Circuit Theory of Time Domain Adjoint Sensitivity

It was originally stated that convolution operations were required to implement adjoint sensitivity in the time domain. In this article, we revisit time-domain adjoint sensitivity with a circuit theoretic approach and an efficient solution is clearly stated in terms of device level. Key is the linearization of the energy storage elements (e.g., capacitance and inductance) and nonlinear memoryless elements (e.g., MOS, BJT DC characteristics) at each time step. Due to the finite precision of computation, numerical errors that accumulate across timesteps can arise in nonlinear elements. A methodology to suppress that error is introduced. Numerical results demonstrate that the proposed method achieves accuracy while significantly reducing computational runtime.