Crystal Oscillators


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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