Theory of Double Ladder Lumped Circuits With Degenerate Band Edge

A conventional periodic LC ladder circuit forms a transmission line that has a regular band edge between a passband and a stopband. 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 a degenera...

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Bibliographic Details
Published inIEEE transactions on circuits and systems. I, Regular papers Vol. 65; no. 1; pp. 3 - 13
Main Authors Sloan, Jeff T., Othman, Mohamed A. K., Capolino, Filippo
Format Journal Article
LanguageEnglish
Published New York IEEE 01.01.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Cavity resonators
circuit theory
Circuits
Coalescing
Complex systems
Degenerate band edge (DBE)
Dispersion
Eigenvectors
ladder oscillators
Ladders
Loading
Oscillators
Periodic structures
Q factors
Q-factor
RLC circuits
slow-wave circuits
Steady-state
Transmission lines
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Summary:A conventional periodic LC ladder circuit forms a transmission line that has a regular band edge between a passband and a stopband. 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 a 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 a 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.
ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2017.2690971