Semi-Recursive Convolution Schemes for Macromodeling of Time-Invariant Linear Circuits

Time-domain macromodeling is a powerful technique for generating compact models of linear time-invariant (LTI) circuits. A common approach involves computing the port impulse response at the gates of the LTI system to evaluate convo-lution integrals, though this is often computationally demanding. To address this, a segment fast convolution (SFC) method has been recently introduced, leveraging piecewise constant (PW C) approximations of impulse responses to speed up the computation. This work proposes an extension of this method, which relies on a piecewise linear (PWL) approximation of the port impulse responses of LTI circuits. Additionally, a quasi-recursive algorithm for the convolution calculation is developed, which allows the reduction of the required number of operations and achieves significant speed improvements.