Generalised relations between P- and Y-matrices and their applications

Abstract

The P-matrix is commonly used to analyse surface acoustic waves (SAW) elements such as the interdigital transducer (IDT) but, when some IDTs are connected through their acoustic ports, their frequency response could be calculated easily in terms of their admittances. Instead of the P-matrix, Y-matrix also allows coupling of the system to another electric or electronic device. Here, the authors present a general method to obtain the Y-matrix (with size N × N) of a SAW device with N electrical terminals connected to N different voltage sources. This method considers the reflections from the edges or any other non-electrical elements that can cause reflections beyond P-matrices. In addition, it has been shown that when there are no reflections and there are two P-matrices, this method converges to well-known previous results. Furthermore, the authors present two cases that could be used to analyse a SAW device: the input admittance and the equivalent P-matrix for a SAW device when a Y-matrix is connected to the electrical port of the SAW device. Also, the authors have calculated the acoustic relations for two SAW devices connected through their electric ports. Furthermore, these methods are exemplified through their application to a SAW system composed of three different IDTs and to an IDT and an inductor connected to its electrical port.

Keywords

• surface acoustic wave devices
• interdigital transducers
• matrix algebra
• frequency response
• generalised relations
• P-matrix
• Y-matrix
• surface acoustic wave element
• SAW elements
• interdigital transducer
• IDT
• acoustic ports
• frequency response
• electric device
• electronic device
• N electrical terminal
• N voltage sources
• nonelectrical elements
• SAW device
• input admittance
• electrical port
• acoustic relations
• SAW system
• inductor