Synthesis of Non-PR Driving Point Impedance Functions Using Analog Computer Units

When the real part of a driving point impedance function is negative at some real frequency, or when the residues of any of its poles on the j \omega axis are negative, the function is not positive real and cannot be synthesized without recourse to active elements. The negative resistors and reactors required under these circumstances fall into two categories: the open-circuit stable, current-controlled, and the short-circuit stable, voltage-controlled types. This paper demonstrates how linear negative resistors and capacitors of both types may be simulated conveniently on electronic analog computers. Two operational amplifiers with a combined gain of 2 are used for each negative element. Examples of the application of this method to the synthesis of nonpositive real impedances and admittances are included, and the dependence of the stability of these networks upon the external circuitry is considered.