Chaos in a differential fourth-order log-domain band-pass filter

The large-signal current-voltage exponential relationship of the bipolar junction transistors is used in log-domain filters to map signals to the logarithmic domain, where the processing occurs, and to convert the filtered waveforms back to the linear domain. However, the inherent internal nonlinearity of such circuits sometimes gives rise to unexpected externally-nonlinear behaviour. In this paper we first present a new log-domain nearly sinusoidal oscillator derived from a single-ended fourth-order log-domain band-pass filter designed using the method of the operational simulation of doubly-terminated LC ladders. When the eight shunt capacitors of the differential version of the above band-pass filter were replaced with four half-sized floating capacitors, under some conditions an unexpected chaotic oscillation was observed at the output of the zero-input circuit. Estimation of the full spectrum of Lyapunov exponents from the positive output current time series confirmed this behaviour.