Re: Phase or frequency modulation?

Liz Tuddenham <liz@poppyrecords.invalid.invalid> wrote:

Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> wrote:
 

Liz Tuddenham <liz@poppyrecords.invalid.invalid> wrote:

Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> wrote:
 
 

... The crystal mode is a mass-spring
oscillation, so an instantaneous change in the spring constant causes an
instantaneous change of frequency.
 
There’s no need for the resonant energy to die out, unlike the case of
external forcing, where a change in the forcing frequency takes on the
order of Q cycles to change the response.

 
Could I ask you to explain this a bit more please.  Where is the
'spring' that is variable?
 
 

 
The spring is the mechanical stiffness of the quartz, plus the
piezoelectric force caused by the interaction with the external circuit.
The mass is the mass. ;)
 
Dorking the load capacitance slows down or speeds up the piezo restoring
force.

 
Interesting, I hadn't come across that before.  Presumably the effect
would be the same if the controlling reactance were an inductor or a
tuned circuit?  In my case, the 'variable reactance' is an
amplitude-modulated 90-degree phase-shifted current injected into the
controlling inductor.
 
 

The Q of a good crystal is high enough that it’s really just the phase
angle of the load at resonance that matters.  How you make that load is
less important, though it still matters.

A bad circuit can produce multiple frequencies, but in a fundamental-mode
oscillator that takes some talent.

Any given resonance of a crystal looks electrically like a series RLC in
parallel with a capacitor. If the parallel cap is small enough, the
impedance of the crystal goes inductive in a narrow frequency range, so it
can be made into a tank circuit, e. g. in a Colpitts oscillator. The
overall circuit resonates when the load reactance is minus the crystal
reactance, and that happens at just one frequency in this case.

If the parallel cap is too large, the impedance is capacitive everywhere,
so you need an inductive load. Unfortunately, due to the crystal’s
impedance peak, there will be two closely spaced resonances, one on each
side of the peak, and probably one or more LC peaks elsewhere, depending on
the details.

It’s often useful to make one half of the Colpitts divider out of a series
LC, to make sure the phase is wrong at the higher overtones, and keep the
gain down to avoid LC oscillations.

(And then there’s startup behavior, but that’s another topic.)

Cheers

Phil Hobbs


--
Dr Philip C D Hobbs  Principal Consultant  ElectroOptical Innovations LLC /
Hobbs ElectroOptics  Optics, Electro-optics, Photonics, Analog Electronics