Circuit stability theory for non-Foster circuits

The successful design of non-Foster circuits requires tests for stability that are accurate and reliable. It is widely known by designers of amplifiers and active circuits that popular tests for the stability of 2-port and n-port circuits can give incorrect results. Despite periodic debate over the past 50 years, the validity of Rollett´s K-factor test has never been proved mathematically; it was argued only on physical grounds. We present linear non-Foster circuits that serve as explicit counterexamples to Rollett´s test. One counterexample circuit is given that is unconditionally stable according to the full statement of Rollett´s test including Rollett´s proviso. Yet the circuit is provably unstable with simple resistive termination, in direct contradiction of Rollett. A second counterexample circuit is shown that gives the stronger result that Rollett´s test cannot be repaired, and indeed many other stability tests are defective too. Armed with these results, a different approach to the design of stable circuits is discussed that has enabled us to build stable non-Foster antenna impedance matching circuits. An example of a stable non-Foster broadband impedance matching circuit for a small loop antenna is given. The design of the circuit was made possible by using a new capability available in certain circuit EDA CAD tools.