RLC resonance occurs when a resistor, inductor, and capacitor respond strongly at a particular frequency. It matters because many engineered systems must select one signal frequency while rejecting others. Radios, audio filters, wireless chargers, sensors, and communication circuits all use resonance to tune or filter signals.
The resonance curve shows how current or voltage amplitude changes with frequency, with a peak at the resonant frequency.
Key Facts
- Inductive reactance: X_L = 2πfL
- Capacitive reactance: X_C = 1/(2πfC)
- Resonance condition: X_L = X_C
- Resonant frequency: f_0 = 1/(2π√(LC))
- Series RLC impedance: Z = √(R^2 + (X_L - X_C)^2)
- Quality factor: Q = f_0/Δf, where Δf is the bandwidth between half-power frequencies
Vocabulary
- Resonance
- Resonance is the condition in which an RLC circuit responds most strongly because inductive and capacitive reactances cancel.
- Reactance
- Reactance is the opposition to alternating current caused by inductors and capacitors, measured in ohms.
- Bandwidth
- Bandwidth is the range of frequencies over which a resonant circuit responds strongly, often measured between the half-power points.
- Quality factor
- Quality factor, or Q, measures how sharp and selective a resonance peak is compared with its center frequency.
- Tuning
- Tuning is the process of adjusting circuit values so the resonant frequency matches a desired signal frequency.
Common Mistakes to Avoid
- Assuming resonance means maximum voltage everywhere is wrong because in a series RLC circuit the current is maximum, while individual inductor and capacitor voltages can be large and opposite in phase.
- Forgetting the square root in f_0 = 1/(2π√(LC)) is wrong because resonance depends on the product LC under a square root, not directly on LC.
- Treating series and parallel resonance as identical is wrong because a series RLC circuit has minimum impedance at resonance, while an ideal parallel RLC circuit has maximum impedance.
- Using ordinary frequency f in formulas that require angular frequency ω is wrong because ω = 2πf, so missing the factor of 2π gives incorrect reactance and resonance values.
Practice Questions
- 1 A series RLC circuit has L = 20 mH and C = 2.0 μF. Calculate the resonant frequency f_0.
- 2 A resonant circuit has f_0 = 100 kHz and a bandwidth of 5.0 kHz. Calculate its Q factor.
- 3 A radio tuning circuit needs to select a narrower range of frequencies around one station. Explain whether its Q factor should be increased or decreased, and describe one circuit change that could help.