Synthesis of multithreshold threshold gates based on negative differential resistance devices

This study presents theoretical analysis and synthesis algorithm for multithreshold threshold gates (MTTGs) built of resonant tunnelling diodes (RTDs). The aim of the synthesis is to find a structure of an MTTG gate and relations between all the RTDs given an arbitrary Boolean function of n variables. The contribution of this study is 3-fold: first the authors formulate a functional model of the MTTG gate in which output is given as the difference of two min functions each taking weighed sums of input signals as arguments. Second, it is shown that any Boolean function can be represented as a min/max composition of hyperplanes (weighed sum of input signals) representing threshold functions. Later a procedure is proposed that transforms min/max composition to a difference of two min functions that corresponds to the MTTG structure. Finally, the authors show that the complexity of the resulting the MTTG gate depends on the number of thresholds k in the threshold decomposition of Boolean function and propose a dedicated threshold decomposition procedure that minimises the resulting number of thresholds. As a result, synthesised MTTG circuit is composed of at most (k + 1)(n + 1) RTD devices and (k + 1)n switching elements.