Analysis and modeling of Fano resonances using equivalent circuit elements

Fano resonance presents an asymmetric line shape formed by an interference of a continuum coupled with a discrete autoionized state. In this paper, we show several simple circuits for Fano resonances from the stable-input impedance mechanism, where the elements consisting of inductors and capacitors are formulated for various resonant modes, and the resistor represents the damping of the oscillators. By tuning the pole-zero of the input impedance, a simple circuit with only three passive components e.g. two inductors and one capacitor, can exhibit asymmetric resonance with arbitrary Q-factors flexiblely. Meanwhile, four passive components can exhibit various resonances including the Lorentz-like and reversely electromagnetically induced transparency (EIT) formations. Our work not only provides an intuitive understanding of Fano resonances, but also pave the way to realize Fano resonaces using simple circuit elements.