Table of Contents
What Is Resonant Frequency?
The resonant frequency of an LC circuit is the frequency at which the inductive reactance equals the capacitive reactance, causing the impedance to reach a minimum (series) or maximum (parallel). At resonance, energy oscillates back and forth between the inductor's magnetic field and the capacitor's electric field with no net energy loss in an ideal circuit.
LC resonant circuits are fundamental building blocks in electronics. They form the basis of radio tuners, bandpass filters, oscillators, and impedance matching networks. Understanding resonant frequency is critical for designing circuits that select or reject specific frequencies from a signal.
The LC Resonance Formula
Where f is the resonant frequency in hertz, L is inductance in henrys, C is capacitance in farads, and ω is the angular frequency in radians per second. The period T equals 1/f.
Applications of LC Circuits
- Radio tuning: Variable capacitors adjust resonant frequency to select radio stations.
- Bandpass filters: Allow a narrow band of frequencies to pass while rejecting others.
- Oscillators: Colpitts and Hartley oscillators use LC tanks to generate sinusoidal signals.
- Impedance matching: LC networks match source and load impedances for maximum power transfer.
Common LC Values
| Inductance | Capacitance | Resonant Freq |
|---|---|---|
| 1 mH | 1 µF | 5.03 kHz |
| 100 µH | 100 pF | 1.59 MHz |
| 10 µH | 10 pF | 15.9 MHz |
| 1 µH | 1 pF | 159 MHz |
Frequently Asked Questions
What happens at the resonant frequency?
At resonance, the inductive and capacitive reactances cancel each other. In a series LC circuit, impedance drops to its minimum (ideally zero), allowing maximum current flow. In a parallel LC circuit, impedance reaches maximum, blocking current at that frequency.
Does resistance affect the resonant frequency?
In an ideal LC circuit, resistance does not change the resonant frequency. However, resistance affects the quality factor (Q) and bandwidth. Higher resistance lowers Q, broadening the resonance peak and reducing selectivity.
How do I convert between inductance and capacitance units?
1 henry = 1,000 millihenrys (mH) = 1,000,000 microhenrys (µH). 1 farad = 1,000,000 microfarads (µF) = 10^12 picofarads (pF). Enter values in base SI units (henrys and farads) for this calculator.