Synthetic rotational Doppler shift on transmission lines and it’s microwave applications

Rotational Doppler shift of a circularly polarized wave impinging normally on a rotating anisotropic surface, causes scattered waves with frequency shift equals twice the surface rotation frequency. We show that virtual rotational Doppler shift can be realized in transmission line platforms through a time-varying junction. In a system consisting of a pair of decoupled but identical transmission lines, voltage waves with a 90-degree phase difference between the two lines mimic a circularly polarized wave. A junction, comprising three time-varying capacitors and a static two-port network, connects the two lines and acts as a synthetically rotating anisotropic surface. As a result, the reflected and transmitted voltage (or current) waves undergo a frequency shift equal to twice the synthetic rotation frequency. Utilizing this effect, a full frequency converter is then proposed by augmenting the synthetically rotating capacitive junction with a dispersive phase shifter, followed by a short circuit. The system efficiently converts the incident tone into a single down- or up-converted tone, with amplification observed in the case of up-conversion. The frequency converter is subsequently employed to design a magnetic-free isolator. Circuit simulations with both ideal and switch-based time-varying capacitors match theoretical predictions.