Thank you. During the era of using a pencil MANY shortcuts and approximations came into existance. With the advent of the PC, no need. So it's good to hear the formula I had assumed to represent phasenoise DOES represent phase noise. However, there are approximations also *if* certain conditions are met.
no, meant v=cos(w*t)+A2*randn()
Actually, I meant exactly additive johnson noise, like resistors add to a signal. Even though the addition of the additive noise can appear to be other noise modulations to that large tone. Again approximations coming into play.
interesting that it's so difficult to tell the differences.
That's why I qualify that A2(t) has to have an amplitude much smaller than A1 -- as you're finding (and as you pointed out in a separate post), the approximation does break down the bigger that A2(t) gets.
I would have thought that 1 degree RMS would be well under the threshold, but I didn't actually run numbers or anything.
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Tim Wescott
Wescott Design Services
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I think such approximations are still useful in helping us to think of phenomenon like this in general terms. If we have to dive for a computer every single time we have a problem to solve, then (a) we won't be able to think about technical stuff sitting in cafes and looking at pretty young women, and (b) we won't have a good intuitive double-check to make sure that our computerized results are not absurd.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
FAR from true. One decent analytical approximation is of more use than a stack of simulation results from here to, roughly, Jupiter.
Cheers
Phil Hobbs
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Dr Philip C D Hobbs
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ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics
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hobbs at electrooptical dot net
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That is because of the higher order sidebands in the phase modulation. When the amplitude of the phase component is small enough compared to the carrier component, the modulation index is so small that the higher order Bessel functions J2(index), J3(index) ... can be regarded as zero.
From the other side, it can be regarded that there will be amplitude modulation in sync with the phase modulation when the sine component is so large that the total amplitude sqrt(A1*A1 + A2*A2) is notably larger than A1.
Just to retrace steps here: my original phase noise expression is most accurate, but extremely difficult to analyze without a PC? that is, v=A1*cos(w*t+phasenoise) very accurate, but to help can be approximated as v=A1*cos(w*t)+A2*sin(w*t), where A2 is some 'small' level of phasenoise in relation to A1
my problem with using the 'approximation' was I didn't see a value for A2 based upon phasenoise and A1. Where with phasenoise, I could simply talk about the noise in terms of degrees, or radians, and be done with it.
A computer does not help here - you have lack of modulation theory.
Please get a good book on communication theory and read the chapters about angle (phase, frequency) modulation. The book should have the needed information about PM sidebands, and that is what you need.
Good one! Time waveforms are real time, but sometimes going back to a very basic helps. I will try that and THEN use real(exp(arg))
I don't know if the oscillator I'm comparing to has much amplitude modulation. mainly hits the rails. But, there probably is an interaction between the volt/sec trajectory, risetime, and hitting the rail that 'creates' an amplitude modulation coherent to a 'modulated rate', but will look at that later after I square away isolating the phase noise effects.
The end goal here is to gain understanding of the 'effects' of specific origins of noise. With the idea, that it is possible to conceive a test condition that is then able to identify the noise origin. Thus, being able to attack weakness in the design to improve performance.
Interestingly, up until now I've been leaving out the pdf. Didn't know that there was so much modulation to the pdf caused by phase noise.
If you use octave, or Matlab?: N=length(v); k=33; plot([-k:k]/k,(2*k+1)/N*hist(v,2*k+1)); makes a normalized plot no matter the value of k, where the area is one no matter what number of bins you use, so you can overlay multiple plots and 'check' the statistics a bit faster, well at least visually.
I'm not sure what you are trying to do here, but it sounds wrong. Please expand.
Typically, the AM is about 10 dB below the PM.
Yes. These are second-order effects.
Phase noise is narrowband (compared to the carrier frequency) low-index amplitude and/or phase modulation of a carrier. Low index means that one can use small-angle approximations, a great simplification.
The advice to read up on modulation theory is well taken. The low-index part greatly simplifies the theory as well.
There are a lot of details to get right, so build cross-checks into your code: Solve things twice, in two different ways, and compare.
The advice to work the code out using a tone signal (versus noise) first is also well taken, because it's easier to see if the tone is messed up.
Good point. It's struck me, during this discussion, that, for determining noise figure of a mixer, "prime noise tones" applied to each element would do the trick. ...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
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| 1962 | I love to cook with wine. Sometimes I even put it in the food.
In a way. It will show that your expression is a formula for angle modulated signal, which will be quite near the approximate expression if we can ignore the higher order sidebands.
The first order sidebands are quite like AM sidebands, but at 90 degree phase difference, which is taken care of using both cos and sin.
Another neat trick to make analytically predictable noise of small peak to average ratio that one can also generate precisely is multisine excitation, where one adds together multiple sine waves of non-harmonic frequency. In many cases, one gets better signal to noise ratio if the lower frequencies are louder than the high frequencies. Google on multisine to be swamped.
As promised! I compared three waveforms, ...by accident
first was v=cosine(w*t+phasenoise) second and here was the accident: v=real(exp(1i*w*t+phasenoise)), you immediately see the error there? and the 'correct' form v=real(exp(1i*(w*t+phasenoise))) for 1, 5, and 25 degrees rms of gaussian random noise interestingly, the cosine one and the third one pretty much were identical, except for variations cuased by statistical variations in the random functions. hmmmm...I could 'force' each style to have identical statistics, like in LTspice. arrrrggg, more work.
The spectrum of ALL noise was FLAT - every case. but there were some nuances that caught me a bit off guard, more like a 'wake up' call. the amplitude of the 'noise' does not track the amplitude of the phasenoise, which makes sense.
25*phasenoise1/phasenoise25, should approximate 1, but it gets squashed to
0.87, by around 13% In other words, as the phasenoise increases, the noise increases but does not quite track in ratio, like with additive noise or amplitude noise. again, as expected.
What was VERY interesting was the pdf of the resulting noise in the first use of cosine, the pdf starts sharp, as in 8:1, where gaussian is more like 3+:1, gets squashed as phasenoise increases to 25 degrees rms. The last form of imaginary exponential was pretty much identical. But the incorrect form actually became sharper with increased 'phasenoise' went up to 17:1 at 25! but that wasn't phase noise that was amplitude modulation noise!
Also of note was that the pdf appears to start to 'split' with excessively large phasenoise of 25 degrees rms. Not even going to think about that right now. When I did 0.2, 1, and 5 degrees rms the pdf was getting slightly squashed, but with 25 it obviously starts splitting! with a double peak.
I don't expect an oscillator to have much phase noise, so can't believe that observation has much value in identifying the origin of oscillator noise.
sadly, google has NOT been my friend so I don't do many searches anymore.
I use multi-tones a lot and have a program from a previous project that will generator a set of tones, of unrelated harmonics, except for the ones single inescapable attribute of making them multiples of BW, or minimum frequency.
else then must use hanning window and there is still too much 'smushing' to be able to see what's realy going on, so best if the basic tones ALL are multiples of BW, but not relate to each other. That way get sharp spikes in the FFT.
Do you recommend a 1/f^2, or 1/f from low to high? that's easy to do too.
AHA! that's my point! now use .tranoise and put some pure tones into the mixer, and let PSpice or LTspice show you the noise figure of that mixer.
If somebody can supply an accurate NPN model that goes into the MC1496 mixer, I'll give you back the .tranoise noise model for it. Then you can put in the pure tones, do anything you want, and compare to what you'd expect.
Jim, you gave me some 3904 models to use, but admitted they did not include 1/f noise, nor tell me whether they were 'minimum' geometry, or not. To get closer predictions, the models should replicate the NPN geometry used in the MC1496 multiplier and include the 1/f, too.
PS: because I have to 'externally' work these noise sources, the .tranoise models I generate tend to have conditions that will actually increase the noise, but only around 3dB. If we can build in the technique, be just like normal simulation.
See "BipolarTransistor_FromPSPCREF.pdf" on the S.E.D/Schematics Page of my website. Add parameter AF to the models you received... twiddle until you match 1/F noise from data sheet. ...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.
not sure how to expand more, except to explain that I'm developing an understanding of the 'effects' of the noise sources on an oscillator, so I can configure a real test to find the origin of any limiting noise floor, in order to attack the design at the source of that limiting noise. all to improve performance.
Thanks, any idea why?
Interesting that phasenoise is 'narrowband' yet 'looks' like broadband being completely flat.
I'm skilled at communication systems, using AM, FM, PM, and spread spectrum - all three types, the two approved by FCC/ECC and one that's not approved, but should be. I also invented a simple really, really low cost low power full-duplex comunication system for use as wireless headset for cellphones. run something like 40 hours on a hearing aid sized button battery. Take THAT bluetooth!
But you have uncovered a trait that is a 'weakness' --- I ALWAYS re-invent the wheel! There's nothing like starting from scratch to make certain that every piece that is there belongs there.
Good advice. And also as part of this double checking I am baring all here. Mistakes, misroutes, all. A bit embarrassing at times, but one can REALLY make great progress that way!
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