F-V converter and Ring Mod. stuff

Don Tillman don at till.com
Wed Feb 21 18:18:39 CET 1996

   Date: Fri, 16 Feb 96 09:33:45 PDT
   From: gstopp at fibermux.com

   When the loop filter consists of a simple R/C lowpass followed by a 
   buffer, the PLL will zoom to the lock point and then "ring" for a long 
   time around it like a spring ("booooiiiiing!"). Adding a resistor 
   between the cap and ground increases the damping and kills the 
   springey effect.

With a simple RC low pass filter tuned to Wl, the loop's response to a
frequency change is a second order low pass with a frequency and Q of:

  Wloop = sqrt(LG * Wl)
  Qloop = sqrt(LG / Wl)

Where LG is the loop gain, which is the gain around the loop at a
frequency of 1 rad/sec.  (We have to pick a frequency cuz the phase
comparator is acting like an integrator.)

So the spring effect is from too much loop gain. 

Note that, with an exponential VCO, the loop gain increases
exponentially with frequency.  This is a good thing for tracking, as
the tracking actually gets faster at higher pitches, but you'll get
more of a spring effect too.  I 'spose it would be best if the filter
could change tuning in parallel with the VCO.

Some nonlinearities before the VCO could also help.

Adding the resistor between the cap and ground does lower the Q, but
also adds a band pass loop response in addition to the lo pass.  You
know that can get interesting.

  -- Don

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