CHOICES IN THE HARMONIC-BALANCE TECHNIQUE

We apply the harmonic balance technique in low orders to three types o f oscillator model. For three equations of the van der Pol type with r ational nonlinear terms, used to model electronic oscillators, we exam ine the choice between: (a) rationalizing before expanding in harmonic s, and (b) obtaining Fourier coefficients of nonlinear terms. Alternat ive (b) is shown to be more accurate, in first order, for the models o f Scott-Murata and of Walker and Connelly, which apply to circuits wit h an inverse tangent nonlinear component. For these equations, in the case of alternative (a), we find acceptable dependence of the second-o rder corrections on the bifurcation parameter. When the harmonic balan ce method is used to set up a semi-classical quantization treatment of a nonlinear conservative oscillator, values of energies are slightly improved by the use of alternative (b). For conservative oscillators w ith cubic or fifth power forces, we compare the standard method using the acceleration equation with an alternative using the energy equatio n. The first is shown to be more accurate in low order.