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描述不均匀传输线中的声反射系数可以归结为求解一种非线性微分方程（Riccati方程），本文探索一条寻找此类方程解析解的新方法，并利用此方法研究了声阻抗转换器，从而大大拓宽了声阻抗转换器阻抗分布的研究范围，作为例子，本文提出了几种阻抗变换形式，并把它们的功率传输效率与已有的均匀及指数型转换器作比较，计算结果表明：当转换器两端与传输介质的阻抗跃变很大时，某些阻抗转换器的传输效率比均匀及指数型转换器高得多．
To describe the acoustic reflection coefficient in the inhomogeneous transmission line can be attributed to solving a kind of nonlinear differential equation (Riccati equation). In this paper, we explore a new method to find the analytical solution of this kind of equation, and use this method to study the acoustic impedance converter As an example, several forms of impedance transformation are proposed in this paper, and their power transfer efficiency is compared with those of the existing uniform and exponential converters. The calculation results show that when the conversion Some impedance converters transmit more efficiently than even and exponential converters when the impedances of the two ends of the device and the transmission medium jump dramatically.