Abstract
A conventional periodic LC ladder circuit forms a transmission line that has a regular band edge between a pass and a stop band. Here for the first time we develop the theory of simple yet unconventional double ladder circuit that exhibits a special degeneracy condition referred to as degenerate band edge (DBE). The degeneracy occurs when four independent eigenstates coalesce into a single eigenstate at the DBE frequency. In addition to possible practical applications, this circuit may provide insight into DBE behavior that is not clear in more complex systems. We show that double ladder resonators exhibit unusual behavior of the loaded quality factor near the DBE leading to a stable resonance frequency against load variations. These two properties in the proposed circuit are superior to the analogous properties in single ladder circuits. Our proposed analysis leads to analytic expressions for all circuit quantities thus providing insight into the very complex behavior near degeneracy points in periodic circuits. Interestingly, here we show for the first time that DBE is obtained with unit cells that are symmetric along the propagation direction. The proposed theory of double ladders presented here has potential applications in filters, couplers, oscillators, and pulse shaping networks.
Highlights
PERIODIC structures and circuits have been utilized in many RF components and devices due to their unique properties such as the existence of electromagnetic band edges and bandgaps [1]–[3]
We have presented for the first time a comprehensive theoretical formulation that explains the physical behavior and the loading properties of double ladder periodic circuits with a fourth order degeneracy
We have demonstrated that a periodic circuit whose unit cell is made of only five lumped elements exhibits a degenerate band edge in the phase-frequency dispersion relation; and we have shown analytically the eigenstates behavior of such periodic circuit near the DBE
Summary
PERIODIC structures and circuits have been utilized in many RF components and devices due to their unique properties such as the existence of electromagnetic band edges and bandgaps [1]–[3]. We propose for the first time a periodic lumped double ladder circuit, whose unit cell is made of just a few reactive elements, that develops a degenerate band edge condition (in contrast to previous investigations that were focused on transmission lines). Because this lumped circuit is very simple, we show for the first time exact analytic steady state solutions for periodic voltage/current eigenstates in periodic double ladders; and the occurrence of an unusual resonance in double ladders with finite size. Throughout this paper we assume steady-state monochromatic signals, and phasors are based on the e j t time convention that is implicitly assumed
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