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

Theoretical and experimental characterisation of a SAW delay line through its Y ‐matrix

“…Through α the energy law is satisfied between c(x) andĉ k () .A detailed explanation of the latter development is reproduced in Appendix. Now that we are able to find the normalised spatial charge density, it is easy to calculate the P-matrix of the IDT, and then the Y-matrix of the delay line were calculated using P-matrix cascading equations [24,28,29] and P-t oY-matrices relations [4,25]. The non-reflective IDT P-matrix is used to model the SAW propagation region inside the delay line, but there are no electrodes at this region; hence the electric charge at the surface is zero, which implies that only P12 and P21 coefficients are not zero.…”

“…To avoid mismatching effects, the experimental setup was calibrated through a short load and thorough calibration kit to move the VNA reference plane to the inputs of the delay line. It is important to note that the mismatching effects could modify the behaviour of the circuit: an example were presented in [25]. Parasitic effects are important at UHF frequencies or higher and even the wires used to bond the SAW devices could be important [32].…”

“…Parasitic effects are important at UHF frequencies or higher and even the wires used to bond the SAW devices could be important [32]. For this reason, some authors have showed a method to consider them through simulations [24,25]. The delay line was mechanically mounted in a PCB and each electrode of the delay line was connected to a microstrip whose characteristic impedance is 50 Ω using a gold thread with length shorter than 2 mm.…”

“…Engan [22, 23] proposed a method to approximate it and calculate the capacitance of the IDT, and based on these equations, Hashimoto [24] presented the equations for single and double electrodes. In this work, we used these equations which are reproduced in the appendix of [25]. The spatial charge density for the double electrodes of the IDT considered here has the same form than that reported in page 53 of [19].…”

“…Parasitic effects are important at UHF frequencies or higher and even the wires used to bond the SAW devices could be important [32]. For this reason, some authors have showed a method to consider them through simulations [24, 25].…”