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Abstract-A general theory for companding log domain filters is proposed which combines not only exponential mappings, but also a new translational mapping approach which guarantees suitable operating conditions in any log domain filter. The filter equations resulting from the use of the theory ultimately contain translinear terms which are known to be realizable using translinear techniques. A discussion of the design of the companding filters, regarding the economical use of translinear loops and the convenient selection of system parameters, is offered which leads to first-and second-order circuit designs. Finally, the noise performance of an example design is investigated using a carefully crafted large-signal simulation technique, showing clearly the advantage of the companding filter approach.

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Resistive noise in active RC and MOSFET-C filters is examined. The effects of impedance and frequency scaling are shown. The relationship between sensitivity and noise is considered. A bound for the product of resistive power dissipation and noise power spectral density is derived. Topology-independent and transfer function-independent bounds for the dynamic range, in filters with power dissipation constraint, are developed.

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