Log-domain filtering: an approach to current-mode filtering

A novel approach to filter design, based on Adams´ `log-domain´ filters, is proposed that yields a truly current-mode circuit realisation. Adams´ idea, which was introduced in a limited context, is generalised to permit a complete distortionless synthesis procedure, which results in circuit implementations readily realisable using complementary bipolar processes. It is shown that, by introducing an exponential map on the state-space description of the desired linear system, a log-domain filter can be fully realised with transistors configured in current mirror-type groupings, current sources and capacitors. Owing to the mapping, the state variables are intrinsically related to current, and not voltage, in the resulting circuits, a fact that emphasises the current-mode nature of the design. A general biquadratic filter section is designed, and, following discussion of cascading sections, a seventh-order Chebychev lowpass filter is designed. All designed circuits are shown to be tunable over a two-decade range in frequency while their characteristics are accurately preserved, even for biquad sections whose f₀Q product is greater than f_T/10. The Chebychev filter is shown in simulation to possess nearly 60 dB dynamic range relative to 0.9% THD, with a cutoff frequency of nearly 5 MHz, using transistor models from AT&T´s CBIC-R 300 Hz complementary bipolar process