In message lDuKh.7998$vV3.3900@trndny09, W3JDR writes
Just to set the record straight....

Someone suggested that you need to 'neutralize' the parallel resonance so
the series resonance can be tuned toward it. This is completely wrong!
It may be 'completely wrong', but my experience with getting out-of-spec
(too LF) VHF overtone crystals up to the required frequency indicates
that it does enable the oscillator to work at a slightly higher
frequency than it 'wants to'. This is because the throughput peak of the
series resonance moves HF when the sudden parallel resonance is removed.
[The assumption is that oscillation occurs at the peak of the series
resonance, which may not be entirely true.]

The
series resonance is, for practical purposes, invariant. The motional
parameters (L and C) of the series resonance are such high reactances (small
capacitance; high inductance) that external components have only a tiny
influence on the series resonance.
This is more-or-less what I said. The influence of the relatively large
series trimmer capacitor will be pretty small.

The series resonant frequency is the lower of the two crystal 'resonances'.
The parallel resonance is above it. When you make a VCXO with any
substantial tuneability, you're probably operating the crystal at its
parallel resonance.
Lots of technical information calls the actual parallel resonance
'anti-resonance', and indicates that there is an 'area of parallel
resonance' between the true series resonance and the spurious parallel
resonance. In this area, the impedance of the crystal rapidly changes
from being zero (at the series resonant frequency) to infinitely
inductive (at the anti-resonant frequency). In many oscillator circuits,
the oscillation occurs neither at the series resonant nor the parallel
(anti-) resonant frequencies. Instead, the actual frequency of
oscillation will be determined by some value of this inductance and the
external capacitors, and also on the phaseshift and amplitude of signal
throughput through the crystal. All very complicated!

This leads to the common observation that you can 'pull'
a crystal up in frequency more than you you can pull it down. You can only
pull the parallel resonance to approach the series resonant frequency, but
you can't pass it because the crystal is effectively a short-circuit at that
frequency.
And neither can you use external elements to pull the series resonance
very far HF, because it runs into the parallel resonance. From my
experience, a swept frequency response through a crystal shows that the
throughput peak of the series resonant frequency never really reaches
its full amplitude before it starts to get pulled down in parallel
resonance hole. Neutralizing the shunt capacitance prevents the parallel
resonance from occurring so close to the series resonance. As a result,
the frequency response throughput curve becomes symmetrical, and the
actual peak is somewhat further HF. Certainly, my oscillators (which
were supposed to operate at the true series resonance of the crystal)
DID move HF when I neutralized the crystal.

[Note that the full frequency response of a crystal with a parallel
neutralizing inductor, from DC to well above the crystal frequency,
consists of a broad notch centred on the crystal frequency (the parallel
resonance of the parallel capacitance of the crystal and the
neutralizing inductor). In the centre of the notch is a very narrow
bandpass (the series resonance of the crystal).]


Also for the record, the crystal's quartz only has one fundamental and
significant natural resonance - the series resonance. The so-called
'parallel resonance' is actually a controlled spurious resonance caused by
the holder capacitance. At frequencies above series resonanve, the crystal's
RLC equivalent looks inductive, and at some frequency the holder capacitance
will resonate that net inductance.
Exactly so.

At the parallel (anti-) resonance, the reactance of the crystal suddenly
jumps from being infinitely inductive to being infinitely capacitive
(0p). As you move further HF, it stays capacitive, progressively
decreasing in reactance. The parallel resonance therefore presents a
brick wall, beyond which external capacitors cannot resonate with the
inductive reactance of the crystal. However, if you neutralize the
crystal, you kill the sudden transition from series to parallel
resonance, and the frequency range over which the crystal is inductive
is considerably extended. This should enable the resonance with external
capacitors to extend further HF than when the crystal is not
neutralized.

As I originally said, neutralization of the crystal was a suggestion,
rather than a panacea. I still reckon that should work. It's worth a
try. Unfortunately, the size required for the inductor (which resonates
with the crystal parallel capacitance of appx only 5pF) is rather large.
If neutralization DOES help, a brute force method of allowing a somewhat
smaller inductor to be used would be to deliberately add MORE parallel
capacity, and lower the value of the inductor to suit. A more elegant
method would be to build the crystal into a simple bridge circuit, so
that a neutralizing capacitor could be used instead of an inductor.
However, I appreciate that the object of the exercise is to make a
simple receiver, and it would be somewhat incongruous to need a very
complicated circuit just for the crystal.

Ian.

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