Abstract-We introduce a new approach to synthesizing Class AB log-domain filters that satisfy dynamic differential-mode and common-mode constraints simultaneously. Whereas the dynamic differential-mode constraint imposes the desired filtering behavior, the dynamic common-mode constraint solves the zero-dc-gain problem, a shortcoming of previous approaches. Also, we introduce a novel push-pull circuit that serves as a current-splitter; it rectifies a differential signal into the ON and OFF paths in our log-domain filter. As an example, we synthesize a first-order low-pass filter, and, to demonstrate the rejection of dc signals, we implement an adaptive filter by placing this low-pass circuit in a variable-gain negative-feedback path. Feedback gain is controlled by signal energy, which is extracted simply by summing complementary ON and OFF signals-dc signals do not contribute to the signal energy nor are they amplified by the feedback. We implement this adaptive filter design in a silicon chip that draws biological inspiration from visual processing in the mammalian retina. It may also be useful in other applications that require dynamic time-constant adaptation.Index Terms-Adaptive filtering, artificial vision, class AB circuits, neuromorphic engineering.
I. LOG-DOMAIN FILTERING
DECREASING supply voltage with integrated circuit miniaturization is increasing interest in current-mode filters. Current-mode operation offers large dynamic range if the nonlinear device transconductance is compensated for in the filter design, such that operation remains linear outside the small-signal region. The existence of such externally linear but internally nonlinear filters was demonstrated by Adams, who first designed a circuit that "when placed between a log converter and an anti-log converter will cause the system to act as a linear filter" [1]. He named these circuits log-domain filters. The log and anti-log operations are readily realized using bipolar transistors or MOSFETs operating in weak inversion; these devices maintain logarithmic voltage-current relationships over six decades.The principle of log-domain filter design is a simple one: use current to represent the signal , voltage to represent its logarithm , and note that . There- fore, to obtain the derivative of the voltage, divide the derivative of the signal, , by the signal, . That is to say, divide the current you wish to supply to the capacitor by the current made by the transistor whose gate (or base) is connected to it. Intuitively, this division compensates for the slope of the exponential at the transistor's operating point, such that its current changes at a constant rate. Current-division is readily realized with logarithmic elements by exploiting the translinear principle [8].In theory, log-domain filters have limitless dynamic range; in practice, dynamic range is limited by the bias current. Seevinck and Frey have both proposed Class AB log-domain filters that address this shortcoming; they both use two copies of the log-domain circuit to filter the d...