电路模型的改进及若干相应结果

指出1段导线可以采用注上3个非负常数L,R，Q或分式（LP^2＋RP＋Q）／p的1段有2个端点的简单曲线来表示，且L恒≠0；可定义电路为有限条导线串并联而成的组件，使电路图可相应简化．提出用等价电路来简化电路的概念，从而得出用电路图来计算拉氏阻抗的较直观简洁的新方法，并证明了在任何电路中都存在拉氏阻抗，并且是个分子次数比分母次数高1的分式；也证明了拉氏电位降定理中的L{u（t）}=ZL{i（t）}可加强为L^s{u（t）}=ZL{i（t）}，其中L^s{u（t））则为u（t）的强拉氏变象．同时也证明了空载电路中电流可通过电路特征表达电路特征定理，即i（t）=g（t）·ue（t）=∫0^1g（t—τ）ue（t）dτ，而ue（t）为外接电动势两端之电位差，g（t）=L^-1{Z^-1}为拟连续、缓增的函数，也被称为电路的电路特征；又证明了电路特征测定定理ue（t）=δ0（t）时，i（t）即为g（t），并且电路特征定理和测量定理对一切电路均成立．

Circuit Model Improvement with Analysis on its Results

A conducting wire can be expressed using a simple two-end curve with three non-negative constant of L, R, Q or formula of （LP^2＋RP＋Q） / p, with L ≠ 0. The circuit diagram can be simplified by defining that the circuit itself is composed of a finite lead in serial-parallel fashion. The author proposes a new concept for simplifying the circuit using equivalent circuit, consequently a new approach is attained for calculating the Laplace impedance using the circuit diagram, leading to the proven conclusion that the Laplace impedance exists in all circuits with numerator one order higher than denominator. It is also proven that L^s{u（t）}=ZL{i（t）} can be enhanced to .L^s{u（t）}=ZL{i（t）} in Laplace voltage reduction theorem, where .L^s{u（t）} is u（t） of strong Laplacian change. Also validated is that the circuit character theorem can be expressed with the passing current by means of circuit character in unloaded circuit, that is, i（t）=g（t）·ue（t）=∫0^1g（t-τ）ue（t）dτ, where ue（t） is potential difference of electromotive force, and g（t）= L^-1{Z^-1} is the circuit character of simulated continuum and increase function. Given ue（t）=δ0（t）, i（t） becomes g（t）, and circuit character theorem and measure theorem then hold for all circuits.