Hierarchical Residual Fitting for Enhanced S-Parameter Accuracy in Devices Exhibiting Complex Delay

Modern distributed devices often exhibit complex time-delay effects. However, existing S-parameter fitting algorithms struggle to capture their frequency-domain behavior accurately and efficiently. This paper proposes a novel Hierarchical Residual Fitting (HRF) algorithm that decomposes the device response into multiple residual layers, each addressing progressively finer delay-induced features. By adaptively fitting and subtracting residual components, HRF achieves substantial improvements in both fitting precision and computational efficiency compared to conventional approaches. Numerical experiments on representative high-speed circuit models demonstrate that HRF reduces the mean fitting error by up to 40% and accelerates convergence by an order of magnitude.