HARMONIC AND INTERMODULATION DISTORTION IN ACTIVE FILTERS

Ahmad  A. MUHIEDDINE

The nonlinearities in operational amplifier filters are analyzed by harmonic balance techniques for single and multi-tone excitations. Various numerical algorithms are compared and configurations with reduced output distortion identified.

The effects of amplifier  nonlinearities on the output distortion of continuous-time active filters are investigated by application of harmonic and spectral-balance analysis.

After reviewing the limitations of alternative nonlinear evaluation techniques such as describing function, Volterra-wiener series and Hopf bifurcations, the harmonic-balance approach is adopted as the most suitable and promising. First, it is refined and applied to delineate the jump-resonance frequency responses of filter circuit excited by a large-amplitude single-tone input signal. Such is the precision with which the harmonics and critical input voltages are predicted that the effects of asymmetry in the amplifier input -saturation characteristic are clarified. The nonlinear algebraic equations obtained after balancing are solved by various numerical root-finding procedures including Newton-Raphson, continuation and relaxation algorithms. Comparison of results leads to recommendation of the most efficient algorithm which converges to a solution in minimal computational  time.

Attention is then directed to the more realistic condition of multitone excitation and the problem of intermodulation distortion. Making the customary restriction to two-tone inputs, spectral-balancing techniques are applied systematically to the cases of equal, comparable and widely disparate amplitudes and frequencies. Evaluation of intermodulation entirely in the time domain together with block-diagram representation of the nonlinear system affords considerable computational economy compared with earlier methods.

Finally, general methods for reducing and minimizing the output distortion of single-amplifier and multiple-amplifier filters are formulated in terms of block-diagram notation. These are verified by numerical evaluation and distortion measurements of various well-known and new second-order active-filter circuits. The implications for the design of high-order filters are then considered . Optimization of the ordering of a particular cascade structure appears to challenge accepted empirical wisdom. In conjunction with recent advances in noise analysis, the techniques presented here for reducing distortion should lead to filter configurations and designs with improved dynamic range.