[sdiy] 3046 vco help?

[Magnus Danielson]

On 18/08/11 23:20, dan snazelle wrote:
> "The "benefit" of this is the lack of high gain in the feedback path, which can make it warmer due to the inherent trigger jitter, but explaining that can be a bit tricky, but I could go into that if you need me to."
>
> first off , thanks so much.....second,
>
> I would love it if you could go into that....the information is really helping me....

Well... OK then.

There is two things making the noise a bit complicated. Let's start with 
the open loop properties.

Consider that you have the voltage rising (or falling) linearly as the 
capacitor accumulates the current and it's voltage reflect the 
capacitors charge. This linear ramp is then being compared against some 
reference voltage by the comparator. There is noise sources in there, 
both guassian (flat) and flicker noise (1/f power noise). When the slope 
comes nearer the reference voltage the exact time of the flipping of the 
comparator becomes dependent on the noise. This is trigger noise. The 
trigger noise will have a jitter depending on the voltage noise and the 
slew-rate, the higher noise voltage or the slower slope, the higher 
jitter. Thus, the time-jitter t_jit comes out of noise voltage e_n and 
slew-rate S as:

t_jit = e_n / S

Where the jitter is RMS in seconds, the noise is RMS in volts and 
slew-rate is in volts per second.

Now, as you can see from this basic formula is that the slew-rate of the 
waveform at the comparator voltage can have a great impact of the amount 
of time jitter we get for a certain amount of noise. We can adjust that 
by the use of amplifiers, so we can amplify the signal out of jitter.

Using a scope and a sine, clarity of the sine can be seen changed as the 
trigger goes on the mid-part (clear) to very fuzzy and unstable if 
trying to trigger the scope on the peak. Good educating exercise on 
trigger-jitter.

Now, while hand-waving around the trigger jitter issue you will see yet 
some more hand-waving... but now confusing on a different degree.

As inherent and amplifier noise exists in a feedback structure such as 
an oscillator, the feedback over an integrator path will cause the phase 
noise of the oscillator to have a power noise corner of 1/f^2, so at 
some frequency the power noice rises with lower frequency. Since we have 
a mixture of flat gaussian noise and flicker noise (having the power 
noise of 1/f) which by itself has a corner frequency where the flicker 
noise rises above the gaussian noise as frequency becomes lower. The net 
effect of these becomes that wide-band the side-band of the carrier has 
flat noise, as you get closer to the carrier, the sideband grows by 1/f 
or 1/f² (depending on which of the two corner frequencies which is 
highest) and then has for really close in side-band 1/f³ properties. 
This analysis was presented by Nick Leeson in a 1966 February article, 
aimed for crystal oscillator noise modeling, but the analysis goes 
beyond crystal oscillators as such. It's inherent of oscillators as such.

Now, notice how amplifier noise becomes critical here... and how 
amplifier gain will be another parameter.

If you are even more interested in this, you can knock yourself out on 
the Allan Deviation article on Wikipedia, since it is the statistical 
tool by which we handle these troublesome noise sources to even have a 
chance of measuring it properly. 1/f^2 and 1/f^3 noise does not converge 
with standard RMS calculation, so it becomes meaningless to use it. 1/f 
noise just make it hard to get good values.

So, while I have been hand-waving a bit here, I have scratched the 
surface to show you some of the tools for analysis of jitter noise that 
we use. I've been sloppy not to explain all things properly but it's 
part of the handwaving. I hope you got a glimps of what I think about 
when it comes to jitter in audio oscillators.

It is amusing to note that in order to get good quality measures on 
really high quality crystal oscillators, one mix them down to audio 
frequencies, and then analyze that. Mixing 10 MHz down to 100 Hz gives a 
time-resolution gain for 100000. Tricks are then done to remove the 
noise of mixing oscillator and other parts... putting the noise-floor 
below the components being used.

Ah well, so much fun and so little time.

Cheers,
Magnus