Frequency response of a PLL. What does it convey

The "frequency response of a PLL" is plotted as

angle_at_vco_output(s)/angle_of_input_wavefom(s) = a classical 2nd
order system described by a the "s" transform, where s = jw. Where w
is in radians.

So what does a plot of this convey. I've read in places that we can
interpret the response as a low pass filter etc. But what we have here
is not input voltage divided by output volatage, but input angle
divided by "output angle".

Ted.

Ted wrote:

> The "frequency response of a PLL" is plotted as
> 
> angle_at_vco_output(s)/angle_of_input_wavefom(s) = a classical 2nd
> order system described by a the "s" transform, where s = jw. Where w
> is in radians.
> 
> So what does a plot of this convey. I've read in places that we can
> interpret the response as a low pass filter etc. But what we have here
> is not input voltage divided by output volatage, but input angle
> divided by "output angle".
> 
> Ted.

Filters don't have to be voltage/voltage.  They can be current/current, 
raw clay in / bricks out (for a brick factory), voltage in / current out 
(for an impedance), numbers in / numbers out (like in a DSP, which is 
what this group is all about), torque in / rotation out, etc.

So what it's filtering is the input signal, which happens to be a phase 
angle, and it's output signal is another phase angle.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

On 27 Jul 2004 18:30:41 -0700, ed_ted_ed@yahoo.com (Ted) wrote:

>The "frequency response of a PLL" is plotted as
>
>angle_at_vco_output(s)/angle_of_input_wavefom(s) = a classical 2nd
>order system described by a the "s" transform, where s = jw. Where w
>is in radians.

Most of mine are at least fourth order, although there are usually two
dominant poles and many second order approximations remain valid.

>So what does a plot of this convey. I've read in places that we can
>interpret the response as a low pass filter etc. But what we have here
>is not input voltage divided by output volatage, but input angle
>divided by "output angle".

Exactly right.

Consider passing a signal with angle (= phase or frequency) modulation
through a PLL.  The PLL will filter the modulation.



Consider phase noise, which is just phase modulation (actually it's a
noise density, with units dBc/Hz).  The transfer function of the PLL
will allow you to work out the output phase noise directly.

You can also work out the transfer function from the (phase noise of)
the VCO to the output.  This has a high pass response.

As a *very* rough approximation, at frequencies below the loop
bandwidth, the output is tracking the input, and the output phase
noise is dominated by the phase noise of the input.  At frequencies
greater than the loop bandwidth, the output phase noise is dominated
by the VCO noise.

Regards,
Allan.