Modeling nonlinear wave digital elements using the Lambert function
Modeling nonlinear wave digital elements using the Lambert function
复制标题
使用兰伯特函数对非线性波数字元素进行建模
DOI：
10.1109/tcsi.2016.2573119
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
J. Smith
中科院分区：
文献类型：
--
作者：
A. Bernardini;K. Werner;A. Sarti;J. Smith
一大类涉及指数的超越方程可以使用Lambert W函数显式化。在过去的十五年里，这个强大的数学工具已被广泛用于寻找包含二极管的电路中电流或电压的闭合形式表达式。迄今为止，电路分析中关于W函数的研究几乎都是在Kirchhoff（K）域进行的，而在波形数字域（WD）中描述二极管电路的显式模型的文献很少。然而，WD域中的非线性元素（NLE）的显式模型是特别可取的，特别是为了避免使用迭代算法。本文探讨了WD域中的W函数的作用范围，它描述了一个程序来搜索明确的波映射，为一个端口和多端口NLE包含二极管。WD模型，描述了任意数量的不同的并联和反并联二极管，一个无变压器的环形调制器和一些BJT放大器的配置，推导出。特别是，一个扩展版本的BJT Ebers-Moll模型，适用于实现终端之间的反馈，介绍。
A large class of transcendental equations involving exponentials can be made explicit using the Lambert W function. In the last fifteen years, this powerful mathematical tool has been extensively used to find closed-form expressions for currents or voltages in circuits containing diodes. Until now almost all the studies about the W function in circuit analysis concern the Kirchhoff (K) domain, while only few works in the literature describe explicit models for diode circuits in the Wave Digital (WD) domain. However explicit models of NonLinear Elements (NLEs) in the WD domain are particularly desirable, especially in order to avoid the use of iterative algorithms. This paper explores the range of action of the W function in the WD domain; it describes a procedure to search for explicit wave mappings, for both one-port and multi-port NLEs containing diodes. WD models, describing an arbitrary number of different parallel and anti-parallel diodes, a transformerless ring modulator and some BJT amplifier configurations, are derived. In particular, an extended version of the BJT Ebers-Moll model, suitable for implementing feedback between terminals, is introduced.