Wave Digital Modeling of Nonlinear 3-terminal Devices for Virtual Analog Applications
Wave Digital Modeling of Nonlinear 3-terminal Devices for Virtual Analog Applications
复制标题
用于虚拟模拟应用的非线性三端器件的波形数字建模
DOI：
10.1007/s00034-019-01331-7
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
A. Sarti
中科院分区：
文献类型：
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作者：
A. Bernardini;A. E. Vergani;A. Sarti
我们提出了一种新的包含任意非线性三端器件的电路建模方法，该电路工作在波数字（WD）域。这种方法定义了一个通用的、灵活的3端设备的WD模型，其端口数量从1到6不等。文献中已经讨论过的3端器件的WD模型可以看作是我们在这里提出的模型的特殊情况，这一事实证实了该方法的普遍性。作为我们方法的应用示例，我们开发了音频电路中三种最广泛类型的晶体管的WD模型，即MOSFET， JFET和BJT。这些模型在这里被设计用于虚拟模拟音频应用；因此，它们的推导旨在最小化计算复杂度，同时尽可能避免端口变量之间的隐式关系。所提出的MOSFET和JFET模型由三阶多项式方程表征；由此，得到了显式的闭式波散射关系。另一方面，描述BJT的Ebers-Moll模型导致WD域中的超越方程无法解析求解。为了解决这一问题，我们提出了一种改进的Newton-Raphson （NR）方法来求解WD域中的隐式Ebers-Moll方程。该迭代方法在不影响效率的前提下，具有明显高于传统NR方法的鲁棒性和收敛速度。最后，讨论了一些包含晶体管的音频电路的WD实现。
We propose a novel modeling method for circuits containing arbitrary nonlinear 3-terminal devices, which operates in the wave digital (WD) domain. This approach leads to the definition of a general and flexible WD model for 3-terminal devices, whose number of ports varies from 1 to 6. The generality of the method is confirmed by the fact that the WD models of 3-terminal devices already discussed in the literature can be seen as particular cases of the model that we present here. As examples of applications of our method, we develop WD models of the three most widespread types of transistors in audio circuitry, i.e., the MOSFET, the JFET and the BJT. These models are here designed to be used in Virtual Analog audio applications; therefore, their derivation is aimed at minimizing computational complexity while avoiding implicit relations between port variables, as far as possible. Proposed MOSFET and JFET models are characterized by third-order polynomial equations; hence, explicit closed-form wave scattering relations are obtained. On the other hand, the Ebers–Moll model describing the BJT results in transcendental equations in the WD domain that cannot be solved analytically. In order to cope with this problem, we propose a modified Newton–Raphson (NR) method for solving the implicit Ebers–Moll equations in the WD domain. Such iterative method exhibits a significantly higher robustness and convergence rate with respect to the traditional NR method, without compromising its efficiency. Finally, WD implementations of some audio circuits containing transistors are discussed.