Imaginary resistor based Parity-Time symmetry electronics dimers

An approach of fabricating Parity-Time symmetry electronic dimers circuits is demonstrated using an imaginary resistor Z whose impedance is frequency independent. Remarkably, the dynamic rate equations of the coupled oscillators so-called ZRC dimers, uniquely consist of first order partial differential equations which result in a 2 ×2 effective Hamiltonians commuting with the joint Parity-Time (PT) operator. The method helps in describing two groups of PT symmetry electronics. The first group has an eigenspectrum that displays a single spontaneous PT transition or a thresholdless (THL) PT transition. The second group is a PT transitionless normal mode spectrum with essentially negative values of capacitors. The dynamics indicate that the system exhibits high frequencies propagation when operation is done before the thresholdless point is reached. The transitionless regime indicates an equilibrium point in the coupling for which the system turns to be conservative regardless the gain/loss values, and beyond which the gain/loss remarkably decays/amplifies wave. In addition, we observe a value of gain/loss above which there is a limitation of signal amplification.