| When it comes to design and analysis for high-speed integrated circuit,the differential algebraic equation is often brought up and how to solve it more accurately takes a vital part in circuit simulators.Different kinds of numerical methods are commonly used to solve differential algebraic equations.Among them,the transient analysis computes the voltage and current in the circuit with respect to a function of time.This analysis is the most meaningful one when time-varying input signals are applied to the circuit.When the transient analysis is applied,the trapezoidal method is commonly used because of its A-stability and no numerical damping property.However,on stiff circuits,the trapezoidal method generates solutions where the sign of the error alternates on every time step.The solution is acceptable,however exhibits a ringing,often called the trapezoidal ringing.In circuit simulators,the algorithm makes the step size very small when the input changes rapidly in order to avoid the ringing.However,if the algorithm misses the sharp fluctuation by mistake,the ringing is still a big problem.In this thesis,the method of calculating additional parameter vectors is proposed to reduce the occurrence of ringing.The author takes advantage of simulation examples to compare differences between the original algorithm and the proposed algorithm and verify the rationality and validity of the proposed algorithm by the specific analysis of the ringing phenomenon,the global truncation error and the computational time.In addition,in view of the local truncation error algorithm of the SPICE software,the author has found the error code on the constant setting.By theoretical analysis and example verification,the accuracy advantage of the proposed local truncation error algorithm is completely proved. |
