Three ports active circulator's reflection type phase shifter (RTPS) circuit transmission lines delayed in time system stability analysis

Abstract

In this article, a very crucial subject is discussed, which is the three ports active circulator transmission lines delayed in time stability analysis. Our circuit is a reflection type phase shifter (RTPS), employing a circulator. Micro strip transmission lines have three ports active circulator, with stability analysis under time delayed. Many radio frequency (RF) systems use active circulator as a passive non-reciprocal three- or four-port device, in which microwave or radio frequency power entering any port is transmitted to the next port in rotation (only). Micro strip transmission lines feed those active circulator ports and face a delay parasitic effect of transferring signals in time. These circulator's micro strip transmission lines delays cause the system to instability. Due to parasitic effects of active circulator's micro strip transmission lines, there is delay in time for input/output RF signals which result in system instability. We define active circulator's micro strip transmission lines delays τ1 for the first port current and τ3 for the third port current. Accordingly, active circulator's micro strip transmission lines delays Δ1 for the first port current derivative and Δ3 for the third port current derivative. We have four delays in time τ1, τ2, Δ1, Δ3 and discuss sub case where separately delays are equal to zero (τ1=τ2=τ and Δ1=Δ3 =0) which describe most of active circulator parasitic effects. The three active circulator ports delayed in time equivalent circuit with micro strip segments can be represented as a delayed differential equation which depends on variable parameters and delays. The investigation of our active circulator element with micro strip lines system differential equation is based on stability switching. Active circulator with transmission lines stability switching analysis is done under different time delays with respect to circulator inputs/outputs currents and currents derivative. All of that is for optimization of a three port active circulator equivalent circuit parameters analysis with micro strip transmission lines to get the best performance.