Synthesis of Dispersive Delay Characteristics by Thickness Tapering in Ultrasonic Strip Delay Lines

Abstract

Tapering the thickness of a dispersive strip delay line operating in the first longitudinal mode can yield a variety of delay characteristics unobtainable with strips of uniform thickness. A strip whose thickness varies in some manner along its length may be thought of as a number of strip sections of constant thickness in series. The additive delay of these series sections can produce an over-all delay characteristic completely different in form from the delay characteristics of the individual sections. A design procedure involving the methods of linear programming has been developed which allows a unique determination of the taper required to produce a given delay function. As a basis for comparison, the delay of a strip delay line of constant thickness departs from a straight-line characteristic by 1.5% of the nominal delay over a fractional frequency bandwidth of 15%. A tapered strip line designed for the same nominal delay and the same delay slope departs from linearity by only 0.5% over a 25% band. A tapered line designed to approximate an increasing parabolic delay characteristic exhibits a delay deviation of only 0.5% over a frequency band of 13%. An “image” line was fabricated having a decreasing parabolic delay characteristic approximating the mirror image of the increasing parabolic characteristic mentioned above. Although most of the applications of delay synthesis have employed the first longitudinal plate mode, the design procedure has also been applied to shear modes in a strip. For delay lines having nominal delays of 1000 μsec, typical insertion losses are 16 to 25 dB, with discrimination against unwanted signals of 35 to 40 dB.