1976 年 32 巻 9 号 p. 531-539
Since the fundamental operation of Surface Acoustic Wave (SAW) filters is about the same as that of transversal filters, the impulse response model has been used in designing the SAW filters. However, the SAW filter having responses which satisfy the specification of several filters used in communication systems, were not obtainable by the simple model, due to the Gibbs oscillation which is caused by the truncation of the Fourier series after a finite number of terms. For this reason, the design methods, which enables reduction of such ripples, have been reported by several authors. However, these design methods were not optimum one because the filters designed by these methods did not always satisfy the specification, or consisted of a structure with either input or output tranducer must be with a single electrodes pair, which causes large insertion loss. In this paper, we present a design of SAW filters using a linear programming technique (LP), which enables optimum design so that the designed filter always satisfies the passband or stopband specification, and both input and output transducers consist of multi-paired electrodes as shown in Fig. 1. The design methods of SAW filters using LP contain both a time domain and a frequency domain. The former is suitable for the optimum design of SAW filters, and the latter is suited for the simplest design of narrow bandpass filters. The reason why LP is used in the design, is that the frequency response of SAW filters is a linear function with regard to the design parameter W_n or H_n, where W_n is the weighting function of apodized electrodes and H_n is the discrete fourier transform coefficient as noted in Eq. (2). The design model of the time domain is shown in Fig. 2. The design problem; "Determine W_n to minimize δ_2 (>0) under constraint that δ_1 is a constant specification value" is defined as LP in Eq. (6). The results of calculation are shown in Figs. 4〜6. and show the effectiveness of the design method. The design model of the frequency domain is shown in Fig. 7 and Fig. 10, the former is the design model with a narrow bandpass filter, and the latter is that with an ideal filter. The design problem; "Determine H_n to minimize δ_2 (>0)" are defined as LP in Eqs. (7) and (8). The results of calculation are shown in Fig. 8 and Fig. 9 for the former, and Fig. 11 for the latter. These results indicate that the designed filters are optimal inspite of their design simplicity.