一种RC链式电路时域响应建模方法
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摘要
针对链式RC电路,提出了一种快速有效的模型来估计RC电路上每一时刻各个节点的输出响应.利用电路原理建立链式RC电路各个节点间的输入输出关系,然后通过一种矩阵变换的方法,计算出链式RC电路输出响应的解析式.实验结果表明:通过该方法得到的时幅响应准确度达到10-9,与波形松弛法多次迭代的准确度相当,但其运算复杂度低于波形松弛法的运算复杂度,其传播时延的误差远低于Elmore模型及其改进模型的传播时延误差.
A fast and efficient model is constructed for the RC chain circuit to output the responses of all nodes each time.Concretely,the relationship between input and output voltage related to nodes is derived by using the circuit principle in the time-domain,and then the output responses of the RC chain circuit are gradually calculated in a mathematical way.Experimental results demonstrate that the proposed model has agood performance with a predicted accuracy and propagation delay and its computational complexity reaches a low level.
A fast and efficient model is constructed for the RC chain circuit to output the responses of all nodes each time.Concretely,the relationship between input and output voltage related to nodes is derived by using the circuit principle in the time-domain,and then the output responses of the RC chain circuit are gradually calculated in a mathematical way.Experimental results demonstrate that the proposed model has agood performance with a predicted accuracy and propagation delay and its computational complexity reaches a low level.
引文
[1]Kolárová E.Statistical Estimates of Stochastic Solutions of RL Electrical Circuits[C]//IEEE International Conference on Industrial Technology.Piscataway:IEEE,2006:2546-2550.
[2]Patil N,Gawalwad B,Sharma S.A Random Input-driven Resistor-capacitor Series Circuit[C]//International Conference on Recent Advancements in Electrical,Electronics and Control Engineering.Piscataway:IEEE,2011:100-103.
[3]Rahman F,Parisa N.A Stochastic Perspective of RL Electrical Circuit Using Different Noise Terms[J].The International Journal for Computation and Mathematics in Electrical and Electronic Engineering,2011,30(2):812-822.
[4]Elmore W.The Transient Response of Damped Linear Network with Particular Regard to Wideband Amplifiers[J].Journal of Applied Physics,1948,19(1):55-63.
[5]Cataldo G,Mita R,Palumbo G,et al.RC-Chain:aSimple Model of Delay with a Ramp Input[C]//13th IEEE International Conference on Electronics,Circuits and Systems.Piscataway:IEEE,2006:557-560.
[6]Mita R,Palumbo G,Poli M.Propagation Delay of an RC-Chain with a Ramp Input[J].IEEE Transactions on Circuits and Systems-Ⅱ:Express Briefs,2007,54(1):66-70.
[7]Gander M,Ruehli A.Optimized Waveform Relaxation Methods for RC Type Circuits[J].IEEE Transactions on Circuits and Systems-Ⅰ:Regular Papers,2004,51(4):755-768.
[8]Al-Khaleel M,Gander M,Ruehli A.A Mathematical Analysis of Optimized Waveform Relaxation for a Small RC Circuit[J].Applied Numerical Mathematics,2013,75:61-76.
[2]Patil N,Gawalwad B,Sharma S.A Random Input-driven Resistor-capacitor Series Circuit[C]//International Conference on Recent Advancements in Electrical,Electronics and Control Engineering.Piscataway:IEEE,2011:100-103.
[3]Rahman F,Parisa N.A Stochastic Perspective of RL Electrical Circuit Using Different Noise Terms[J].The International Journal for Computation and Mathematics in Electrical and Electronic Engineering,2011,30(2):812-822.
[4]Elmore W.The Transient Response of Damped Linear Network with Particular Regard to Wideband Amplifiers[J].Journal of Applied Physics,1948,19(1):55-63.
[5]Cataldo G,Mita R,Palumbo G,et al.RC-Chain:aSimple Model of Delay with a Ramp Input[C]//13th IEEE International Conference on Electronics,Circuits and Systems.Piscataway:IEEE,2006:557-560.
[6]Mita R,Palumbo G,Poli M.Propagation Delay of an RC-Chain with a Ramp Input[J].IEEE Transactions on Circuits and Systems-Ⅱ:Express Briefs,2007,54(1):66-70.
[7]Gander M,Ruehli A.Optimized Waveform Relaxation Methods for RC Type Circuits[J].IEEE Transactions on Circuits and Systems-Ⅰ:Regular Papers,2004,51(4):755-768.
[8]Al-Khaleel M,Gander M,Ruehli A.A Mathematical Analysis of Optimized Waveform Relaxation for a Small RC Circuit[J].Applied Numerical Mathematics,2013,75:61-76.