Nonlinear dynamics of first- and second-order log-domain circuits

Log-domain filters use the large-signal exponential current-voltage relationship of the bipolar junction transistor to convert signals to logarithmic form, where they are processed, and to map them back to the linear domain after processing. Due to their internally nonlinear nature, application of standard linear circuit design techniques to such networks can give rise to unexpected externally nonlinear behavior. Methods of nonlinear dynamics are used here to explain the undesired nonlinearities recently observed in a differential first-order log-domain integrator and to investigate the input/output behavior of the corresponding low-pass filter. The nonlinear behavior of a floating-capacitor differential second-order log-domain bandpass filter is also investigated and explained.