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本文介绍一种旨在减少电路变量的线性开关电容电路(简称SC电路)的分析方法。这种方法借消去所谓开关刀节点(Pivot nodes)而使电路变量数显著减少。与文[1]中的方法相比,该法所减少的电路变量的个数为SC电路中单刀双掷开关的个数。为在计算机上自动形成消去开关刀节点后的电路的时域方程,在描述SC电路时,将采用以下4种电路元件模型:1.一般电容(它的两个极板永久地与某两节点相连);2.开关电容(它的一个或两个极板通过开关与电路中某些节点相连);3.独立电压源(表示电路的激励信号);4.电压控制电压源(表示运算放大器)。用本文所介绍的方法所导出的SC电路的时域方程与以节点电压为变量的时域方程具有完全相同的形式,但方程的变量数却显著地减少,从而使电路分析所需的计算时间明显减少。文中介绍的方法不仅适用于SC电路的时域分析、频域分析,而且结合文献[2]的基本思想还能方便地实现灵敏度分析。
This article describes an analysis method to reduce the linear switched-capacitor circuit (referred to as the SC circuit) of circuit variables. This method significantly reduces the number of circuit variables by eliminating the so-called Pivot nodes. Compared with the method in [1], the number of circuit variables reduced by this method is the number of SPDT switches in the SC circuit. In order to automatically form a time-domain equation for a circuit on a computer after the switch node is eliminated, the following four circuit element models will be used in describing the SC circuit: 1. A common capacitor whose two plates are permanently connected to both nodes (One or two plates of which are connected with certain nodes in the circuit through the switch); 3. an independent voltage source (indicating excitation signal of the circuit); 4. a voltage control voltage source (representing an operational amplifier ). The time-domain equations of the SC circuit derived by the method described in this paper have exactly the same form as the time-domain equations with node voltage as the variables, but the number of variables in the equation is significantly reduced, so that the calculation time required for the circuit analysis obviously decrease. The method described in this paper is not only suitable for the time domain analysis and frequency domain analysis of SC circuits, but also the sensitivity analysis can be easily implemented in combination with the basic idea of [2].