4.2 Log Domain Filtering

As we have seen from the discussion above, the circuit of Figure 4.1 suffers from the fact that its small signal range is significantly limited, in that the circuit loses 20 dB of potential dynamic range. This limitation is due essentially to the nonlinearity of the transistor. The log domain filtering idea allows us to recover this lost dynamic range by pre- and post-distorting the signals in the filter. Specifically, consider the circuit of Figure 4.3, under the assumption that all base currents may be neglected. Please note that we will continue to make this assumption in all of the discussion to follow, until later when we specifically address the impact of nonideal transistor performance on log domain filters. Q ₁ pre-processes the input current, I _in, producing a voltage, V ₀, which is logarithmically related to it. This predistorted input is applied to the base of Q ₃ with a level shift (Q ₂ accomplishes this), V _LS. Q ₃ and the capacitor and current source are the 'core filter' of Figure 4.1. Finally, the output, V, of this core filter is post-processed via Q ₄ to produce the final output, I _out, which is exponentially related to the capacitor voltage. To the uninitiated, it is not clear that the additional nonlinear processing in this circuit does not simply further corrupt the already distorted signal. However, as the following analysis shows, the additional nonlinear processing...