SUMMARY
A study of varactor tuned LC circuits is presented. Nonlinear time domain circuit differential equation is rewritten in terms of phase plane variables, which can then be solved in closed form. General expressions are derived, which are applicable to any capacitanceβvoltage relationship. Two types of circuit structures, namely singleβended and balanced, with MOS diodes as the variable capacitance elements, are specifically considered. The nature of the voltage waveforms across the two circuits is determined by phase plane plots. Variation of voltage with time is calculated numerically. It is shown that the voltage waveform for the singleβended circuit is asymmetric, with higher harmonics present. Furthermore, the fundamental resonant frequency is dependent on amplitude of oscillation and could decrease to 94% of its small signal value for large voltage swings. Near 34% control over frequency is calculated, for a bias voltage range of 8 to 1. On the other hand, the balanced structure results in symmetric voltage waveform, with negligible harmonic content. Dependence of frequency on amplitude is weak, only decreasing to 98% of its small signal value, for the largest swings. The tuning range is marginally improved by the balanced structure. The results are compared with those obtained from Fourierβbased calculations and experimental data in literature, and good agreement is obtained. Copyright Β© 2011 John Wiley & Sons, Ltd.