The bandwidth of an RLC circuit defines the frequency range where the circuit passes signals with minimal attenuation. Within the -3dB bandwidth, the output is at least 70.7% of the peak resonant value. Outside this range, the signal is increasingly attenuated. High Q circuits have narrow bandwidth (high selectivity).
⚠The -3dB points are where the reactance equals the resistance (series) or the admittance equals conductance (parallel). At f₁ and f₂: |Z| = √2×R for series, phase = ±45°.
Understanding RLC Bandwidth
Bandwidth is a measure of the range of frequencies a resonant circuit can pass. It is determined by the Q factor, which depends on energy loss per cycle. Narrow bandwidth (high Q) means the circuit is very selective, ideal for radio tuning. Wide bandwidth (low Q) means the circuit passes a broader range, useful for audio or data transmission.
Narrow Band (High Q)
Q>50, Δf < 2% of f₀. High selectivity, rejects adjacent channels. Used in radio receivers and spectrum analyzers.
Wide Band (Low Q)
Q<5, Δf > 20% of f₀. Broad response, less distortion. Used in audio crossovers, wideband amplifiers, and data communication.
Cutoff Points
At f₁ and f₂: phase = ±45°, |Z| = √2×R (series). Output = 70.7% of peak. Power = 50% (half-power points, -3dB).
Geometric Mean
f₁ × f₂ = f₀². The resonant frequency is the geometric mean of the cutoff frequencies. Example: 995kHz × 1005kHz = 1MHz².
Teaching Example: R=10Ω, L=10mH, C=1μF (Series).
f₀ = 1591.5 Hz. Q = ω₀L/R = (10000×0.01)/10 = 10.
Δf = 1591.5/10 = 159.2 Hz. f₁ = 1591.5 - 79.6 = 1511.9 Hz. f₂ = 1591.5 + 79.6 = 1671.1 Hz.
Passband: 1512Hz to 1671Hz (159Hz wide, Q=10).
Applications
Radio ReceiversAudio FiltersWireless CommsSpectrum AnalysisEMI Testing
Frequently Asked Questions
What is RLC bandwidth?▼
Δf = f₀/Q. Frequency range between -3dB points. Narrow = selective. Wide = broadband.
Increase Q: reduce R (series) or increase R (parallel). Narrower bandwidth = higher selectivity. Trade-off: longer settling time.
What is 3dB bandwidth?▼
The -3dB (half-power) bandwidth where output drops to 70.7% of peak. Power = 50%. These points define the effective passband of a filter or resonant circuit.
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