Parallel RLC resonant circuit is also used to model a resonator in the resonance mode. Resonator is a system, that is experiencing the resonance phenomena. Resonance in RLC circuit occurs when power stored at inductor is equal to power stored at capacitor.

The example of parallel RLC resonant circuit is depicted below.

In case of parallel connection Zin=1(1R+1jωL+jωC). So power delivered to resonator is Ptot=V22(1R+jωLjωC).

Power stored at the inductor L is PL=V24ω2L. Power stored at the capacitor C is PC=V2C4. And power that dissipates at the resistor PR=V22R.

So Ptot=I2Zin2=PR+2jω(PLPC). Here we can find that Zin=Ptot+2jω(PLPC)12I2.

Resonance phenomena occurs when energy stored at inductor is equal to energy stored at capacitor, then Zin=2PtotI2=R.

The resonance frequency here is ω0=1LC (the same as for series RLC resonant circuit). Quality factor for unloaded RLC circuit is Q0=ω0RC.

Let’s consider circuit behaviour near resonance frequency ω0+ω, where ωω0. So Zinω0ω0+2jQ0ω.