Re: [Discuss-gnuradio] pll_refout_cc - finding optimum alpha & beta ??

[Eric Blossom]

On Thu, Mar 16, 2006 at 03:04:31PM -0500, Charles Swiger wrote:
> I'm looking for clues on the transfer function for gr.pll_refout_cc()
> as to how to find optimum values for alpha & beta. 
> 
> Using experimental methods: http://webpages.charter.net/cswiger/pll/
> ( script requires special versions of gr_pll_refout_cc.h,i )
> 
> Interesting how, as the input signal is reduced in amplitude and
> disappears DOWN into the grass, the output signal remains constant
> and the grass comes UP to swamp it! Neat.
> 
> Interesting tutorials: http://www.complextoreal.com/
> 
> --Chuck

Chuck, I could have this totally wrong (the code definitely needs some
comments), but it's a second order control loop.  We're adjusting both the
estimates of the phase and the derivative of the phase (commonly
called frequency ;)) 

I believe that setting

  alpha = some value
  beta = 0.25 * alpha * alpha

will result in a critically damped control loop.
Try some experiments that maintain this relationship.

Eric