Moments-Based Computation of Intermodulation Distortion of RF Circuits

Adjoint sensitivity analysis of nonlinear distortion in RF circuits

“…It is important to note that the matrix Φ has the same structure as a Jacobian matrix but is evaluated only at DC which makes it very sparse. As for the remaining moment vectors M n , these are found by recursively solving (5). As can be seen from (4) and (5), the computation of the moment vectors is a solution of a set of linear algebraic equations where the left-hand-side matrix is the same throughout and is therefore very efficient.…”

“…In [5], [6] an efficient method for computing the value of IP3 was proposed. This approach is based on the computation of the Harmonic Balance moments and does not require the solution of the Harmonic Balance equations.…”

“…This reduces the CPU cost of finding the value of IP3 to that of solving a system of sparse, linear equations. However, the approach in [5], [6] does not provide any insight into the sensitivity of IP3 with respect to various circuit parameters. In this paper we present a new approach for computing the sensitivity of IP3 based on the adjoint sensitivity method [7], [8].…”

“…This approach has also been extended to cover the sensitivity analysis of nonlinear circuits operating under large signal periodic and almost-periodic conditions as is the case with the Harmonic Balance method [9]. The new approach proposed in this paper benefits from the same CPU cost advantage as [5], [6] while providing the sensitivity of IP3 with respect to all circuit parameters. This would provide a critical advantage enabling circuit optimization, design space exploration and design centering.…”

“…This would provide a critical advantage enabling circuit optimization, design space exploration and design centering. It is to be noted that similarly to the approach in [5], [6] this method is general and easily automated for any arbitrary circuit topology.…”