  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.
