A Time-Mode Translinear Principle for Nonlinear Analog Computation

This work proposes a novel translinear principle based on time domain processing of signals. The exponential relationship between voltage and time in an RC circuit is exploited to implement a logarithmic voltage-to-time converter and an exponential time-to-voltage converter. These circuits are the time domain analogs of the voltage mode translinear circuits that exploit the exponential relationship between current and voltage in BJTs and subthreshold MOS transistors. Just as Kirchoff's voltage laws provide a natural form of addition for the voltage-mode translinear principle, the progression of time can also be a natural source of addition for the proposed time-mode analog of this principle. In this work a time-mode adder circuit is used to realize a translinear principle in time. This paper describes the theory behind this time-mode translinear principle. Furthermore, the design of nonlinear circuit functions, e.g., multiplication and power law, based on the time-mode translinear principle is described. Simulation and measurement results for a two-input single quadrant multiplier are presented. The chip was fabricated in a 180 nm CMOS process with simulation results agreeing closely with experimental results. We also present error analysis for such circuits and provide a brief discussion on future prospects of this approach.