Approximate closed-form expressions for transducer capacitance, transducer coupling, piezoelectric velocity shift, and piezoelectric reflectivity

Many important properties of SAW transducers can be expressed in closed-form with excellent accuracy by using an electrostatic approximation for the solution to the electric fields under an array of regular electrodes. These include transducer capacitance, piezoelectric transducer coupling, the piezoelectric component of velocity shift, and the piezoelectric component of electrode reflectivity. While these have been long known, in practice they are often not used simply because these expressions contain Legendre functions which are not readily available as intrinsic functions in most computer languages. This paper presents an alternative set of closed-form expressions for these same parameters which only involve well known trigonometric and exponential functions. It will be-shown that these alternate expressions have less than 1% error for mark to period ratios between 0.15 and 0.85. Also, they generally have less than 0.25% error for mark to period ratios between 0.25 and 0.75