Synthesis with negative resistors

Abstract

In the realisation of networks for higher frequencies, the usual tendency of avoiding inductors is not always justifiable. In the paper, several realisation techniques for driving-point functions, using all three standard components (RLC) and a single negative resistor, are proposed. A realisation based on Darlington's procedure is applied to the synthesis of a broad class of functions, called negative real functions, It is shown how any real rational function may be converted into a negative real one by the techniques of predistortion and resistance padding. Some constraints are given for a function to be realisable by applying a tunnel diode instead of the negative resistor. A modification of an RC-n.i.c. synthesis procedure is presented, resulting in a transformerless realisation of any rational function by means of an RLC network with a single negative resistor. Synthesis of a function having either its zeros or its poles in the left half of the complex-frequency plane is shown to be possible through partial-fraction expansion, combined with the use of a negative resistor. The resulting network is transformerless, and presents a very simple topology. Constraints on functions realisable by RLC components and tunnel diodes are discussed.