A Design approach for sub-harmonic generation or suppression in non-linear circuits

A design approach for the generation or suppression of sub-harmonic frequencies in non-linear circuits under large-signal drive is described. A standard Harmonic-Balance algorithm is first used for the large-signal analysis at fundamental frequency and higher-order harmonics; a conversion matrix is then computed for the calculation of potential frequency conversion between harmonic and sub-harmonic frequency components. Cross-frequency stability circles are drawn based on the conversion matrix, and the condition for the insurgence of sub-harmonic instabilities is set as the fulfilment of the Barkhausen oscillation criterion between different frequencies. The instability can be either imposed or avoided by suitably choosing the loads at sub-harmonic frequencies.