Oscillators
with Crystals Having Two Sets
of Electrodes
The original crystal oscillator devised by Dr. Nicolson, as well as a
number of the earlier crystal oscillators tested by Dr. Cady, employed crystals
with, effectively, two pairs of electrodes. The basic circuit is shown in
figure 1-156. The re quired phase inversion of, the amplifier output voltage is
provided by the crystal unit operating at a mode for which the polarities of
the plate and grid terminals with respect to ground are 180 degrees out of
phase. The circuit shown operates the crystal unit very
near its
series-resonance frequency. In practice, a capacitor is normally connected
between crystal and ground, so that the circuit is more commonly employed for
parallel- mode tested crystal units. Still, it is not without some JiCefl8e
that we classify this type of oscillator as a parallel-mode type. The crystals
most applic able for this class of circuit are the very-low- frequency elements
of the X group, which vibrate in lengthwise extensional or flexural modes. The
electrode connections that permit the desired phase inversion depend upon the
particular crystal element. Assume that electrodes numbers I and 3 are on one
side of the crystal, and that 2 and 4 are on the opposite side, as indicated in
figure 1-156 (A). For a flexure element, such as element N, where electrodes 1
and 3 parallel each other down the length of the crystal, as shown in figure
1456 (B), the flexure mode is excited when the potential across 1 and 2 is
oppositely polarized to that across 3 and 4. If the same electrode arrangement
is to be used to excite an extentional mode (or the flexural mode of the duplex element J) the
polarities of
the two sets of electrodes must be in phase. In this case, the connections of one set of
electrodes should be reversed in the circuit shown in figure 1456(A). For
example, plates 2 and 3 should be connected to ground and plate 4 should be
connected to the grid, if the proper pha8e inversion is to be obtained. A
crystal having the two sets of electrodes at opposite ends of the crys tal, as
shown in figure 1-156(C), would be driven at the second harmonic of the length
extensional mode (or of the fiexural mode of a duplex ta, if connected as shown
in figure 1-156(A). Greater stability and a smaller crystal are possible for a
given frequency by operating at the fundamental mode. To permit this, if the
crystal unit is plated as shown in figure 1456(C), the connections of one pair
of electrodes should be the reverse of those shown in figure 1-156(A). If it
can be assumed that the current in the grid circuit is negligible compared with
the crystal current between term inals I and 2, and if the stray capacitance
bet ween the two sets of electrodes is ignored, the equivalent circuit between
terminals 1 and 2 will appear approximately as shown in figure 1-156 (D). L, C,
and C0 represent the parameters of a fully plated crystal. A more exact
analysis of this type of crystal unit can be found in the book
“Electromechanical Transducers and Wave Filt ers” by W. P. Mason, D. Van
Nostrand Co.
Figure 1-157 shows a practical oscillator design employing crystal units having
two sets of electrodes. Although the electrode connections shown for CR would
indicate that the plate and
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