Robust Harmonic-Probe Method for the Simulation of Oscillators

This paper considers the harmonic balance method (HB) in conjunction with the probe insertion technique. In general, the nonlinear equations modeling the circuit in the frequency domain are solved with the Newton iterative method. It is known that, in many cases, probe insertion in the original circuit shows better convergence properties of the Newton method and therefore of the harmonic balance when simulating autonomous circuits. The probe technique is considered here in detail, and numerical aspects are discussed mainly for what concerns the condition number of the Jacobian matrix related to the Newton method. The probe technique is then improved by exploiting properties of the power exchanged between the probe and the circuit in which it is inserted; moreover, an automatic probe insertion mechanism is detailed.