Time-Domain Numerical Simulation of Electronic Circuits and Surface Acoustic Wave Devices Using Their Admittance Parameters

We present a method to calculate the transient response of electronic circuits when these contain elements whose behaviors are given by their admittance matrices in the frequency domain. After describing this method in detail, an amplifier with resistive networks and interdigital transducers using specific input signals was proposed to test the method, and these results agreed when compared with those obtained with a simulation program with integrated circuit emphasis (SPICE)-based program. Besides, the simulation of two oscillators are presented; the first has a feedback network consisting of serial-connected equivalent circuits of crystals, and the second uses a feedback network with a surface acoustic wave (SAW) delay line. For the first oscillator, the waveforms obtained using this method and a SPICE-based program considering two different numerical integration methods were compared, and they looked similar, but all signals have different rise times because these simulations are very sensitive to inherent numerical errors. The simulation of a SAW delay line oscillator and its input and output voltages and currents were obtained, and its fundamental frequency was 77.77 MHz. These simulated results were validated experimentally through the oscillation frequency, which was found using the $-parameters of the amplifier and the delay line and an oscillation criterion, and it was measured directly in the circuit. The experimental oscillation frequencies were 76.9 and 77.5 MHz, respectively, and the errors between simulation and experimentation were approximately 1%.

I. Introduction

Simulation program with integrated circuit emphasis (SPICE) is a tool whose development began in the early 70s [1], [2]. Since its inception, this program has undergone several modifications to improve performance, accuracy, and include more electronic devices and appropriate parameters for those devices manufactured by certain processes. SPICE-based programs are commonly used to design and simulate electronic circuits in time and frequency domains. Although these programs are powerful tools and they can simulate many electronic elements, they cannot include elements such as interdigital transducers (IDT), surface acoustic wave (SAW) delay lines, or any other SAW device. Few attempts have used SPICE with SAW devices, e.g., Bhattacharyya et al. [3] used the Mason’s model [4], [5] to obtain the frequency response of an IDT. However, there are plenty inconveniences and limitations when using the original Mason’s model or the modified versions that include second-order effects [6], [7] and some of the inconveniences and limitations are: modeling apodized IDTs with irregular geometry can be hard, it is not possible to include experimental data or parameters obtained through experimentation, SPICE in the frequency domain does not consider the nonlinear behavior of electronic devices although a nonlinear method has been proposed [8], and from a general perspective, any other element that cannot be modeled properly using an equivalent electrical network cannot be used in this kind of simulations. To overcome these limitations, we present a method to make simulations in the time domain of electronic circuits that contain SAW devices (or any other circuit) whose behavior is given by an admittance matrix in the frequency domain presented (mixed method). Some other methods to make simulations of electric/electronic circuits with elements whose behaviors are given in both time and frequency domains have been previously reported to calculate the steady state of power electric systems [9], [10] or RF circuits [11], [12]; however, no other similar method has been reported previously to calculate the transient response of electronic circuits that include SAW devices (even SPICE cannot do this kind of mixed simulations). Some examples are presented to show the application of this method when electrical networks formed by resistors, inductors and capacitors, or IDT are connected to an amplifier. The method was applied after calculating their admittance parameters in the frequency domain, and they agreed with the results obtained in SPICE. Afterwards, the results obtained when an IDT is connected to each terminal of the amplifier and the simulations of two oscillators are presented; one of them only has resistors, capacitors, and inductors, while the other contains a SAW delay line as a feedback element. To verify these results, the latter oscillator was built, and the simulation and experimental frequencies of the signals agreed.