RLC Filter Calculator
This RLC Filter Calculator analyzes ideal second-order RLC networks, including series output measured across R, C, or L, series impedance, ideal parallel R || L || C resonance reference, and bounded response sweep tables.
It is intentionally broader than an LC resonance calculator: it includes Q factor, bandwidth, half-power frequencies, impedance, magnitude response, phase, and topology-specific engineering boundaries.
Engineering tool
RLC Filter Calculator
Analyze ideal second-order RLC filter resonance, Q, bandwidth, impedance, phase, and response for series and parallel reference circuits.
Series resistance or ideal parallel branch resistance.
Ideal inductance used in the second-order network.
Ideal capacitance used in the second-order network.
Frequency where impedance and response are evaluated.
Result console
- Gain
- 1
- Gain
- -0dB
- Phase
- -0°
- Resonant frequency
- 1.591549kHz
- Q factor
- 10
- Bandwidth
- 159.154943Hz
- Lower half-power frequency
- 1.51396kHz
- Upper half-power frequency
- 1.673115kHz
- XL
- 100.000036Ω
- XC
- 99.999964Ω
- Net reactance
- 0.000072Ω
- |Z|
- 10Ω
- Impedance phase
- 0°
- Filter behavior
- Near Resonance
Ideal model assumes an ideal voltage source, no extra load, zero inductor DCR, zero capacitor ESR, and no parasitics.
Formula reference
RLC Filter Formulas
The ideal RLC formulas assume an ideal voltage source, no additional load, zero inductor DCR, zero capacitor ESR, and no parasitic effects.
f0 = 1 / (2π√(LC))XL = 2πfLXC = 1 / (2πfC)Series Z = R + j(ωL - 1/(ωC))Series Qs = ω0L / R = 1/(ω0CR) = sqrt(L/C)/RSeries BW = R / (2πL)Series fL = (sqrt(R² + 4L/C) - R) / (4πL)Series fH = (sqrt(R² + 4L/C) + R) / (4πL)Parallel Y = 1/R + j(ωC - 1/(ωL))Parallel Qp = R/(ω0L) = ω0RC = R sqrt(C/L)Parallel BW = 1 / (2πRC)Variable definitions
- R
- Resistance in ohms
- L
- Inductance in henries
- C
- Capacitance in farads
- f0
- Ideal resonant frequency
- ω0
- Ideal resonant angular frequency
- XL
- Inductive reactance
- XC
- Capacitive reactance
- Qs
- Series RLC quality factor
- Qp
- Ideal parallel RLC quality factor
Worked Examples
Series resonance
Known: R = 10 Ω, L = 10 mH, C = 1 µF
f0 = 1/(2π√LC) ≈ 1591.55 Hz.
Series Q
Known: Same values
ω0L ≈ 100 Ω, so Qs = ω0L/R ≈ 10.
Series bandwidth
Known: Same values
BW = R/(2πL) ≈ 159.155 Hz and f0/BW ≈ 10.
Exact half-power points
Known: Same values
fL ≈ 1513.96 Hz and fH ≈ 1673.11 Hz; fH - fL ≈ 159.155 Hz.
At resonance
Known: f = f0
XL ≈ XC, net reactance ≈ 0, and series impedance ≈ R.
Across R at resonance
Known: Output across R
Gain ≈ 1 V/V and gain dB ≈ 0 dB in the ideal model.
Below resonance
Known: f well below f0
XL < XC, so the series network is net capacitive.
Above resonance
Known: f well above f0
XL > XC, so the series network is net inductive.
Series Q equivalence
Known: Same values
ω0L/R, 1/(ω0CR), and sqrt(L/C)/R all produce Qs ≈ 10.
Parallel resonance
Known: R = 1 kΩ, L = 10 mH, C = 1 µF
f0 ≈ 1591.55 Hz and ideal parallel Qp ≈ 10.
Parallel Q equivalence
Known: Same parallel values
R/(ω0L), ω0RC, and R sqrt(C/L) all match.
Parallel bandwidth
Known: Same parallel values
BW = f0/Qp ≈ 159.155 Hz and 1/(2πRC) gives the same value.
Across C low frequency
Known: Series output across capacitor
At very low frequency, |H| approaches 1.
Across C high frequency
Known: Series output across capacitor
At very high frequency, |H| approaches 0.
Across L low frequency
Known: Series output across inductor
At very low frequency, |H| approaches 0.
Across L high frequency
Known: Series output across inductor
At very high frequency, |H| approaches 1.
Frequency unit equivalence
Known: 1000 Hz vs 1 kHz
Both convert to the same internal frequency in hertz.
Sweep table
Known: 100 Hz to 100 kHz, 50 log points
The result is 50 finite ordered response rows.
RLC Filter
RLC networks are second-order circuits. Their behavior changes with topology, output point, source impedance, and load impedance.
Series RLC
The same series RLC chain can act as band-pass across R, low-pass-type across C, or high-pass-type across L.
Parallel RLC
This page models only the explicit ideal R || L || C reference. It does not include inductor ESR, capacitor ESR, source resistance, or load coupling.
Resonance
Ideal resonance occurs when inductive and capacitive reactance cancel.
Quality Factor
Series Q is ω0L/R. Parallel Q is R/(ω0L). These formulas are not interchangeable.
Bandwidth
Higher Q produces narrower bandwidth, but high Q is not automatically better because ringing and tolerance sensitivity increase.
Half-Power Frequencies
The series across-R band-pass half-power points use exact equations. f0 ± BW/2 is only a narrowband approximation.
Real Components
Inductor DCR, capacitor ESR, parasitics, self-resonance, PCB layout, source impedance, and load impedance all shift practical response.
Common Mistakes
Support reference
FAQ
What is an RLC filter?
An RLC filter is a second-order circuit that uses resistance, inductance, and capacitance. Its response depends on topology and where the output voltage is measured.
How do I calculate RLC resonant frequency?
For the ideal models used here, resonant frequency is f0 = 1 / (2π√LC), where L is in henries and C is in farads.
What is the Q factor of a series RLC circuit?
For an ideal series RLC circuit, Qs = ω0L / R. Equivalent forms are Qs = 1 / (ω0CR) and Qs = sqrt(L/C) / R.
What is the Q factor of a parallel RLC circuit?
For the ideal R || L || C reference topology, Qp = R / (ω0L). Equivalent forms are Qp = ω0RC and Qp = R sqrt(C/L).
How do I calculate RLC bandwidth?
Series RLC bandwidth is BW = R / (2πL). For the ideal parallel R || L || C model, BW = 1 / (2πRC). In both cases Q = f0 / BW for the modeled topology.
What are the lower and upper half-power frequencies?
For the series across-R band-pass response, the half-power frequencies occur where |XL - XC| = R. The calculator uses the exact second-order relationship, not f0 ± BW/2.
Why does a series RLC circuit act as a band-pass filter across the resistor?
At resonance, XL and XC cancel, so series impedance is R and resistor voltage is maximized. Away from resonance, reactive impedance increases and less voltage appears across R.
Can a series RLC circuit act as a low-pass filter?
Yes. If output is measured across the capacitor, the same series RLC network has a low-pass-type second-order response.
Can a series RLC circuit act as a high-pass filter?
Yes. If output is measured across the inductor, the same series RLC network has a high-pass-type second-order response.
What happens at resonance?
In the ideal series RLC model, XL equals XC and the net reactance is zero. In the ideal parallel RLC model, branch susceptances cancel and impedance reaches R.
What is the difference between series and parallel RLC resonance?
Series RLC resonance minimizes series impedance, while ideal parallel RLC resonance maximizes impedance. Their Q equations are not interchangeable.
How do ESR and source/load resistance affect an RLC filter?
Inductor DCR, capacitor ESR, source impedance, and load impedance change damping, Q, bandwidth, gain, and cutoff behavior. This calculator uses ideal unloaded component models plus the explicit R value.
Planned Engineering Guides
Planned guide
RLC Filters Explained
Planned guide
Series vs Parallel RLC Circuits
Planned guide
RLC Resonance and Bandwidth
Planned guide
Understanding Q Factor in RLC Filters
Planned guide
RLC Frequency Response
Planned guide
Real-World Inductor and Capacitor Losses
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LC Filter Calculator
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Engineering Disclaimer
This calculator uses ideal RLC circuit equations for engineering estimates and education. It does not replace SPICE simulation, datasheet review, measured frequency response, or source/load-aware design validation.