Harmonic Balance for 5G Applications Based on a New Quadratic Formulation

Abstract

A closed form for Harmonic Balance (HB) is derived in this work based on the Nonlinear Quadratic Formulation (NQF) that calculates the Harmonics relations in precise closed form nonlinear equations in this work. These closed form nonlinear equations relating the harmonics are solved using the Newton-Jacobian method. The ability of this method to yield the closed form solution of the Jacobian is an additional advantage. Existing methods use time sampling of the time domain signals to create fitting equations from which the harmonics are calculated, resulting in the need for time domain simulations as well as requiring special sampling methods for accuracy. These methods especially suffer when fast rising edges exist in the signals due to the need for high sampling at the edges. The method presented here does not suffer any of these issues. The verification of the proposed method is done through the implementation on Matlab and utilised on a few fundamental nonlinear circuits. It is demonstrated that the NQFHB method is more effective than other methods that use time domain sampling. The NQF-HB method is remarkable for its very easy and short calculation procedure. The NQF-HB method is another illustration of how the NQF can result in unique solutions that are fast, efficient, and accurate.