMATTR Value {Rb} SYMBOL res 2608 -720 R0 SYMATTR InstName Rload SYMATTR Value 2k SYMBOL cap 2512 -704 R0 SYMATTR InstName Cload SYMATTR Value 10pF SYMBOL Misc\\signal 1440 -752 R0 WINDOW 123 24 44 Left 2 WINDOW 39 0 0 Left 2 SYMATTR Value2 AC 1 SYMATTR InstName V1 SYMATTR Value "" SYMBOL res 1776 -736 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName Rin SYMATTR Value 1k SYMBOL res 2384 -528 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName Rboost SYMATTR Value {Rb2} SYMBOL cap 1760 -768 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName Cin

SYMBOL res 2160 -848 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName Rfdbk SYMATTR Value 10k SYMBOL cap 2160 -496 R270 WINDOW 0 32 32 VTop 2 WINDOW 3 0 32 VBottom 2 SYMATTR InstName C1

SYMBOL cap 2304 -1056 R270 WINDOW 0 32 32 VTop 2 WINDOW 3 0 32 VBottom 2 SYMATTR InstName Cfdbk SYMATTR Value 1nF TEXT 2824 -856 Left 2 ;.tran 0 {Tstop} {Tstart} {dt/20}\n.save V(out) TEXT 2856 -800 Left 2 !.options plotwinsize=0;\n.param k=1.38e-23 T=300\n.param fmax=50000 N={2*fmax} \n.param dt={1/2/fmax}\n.param Tstop=1.1 Tstart=0.1\n.param BW=1 TEXT 2824 -920 Left 2 ;.ac dec 200 {BW} {fmax} TEXT 2824 -888 Left 2 !.noise V(out) V1 dec 200 {BW} {fmax} TEXT 2864 -592 Left 2 ;.param N={Tstop*2*fmax} TEXT 2680 -1040 Left 4 ;RC OSCILLATOR using LT1115 TEXT 1968 -408 Left 2 !.param Rb=1k TEXT 2248 -448 Left 2 !.param Rb2=5.1k

5

the spectrum analyzer will display the power spectral density PSD of the ph ase noise. The integral of the PSD is in your example, 1 deg RMS. Of cou rse there are many different shapes of PSD that will integrate to 1 deg RMS . Phase noise PSD shape is typicaly steeper close in and becomes more flat further out, you can google that.

THe spectrum will look insted of a narrow spike, like a noise hump with th e quanties dependent upon the specific PSD shape and the settings of the SA most importantly the RES BW setting.

Mark

thank you for your reply.

I expected a spike with 'skirts' but did NOT get that, perhaps I modeled the phase noise incorrectly.

I used a simple cosine function of time with phase noise inside the argument.

v=cos(2pift+phasenoise), where the phasenoise was 1 degree rms with gaussian distribution .

produced a FLAT noise spectrum!

thought I'm doing something wrong, because I expected some type of 'spreading' of the pure tone, didn't happen

[snip]

Never saw the post. And it's not in Trash. What was the question? ...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

| 1962 | I love to cook with wine. Sometimes I even put it in the food.

Hey Robert:

Consider a system that generates the following signal:

A1 * cos(w * t) + A2(t) * sin(w * t)

where A1 is a constant and A2(t) is a Gaussian random process whose amplitude is much smaller than A1.

What you'll see -- mostly is phase noise whose statistics are determined by the statistics of A2. So the above is a pretty good model for a source with phase noise.

Now consider a system

(A1 + A2(t)) * cos(w * t)

with the same A1 and A2(t) as above. Now the noise is entirely amplitude noise -- but on a spectrum analyzer, the two signals will look identical.

I don't know why your Octave simulation came out with the oddball results in phase, but I hope the above clarifies why the phase noise and amplitude noise seemed to look the same on a spectral plot.

--

Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com

ok you are in simulation land and not the lab...

instead of starting with a noise signal, get your simulation to work "right" with a TONE phase modulation.

After that is working, replace the tone with various types of noise.

White noise into a phase modulator probabably does result in a flat PSD.

Mark

I reposted it entirely in a response to Chester. Didn't THAT show up either?

thanks,

what was wrong with the model: v=A1*cos(w*t+phasenoise), where phasenoise is a a gaussian distribution of

1 degree rms?

and additive johsnon noise model: v=A1*cos(w*t)+A2*randn(), where randn is a gaussian distribution of 1 rms?

yes, They BOTH yield the same spectral 'look', yet DIFFERENT pdf's

I will check your model,

yes, true in simulation land, that's why I asked. I have a pure tone AND additive noise working perfectly.

The noise floor of phase noise has to be related to the amplitude of the oscillator, so didn't understand what you mean by 'replace' with noise sources, since removing the oscillator's tone with its phase noise also removes all the phase noise ??

"...into a phase modulator..." is a little too vague for me, didn't grok what you were trying to convey.

Your posts are showing just fine here, Robert.

the distribution you force with that 'extra' tone has an inverse tangent effect

check the histogram for sin(w*t), then multiply times gaussian and you end up with ?? distribution. in other words, the sine spends a lot of 'time' at +/- 1; do you see my point? WAIT! so what it spends time at +/-1 ! that's the same as simple +1 times it, which is y model. Ok, you have me VERY curious. I'll look at the 'details' of resulting pdf, etc.

In my model, the phase noise 'centers' around 0 degrees and either goes slightly +/- from there, with gaussian pdf.

my conclusion is that your proposed model for phase noise is NOT quite so good, because it's uncontrollable, and it plays havoc with the original pdf. hmmmm, if truly random and truly gaussian, may have only slight effect. may cause 'spike' just like I saw.

will let you know.

Thanks, feel a bit better.

The models I show are useful in pointing out how pure amplitude, (mostly) pure phase, and purely additive random Gaussian noise can all have the same impact on the signal's spectrum.

They're also good for quickly realizing that a carrier with a small amount of uncorrelated additive noise, when run through a clipper, will only have its noise level reduced by 3dB.

--

Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com

There is nothing wrong, but this is pretty unwieldy to analyze. For details, get a data communication textbook and read the part on angle modulation (covering phase and frequency modulation).

Tim's expression is an approximation for small deviations, taking only the first sideband pair into account.

Amplitude modulation creates one pair of sidebands, with the amplitude proportional to modulation depth.

Angle modulation creates multiple pairs of sidebands, with the amplitude of n:th pair proportional to Bessel function Jn(modulation index).

Maybe you intended to have the AM model: v = (A1 + A2 * randn()) * cos (w*t) ?

--

Tauno Voipio

Wow! apologies for doubting. That EXACTLY matches phase noise in flat and pdf!

but ONLY for extremely small phase noise in my model shown as v1.

these two are similar: v1=cos(w*t+phasenoise) v2=cos(w*t)+[phasenoise]*sin(w*t)

don't know how to 'set' phasnoise for v2, but they look similar!

for some reason as the phasenoise gets above 1 degree rms in v1 the distribution appears to start changing. will check that.