Mixed Matrix Representation of SAW Transducers

A new cut of quartz is proposed for use in temperaturecompensated dispersive surface acoustic wave (SAW) devices in the reflection array compressor (RAC) confi iat ion. Experimental and was supported by the Department of the Army. of Technology, Lexington, MA 02 173. Manuscript received May 31, 1979;revised July 18, 1979. This work The author is with the Lincoln Laboratory, Massachusetts Institute theoretical evidence is presented for the existence of a rotated Y cut of quartz which possesses two temperature-compensated SAW propagation directions located at right anglmp one another. The rotation angle of this cut is estimated to be 34 2’. Surface acoustic wave (SAW) devices in the reflective array compressor (RAC) configuration are now well established as an attractive means for obtaining dispersive delay lines with accurate phase response and large time-bandwidth products [ l ] . To date, little consideration has been given to the possibility of fabricating RAC devices with good temperature stability. A temperaturestable RAC device requires zero temperature coefficient of delay (TCD) in two perpendicular directions and thus the achievement of temperature stability is considerably more difficult for a RAC than for a straight delay line where the well-known ST cut of quartz [ 21 provides zero TCD for surface waves propagating parallel to the X axis. Theoretical analysis [31 of the amplitude and phase response of a RAC shows that a nonzero TCD in either of the perpendicular propagation directions leads to undesirable temperature-dependent phase shifts in the device response. Thus ST quartz with propagation along and perpendicular to the X direction does not yield a temperature-stable RAC. The TCD at 90’ to the X axis is approximately 45 x 10-6/oC [4 ] . Recognizing this limitation, other cuts of quartz appropriate for temperature-stable RAC devices have been investigated. We propose, on the basis of previous theoretical calculations [ 21, [ 41 , [ 5 1 and measurements carried out by us, a new cut of quartz which has zero first-order TCD along two perpendicular propagation directions. This new cut is an approximately 34O-iotated Y cut and the propagation directions are at +45’ to the X axis. REVIEW OF THEORETICAL CALCULATIONS Slobodnik 141 and Hauden et al. [ 51 have calculated the first-order TCD on both ST and Y-cut quartz plates as a function of propagation direction 8 relative to the X axis. Schulz e t al. [ 21 have performed the same calculations for A T and AC quartz. Fig. 1 shows the results of Slobodnik for ST quartz. ST, AT, and AC are all rotated Y cuts having rotation angles y equal t o 42.5’, 35.25’, and 31’, respectively. (7 and 8 are defined in the inset at the bottom of Fig. 2.) The general shape of the curve shown in Fig. 1 is typical of the results for the other rotated Y cuts. These curves have two significant features in common: 1) all are symmetric about the X axis, and 2) the TCD passes throough zero when the SAW propagation direction 8 is near -+45 to the X axis. The angle 80 at which the TCD equals zero changes monotonically as 7 changes. The thoeoretical calculations indiEate that for ST quartz, B o = 56 ; for the A T cut, 8 0 = 48 ; for the cut, AC O0 = 47’; and for the Y cut, B o = 35’. Crystal symmetry requires that surface wave properties of the rotated Y cuts are symmetric about the X axis. Thus surface wave velocity, TCD, etc., display reflection symmetry about the X axis. Fig. 2(a) shows the results of calculations of the TCD at 8 = 45’ plotted versus y . Also plotted in Fig. 2(a) are experimental points explained below. A line has been drawn througii the experimental points to estimate the value of y for which the TCD = 0 at 8 = 45’. Fig. 2(b) shows B o , which is defined as the angle of surface-wave propagation where the TCD = 0, plotted versus y. These points are extracted from 0018-9537/79/1100-0428$00.75 O 1979 IEEE