John Larkin said:
It's easier to analyze a crystal oscillator in the frequency domain,
open-loop. You can resolve the oscillation frequency to arbitrary
precision and optimize the phase slope at resonance (0 degrees around
the loop point) for low phase noise. You really can't tell much about
crystal oscillator behavior from a time-domain analysis, except gross
stuff like amplitudes. There's practical no way to measure the
oscillation frequency to ppm precision from a time-domain analysis.
I really don't think frequency domain loop analysis will give the true
oscillation frequency. The loop is not linear - the transistor is cut off
most of the time. As the brief description shows, the voltages and currents
injected into the crystal are not sinusoidal, but are highly distorted. So
it's not possible to treat them as pure sine waves, which is needed to
optimize the phase slope.
It makes little sense to calculate frequency to arbitrary precision when
the crystal and circuit parameters are not known to that precision. That's
what the trim capacitor is for. All you need to know is if it has the range
needed to meet worst-case circuit and crystal parameters. You can get this
information much better in the time domain.
You can get pretty accurate frequency information of the actual
oscillation frequency in the time domain by counting over many cycles. But
the oscillator has to be in steady-state.
Time domain gives information not available in frequency domain, such as
collector waveform and phase relation to the tank current, and various
waveforms, currents and time relationships everywhere in the circuit.
Frequency domain analysis doesn't tell you if the oscillator is clipping.
This hurts phase noise.
Hajimiri and Lee have described the importance of timing the peak of the
collector current pulse to coincide with the peak amplitude of the
oscillator waveform. You cannot get this information in the frequency
domain.
As the brief analysis shows, there are different phase shifts and
distortions throughout the circuit, so you need time domain to tell where
they are and how to deal with them.
Many crystals are destroyed by running at too high a power level. You
cannot get this information in the frequency domain. You need the time
domain to tell how much power is dissipated in the crystal, and how well
the oscillator handles worst-case tolerances in crystal and circuit
parameters.
Just poking an initial condition won't "quickly settle to
steady-state" ... not in 150 cycles, with a Q of 64K. It only looks
steady-state because the Q is so high! Check it again every, say,
30,000 cycles to spot any trends.
Nope. MC8 allows you to go from one peak to the next with 6 digits or
more of amplitude resolution. You can easily see from one cycle to the next
if the amplitude is increasing or decreasing. If the amplitude is not
changing, the oscillator is in steady-state operation.
The advantage of this method is it doesn't introduce serious transients
into the oscillator that take a long time to die out. After a brief burble
at the beginning, it quickly settles into steady-state operation.
Goosing an oscillator to get it going is hardly a new idea.
Normally, "goosing" an oscillator means forcing a pulse or step somewhere
in the tank. The amount of energy is difficult to control, and it usually
does not bring the oscillator to full amplitude. You then have to wait many
cycles for the oscillator to reach steady-state, which takes a long time in
SPICE.
You can fiddle with the pulse amplitude to try to make it reach steady
state sooner, but this usually introduces severe transients that take a
long time to die out.
If you make any changes to the circuit parameters, the energy introduced
into the tank changes, so you may have to fiddle with the step amplitude
some more. This wastes a lot of valuable time.
The method described sets the initial condition by placing a predetermined
current through the tank inductor. This is the normal peak current when the
oscillator is running, so there are no large circuit transients such as
those introduced by injecting a step or pulse into the tank.
The initial current causes the oscillation to start in a known phase with
known amplitude. This sets the power level dissipated in the crystal to a
known level, which is critical for some crystals. The brief transient at
the start of Transient Analysis only takes a couple of cycles to die out
and the circuit quickly settles into steady-state operation.
As described in the paper, the feedback capacitors and emitter resistor can
be easily trimmed to maintain the desired power level.
Since you no longer have to wait hundreds or thousands of cycles to reach
steady-state, you can quickly see the effect of changes in crystal and
feedback parameters, and you can ensure the oscillator will operate
satisfactorily with worst-case parameters. This is difficult or impossible
to do in the frequency domain.
Regards,
Mike Monett
