Hi Everyone,

I have a fundamental question to ask.

Assuming a 3rd order charge pump PLL.
If you do a AC analysis to check the loop stability,
the inital phase will start from -180 because there are
already two poles at origin contributed by VCO & the 2nd order loop filter.

Now I know that the Phase Margin (PM) is measured at the cross over freq point = phase - (-180) degrees.
The phase around the crossover point will be "helped"
by the zero in the loop filter; hence it will be lesser than
-180 ie zero contributed +90 phase.

Now for my question: from theory, an oscillation will start if the phase is -180deg and loop gain >>1. So from
the 0Hz to crossover freq region where the loop gain is high and phase is -180deg. does that mean the loop have the tendency to oscillate ???


Thanks in advance!

Simon,

  Two things:

1) See "Frequency Synthesis by Phase Lock", by W. Egan,
    in particular, Chapter 6 discusses Higher Order Loop  
    filters.

2) Also, though I can't find a reference, I believe that the
   condition for stability is little different than you
   describe. It is more like the loop is stable if the slope of
   the magnitude at  gain=1 is 20dB/dec.  So as long as
   there is one more  pole than zero in the loop, the loop
   should be stable.

A little additional discussion, if you think of the Barkhausen Criterion, oscillation is only sustained at gain=1.  So the above rule is just implying the system is well-behaved at the unity gain cross-over, i.e., there is not enough excess phase from the higher order to poles to cause oscillation.

                                               Best Regards,

                                                  Art Schaldenbrand

I accidently posted this in the wrong location. Here is where I meant to post it.

Your question touches a more general question, one that is frequently asked in controls classes. The question has to do with conditional stability. What if the Nyquist plot crosses the negative real axis several times before diving into the unit circle with a respectable (and stable) phase margin? Usually, there's enough phase shift at high frequencies that the Nyquist plot crosses over at least once after crossing into the unit circle. Assuming there are no open loop poles in the RHP, the system is defined as conditionally stable, meaning that the system is unstable only if the gain is decreased by some amount or increased by another amount. In this case, the system is stable but the are several places where gain exceeds unity and phase = 180 (total feedback phase = 360). I have yet to hear an intuitive answer to this apparent paradox. I suspect this is simply one of those times we must abandon our intuition and adhere to a strict interpretation of the Nyquist stability criterion.

I would also like to point out one other thing about your example. You say the phase is 180 at DC. There are very few true integrators in the real analog world. For example, all physical capacitors have some leakage. The PLL is probably only first order at DC and therefore does not actually have 180 degrees of phase shift at DC.

Also, if you check the text books, the Nyquist contour takes a jog around the origin when the open loop gain has poles there. The resulting Nyquist plot does not actually touch the negative real axis at DC.