基于 H_i(S)和 D_i(S)递推计算的梯形网络理论

本文提出的梯形网络理论,可以比较全面和系统地解决各种类型梯形网络的分析问题。本文所提出的方法同现有其他方法相比较,具有简捷、明了、便于编制程序上机计算等优点。对于某些常用工业过程的模拟电路,诸如复杂的 RC 梯形网络,各种类型的塔形梯形网络,带负载的均匀 RC 梯形网络,运用本文的方法都可迅速和正确地求出其传递函数。此法用于分布参数的梯形网络,也取得了满意的结果。

THE THEORY OF LADDER NETWORKS BASED UPON RECURRENCE OF H_i(s)AND D_i(s)

In this paper the theory of ladder networks using recursion of the voltagefunctiowns H_i(s)and the current functions D_i(s)is presented.LetH_i(s)=V_i(s)/V_0(s) and D_i(s)=I_i(s)/I_0(s),the recursion formulas of H_i(s) and D_i(s) areH_0(s)=1,H_1(s)=P_0(s),(?)=P_(i-1)(s)H_(i-1)(s)-Q_(i-1)(s)H_(i-2)(s),where P_0(s)=1+z_0Y_0,(?)=1+z_i/z_(i-1)+z_iY_i,(?)=z_i/z_(i-1)and D_0(s)=1,D_1(s)=R_0(s),(?)=R_(i-1)(s)D_(i-1)(s)-W_(i-1)(s)D_(i-2)(s)where (?)=1+Y_(i+1)z_i+Y_(i+1)/Y_i,(?)=Y_(i+1)/Y_i.Simultaneously,H_i(s) and D_i(s) may also be expressed by determinants.Ifthe ladder network is parallel with an admittance,Y_L,the voltage functions andthe current functions may be expressed as follows:H_(L,0)(s)=1,H_(L,1)(s)=H_L(s)+P_L(s),(?)=H_i(s)+P_L(s)M_(i-1)(s)and D_(L,0)(s)=1,D_(L,1)(s)=D_1(s)+R_L(s),(?)=D_i(s)+R_L(s)N_(i-1)(s)where P_L(s)=z_0Y_L,R_L(s)=-Y_1Y_L/(Y_0+Y_L)Y_0,and M_(i-1)(s) and N_(i-1)(s) can also be computed by recurrence or expressed by deter-minants.Accrding to the formulas presented above the various types of ladder networksas the complicated ladder networks,the ladder networks with elements in geometricaland arithmetic progression and with elements of distributed parameters can beeasily analysed.Then the transfer functions of these ladder networks can beobtained.Other methods to solve the same problems are very difficult.