# Resonant Frequency of AC Circuit with Coil, Capacitor and Resistance

• xswtxoj

#### xswtxoj

I don't understand when you have an AC Circuit that has a coil, capacitor and resistance. What factor will the resonant frequency change when the frequency is tripled?

The resonant frequency of a circuit is equal to

fR= wR/(2 pi) = (1/(2 pi) 1/sqr(L C)

so to triple the resonant frequency, the product of L and C has to be decreased by a factor of 9.

The Q of the resonant circuit is equal to wRL/R for a series resiistance, or R/(wRL) for a parallel resistance.

I attach a resonance curve for a 160 microHenry inductance with a 160 picoFarad capacitor.
There is a series resistor of 100 ohms. The resonant frequency is 1 MHz, and sqrt(L/C) = 1000 ohms, so wL/R = Q = 10. The excitation is a swept frequency of a 1-amp current source from 300 kHz to 2 MHz. The dotted line is the phase of the circuit impedance, starting near + 90 degrees, and ending near - 90 degrees.

#### Attachments

• LC_resonance_curve2.pdf
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