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Resources regarding Phase Locked Loops?

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Phil Hobbs

Jan 1, 1970
0
Fred said:
Robert Latest a écrit :

Cleaning a signal with a PLL is just getting the signal through a narrow
BPF (and adding some noise and phase error too).
Mixing two PLL'ed signals the translates your BPF center frequency to
zero, transforming it to an LPF.

Multiplying the signal first and LPFing it after is just the reversing
the operations (first translate your frequency, then LPF it).

This is true only if (1) one signal is very quiet, and (2) you're using
a SSB mixer or a zero-Hz IF, so there's no sideband folding.

To see (1), consider multiplying a signal by itself, as in an AM
detector. One can't replace the RF and IF filters in an AM radio by an
audio filter--after all the intermodulation, it's too late.

To see (2), consider image rejection in a superhet. Ordinary mixing
makes components at F_rf+F_lo and F_rf-F_lo land on top of each other.
Even if there's no signal at the image frequency, if you leave out the
filter you lose 3 dB in SNR due to the noise at the image.
They are both mathematically equivalent, but I'd try to avoid the PLL
noise.
If the frequency is low enough I'd go for the multiplier first and LPF
later, and otherwise probably for a DBM and LPF.

The PLL is going to have most of what you'd need for a mixer/filter
measurement already in it--a phase detector and lowpass filter, plus
probably a bandpass filter to allow the loop to acquire lock in the
first place (there are other methods, but this is a common one).

The BPF/mixer/LPF approach is good if the phase difference you need to
track is small, the signal amplitudes are stable, and you know pretty
well what it is already (e.g. that the relative phase is always 0.1 to
0.4 cycles). Otherwise it's a mess--the slope of Vout vs phase will
depend on the amplitude, and you'll only get the phase modulo pi radians
anyway.

You can use a limiting amplifier ahead of the mixer, which fixes the
amplitude dependence problem, but will inevitably cause some AM-PM
conversion--the amplitude noise will turn into phase noise.

Using a PLL to clean up the noisy signal has two advantages here: first,
it gives you the constant amplitude you need without needing a limiter,
so you potentially have better phase accuracy; and second, you can use a
frequency divider in the loop to allow you to track over a wider range
in phase (many cycles, potentially). The PLL's low AM-PM conversion
arises from running the phase detector at null (zero volts dc
output)--changes in signal amplitude cause changes in slope (and hence
in loop gain) but since zero times anything is still zero, amplitude
changes ideally don't cause any phase error at all.

There's a phase ambiguity in loops with dividers, because when you turn
the box on, the counter will wake up in some state M, that won't in
general be the correct relative phase.

The other disadvantage of PLLs, as others have pointed out, is that
noise and loop dynamics cause the PLL output to have additional phase
variations. This is generally quite benign if the PLL is properly
designed, by which I mean that the loop is properly
frequency-compensated and the input signal to the phase detector doesn't
contain large components with offset frequencies >~ the loop bandwidth.

Another approach that has many of the same advantages is to make a
phase-tracking loop with a phase shifter instead of an oscillator, and
use its output directly. I did a digitizing version of this in grad
school, which worked great.

Cheers,

Phil Hobbs
 
P

Phil Hobbs

Jan 1, 1970
0
Phil Hobbs wrote:
Ordinary mixing
makes components at F_rf+F_lo and F_rf-F_lo land on top of each other.
Even if there's no signal at the image frequency, if you leave out the
filter you lose 3 dB in SNR due to the noise at the image.

Synapse failure--should be F_lo+F_if and F_lo-F_if.

Cheers,

Phil Hobbs
 
J

John Larkin

Jan 1, 1970
0
Robert Latest a écrit :

Cleaning a signal with a PLL is just getting the signal through a narrow
BPF (and adding some noise and phase error too).
Mixing two PLL'ed signals the translates your BPF center frequency to
zero, transforming it to an LPF.

Multiplying the signal first and LPFing it after is just the reversing
the operations (first translate your frequency, then LPF it).

They are both mathematically equivalent, but I'd try to avoid the PLL
noise.
If the frequency is low enough I'd go for the multiplier first and LPF
later, and otherwise probably for a DBM and LPF.

One of the ways to measure the phase noise of an oscillator is to
build two of them, offset them in frequency a bit (making sure they
don't lock!), mix their outputs, and analyze the result.

We do the same sort of thing with digital delay generators. It hard to
measure a DDGs jitter versus delay, because it's hard to find
something as a zero-jitter reference. So we measure the jitter between
two identical ddg's versus delay, and multiply by 0.707.

John
 
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