4.7 Noise in Log Domain Filters

We now turn to one of the most complex issues in understanding log domain filters that is, noise. As we have seen from the start, log domain filters permit the use of as much as 20 dB of additional headroom in transistor-based active filters. However, this increase in headroom is offset by the fact that signal swings are limited relative to the noise floor. To understand the real trade-offs involved regarding noise in log domain filters, let us consider a single transistor that might be part of a log domain filter. We restrict attention to class A filters to begin. The DC bias current in that transistor must be chosen such that under peak signal swings the total current can never drop to zero. Thus, we may assume that the DC bias current is approximately equal to the peak signal swing, since there is no value in having significantly larger bias currents, because this would only waste power and, as we shall see, increase the noise floor. However, it should be noted that in practice one would want to make the DC bias a little larger than the expected maximum signal swing so that the total current in the transistor would never fall below some minimum current chosen to ensure reasonable bandwidth and matching requirements. This observation stems from the fact that transistor bandwidth and current gain are severely degraded at very low emitter currents.

Having made a preliminary estimate for maximum signal...