[time-nuts] PLL Digital Loop Filter

Attila Kinali attila at kinali.ch
Tue Mar 21 07:39:07 EDT 2017

On Mon, 20 Mar 2017 21:32:28 -0700
James Peroulas <james at peroulas.com> wrote:

> I'm trying to understand how to design and analyze the loop filters in a
> digital PLL. Specifically, because of digital processing delays, the phase
> offset measured at time t will only produce a change on the VCXO input at
> time t+T, where T is the sampling period of the digital loop.

You have the same delays in analog filters as well. As a rule of thumb
you can assume that the delays are in the same order of magnitude as
with the equivalent analog filters, not accounting for the delays due to
pre- and post-processing of the signal.
The analysis of digital PLLs works the same as with analog ones, you
just exchange the Laplace transform with the Z-transform. You can add
arbitrary delays due to pre/post-processing as a simple multiplication
by 1/z for each clock cycle of delay.

> I've found plenty of texts describing analog loop filters. Are there any
> recommendations for digital loop filter PLL design?

The PLL book by Best contains two chapters on how to design digital PLLs.
I can also recommend "Understanding digital signal processing" by Lyons,
which is a very hands-on description how to do filters and perform other
signal processing tasks.

				Attila Kinali

It is upon moral qualities that a society is ultimately founded. All 
the prosperity and technological sophistication in the world is of no 
use without that foundation.
                 -- Miss Matheson, The Diamond Age, Neil Stephenson

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