Log-domain and Square-root Domain Filters

Abstract

The motivation for research on switched current filters, reduction of power supply voltage, and consequent reduction in the voltage swing at the internal nodes in the filter has led to investigation on log-domain filters. The basic idea, known in speech coding to achieve large dynamic range using small number of bits, is called companding. Tsividis, Gopinathan, and Toth [5.1] have pointed out that while companding in telecommunications was divided between transmitter and receiver at distant locations (see figure 5.1 (a)), companding could be exploited on a chip as well (figure 5.1 (b)). Note that in figure 5.1 (b), the control signal could be based on the envelope of the signal x’ itself or transmitted separately as a. Linear operations can be implemented using the concept of companding while having the advantage of a better SNR. The input signal is compressed before being processed and then expanded at the output, to restore it to its original dynamic range. The resulting small internal swings lead to higher operating frequencies, lower distortion, and lower internal interference in the circuit. These aspects are discussed in detail in this chapter. We mainly consider various types of mapping from linear domain to non-linear domain, e.g., log, tan h and cos h, sin h, exponential state-space as well as square-root domains.