Theory of Double Ladder Lumped Circuits With Degenerate Band Edge

TL;DR

This paper develops a novel theory for double ladder circuits exhibiting degenerate band edge (DBE), revealing unique resonant behaviors and providing analytical insights into complex degeneracy phenomena in periodic circuits.

Contribution

It introduces the first theory of double ladder circuits with DBE, showing their superior properties and symmetric unit cell design, with potential applications in various RF components.

Findings

Double ladder resonators show stable resonance frequency near DBE.

Loaded quality factor exhibits unusual behavior near DBE.

Analytic expressions derived for circuit quantities.

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.