linear FM : was RE: [sdiy] Temperature Compensated VCO attempt - help?

[René Schmitz]

At 22:35 04.02.03 +0100, Magnus Danielson wrote:
>Please go ahead and bore me to death on the issue.

Can do! :-P

If we assume the probability of the sign change to be equally distributed. (A good 
bet, because they are principially uncorrelated.) Then the probability of the two 
events occuring simultaneously would be the time of the pulses vs the cycle time. 
(I'm assuming a state machine which changes direction on the thresholds and also 
when the FM changes state.) If we assume the threshold-reached pulse is 500ns and 
the cycle time of the oscillation is 1ms. Then the probability for both to occur 
simultaneous is 500ns/(1ms-500ns)*P or about 0.05%*P. Where P is the probability 
for a FM sign change within one cycle of the FM waveform which is finite. 
(Let there be one sign transition per 1ms, and you end up with an oscillator which 
runs on the average for 2000 cycles, or 2 seconds.) I simply doubt that one can 
neglect that!

>This lack of determism is also what cause our classic oscillators to have
>phase noise. It's there... just live with it.

Right, but I think noise is _yet_ another problem. I think the above will hold even 
if there is no noise in the threshold mechanism. I use the word nondeterminism in 
the sense of "not knowing ahead" when the state changes occur (and also not when 
they do simultaneously). IMHO a state based approach is very difficult, because the 
probability to go into an unwanted state (call it metastability, your integrator 
running towards the rails or whatever) is just too high. 

Cheers,
 René


-- 
uzs159 at uni-bonn.de
http://www.uni-bonn.de/~uzs159