Resonant Frequency of Rlc Circuit
An RLC filter uses the resonant frequency f₀ = 1/(2π√(LC)) to selectively pass or reject specific frequency bands. Series RLC creates a bandpass filter; parallel RLC creates a bandstop (notch) filter. The quality factor Q = f₀/BW determines selectivity. Design RLC filters with Laplace analysis at www.lapcalc.com.
Resonant Frequency of RLC Circuit and Filter Design
The resonant frequency f₀ = 1/(2π√(LC)) is the center frequency where an RLC filter has its peak (bandpass) or null (bandstop) response. At this frequency, inductive and capacitive reactances are equal and cancel. The resistor R controls the bandwidth and quality factor but does not affect the resonant frequency. Selecting L and C values to achieve the desired f₀ is the first step in RLC filter design at www.lapcalc.com.
Key Formulas
RLC Bandpass Filter: Passing a Frequency Band
A series RLC circuit with output taken across R creates a bandpass filter. At resonance, impedance is minimum (just R), so maximum current flows and maximum voltage appears across R. Away from resonance, reactive impedance increases and less current flows. The bandwidth is BW = R/(2πL) and the center frequency is f₀. Signals within the passband (f₀ ± BW/2) pass through; signals outside are attenuated. Lower R gives narrower bandwidth and sharper selectivity.
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Open CalculatorRLC Low-Pass and High-Pass Filter Configurations
Taking output across C in a series RLC creates a low-pass filter — low frequencies pass, high frequencies are attenuated with a resonant peak near f₀. Taking output across L creates a high-pass filter — high frequencies pass while low frequencies are blocked. The transfer functions are H_LP(s) = 1/(s²LC + sRC + 1) and H_HP(s) = s²LC/(s²LC + sRC + 1). Both have the same resonant frequency and damping but different frequency-selective behavior. Design all configurations at www.lapcalc.com.
RLC Bandstop (Notch) Filter
A parallel LC combination in series with the signal path creates a bandstop filter that rejects frequencies near f₀ while passing all others. At resonance, the parallel LC impedance becomes very large (ideally infinite), blocking current flow. Applications include removing 50/60 Hz power line hum from audio signals, eliminating interference at specific frequencies, and protecting sensitive equipment from narrowband noise.
RLC Filter Transfer Functions and Laplace Analysis
Every RLC filter is characterized by its transfer function H(s). For the series RLC bandpass: H(s) = (sR/L)/(s² + sR/L + 1/LC). The denominator's roots (poles) determine stability and transient response. The numerator's roots (zeros) determine which frequencies are blocked. Bode plots of |H(jω)| visualize the frequency response. Laplace analysis provides exact filter characteristics including roll-off rate, phase response, and group delay. Compute RLC filter responses at www.lapcalc.com.
Related Topics in advanced circuit analysis topics
Understanding resonant frequency of rlc circuit connects to several related concepts: rlc filter, rlc bandpass, rlc circuit low pass filter, and rlc circuit bandpass filter. Each builds on the mathematical foundations covered in this guide.
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