Electric circuit model of microwave optomechanics

We report on the generic classical electric circuit modeling that describes standard single-tone microwave optomechanics. Based a parallel RLC in which mechanical oscillator acts as movable capacitor, derivations of analytical expressions are presented, including key features such back-action force, input-output expressions, and spectral densities associated, all regime. These coincide with quantum treatment performed optomechanics when occupation number both cavity large. Besides, derived analytics transposes optical elements properties into electronics terms, is mandatory for quantitative measurement design purposes. Finally, direct comparison between model addresses bounds regimes, highlighting truly quantum, those not.