LC Filter Calculator
This LC Filter Calculator analyzes ideal loaded LC low-pass and high-pass filters. It calculates the LC natural frequency, characteristic impedance, loaded Q, damping ratio, actual -3 dB frequency, peaking reference, transfer gain, phase, component values, and bounded frequency sweep tables.
It is intentionally different from the LC Resonance Calculator. Resonance gives the L-C natural frequency relationship; filter response also depends on topology and the output-node shunt load resistance.
Engineering tool
LC Filter Calculator
Analyze loaded LC low-pass and high-pass filter response, natural frequency, Q, damping, actual -3 dB frequency, component values, and bounded frequency sweep tables.
Ideal inductor value. DCR and core loss are not modeled.
Ideal capacitor value. ESR, ESL, and self-resonance are not modeled.
Output-node shunt termination resistance for the defined topology.
Frequency where loaded response and reactance are evaluated.
Result console
- Gain
- 0.70710653
- Gain
- -3.0103dB
- Phase
- -90°
- Characteristic frequency
- 1.591549kHz
- Actual -3 dB frequency
- 1.591549kHz
- Loaded Q
- 0.70710678
- Damping ratio
- 0.70710678
- Characteristic impedance
- 100Ω
- Butterworth RL reference
- 70.710678Ω
- XL
- 100.000036Ω
- XC
- 99.999964Ω
- f / f0
- 1.00000036
- Response state
- Near characteristic frequency
- Peaking expected
- No
This V1 model assumes an ideal voltage source, finite output-node shunt load resistance, zero inductor DCR, zero capacitor ESR, and no parasitics.
The LC natural frequency is not automatically the -3 dB cutoff for every loaded LC filter.
Formula reference
LC Filter Formulas
f0 = 1 / (2π√LC)ω0 = 1 / √LCZ0 = √(L/C)XL = 2πfLXC = 1 / (2πfC)Q = RL√(C/L) = RL/(ω0L) = ω0RLCζ = 1 / (2Q)Low-pass: Zshunt = ZC || RL, HLP = Zshunt / (jωL + Zshunt)High-pass: Zshunt = ZL || RL, HHP = Zshunt / (1/(jωC) + Zshunt)Gain dB = 20 log10(|H|)Variable definitions
- L
- inductance in henries
- C
- capacitance in farads
- RL
- output-node shunt load resistance
- f0
- ideal LC natural or characteristic frequency
- Z0
- characteristic impedance
- Q
- loaded quality factor for the defined topology
- ζ
- damping ratio
- H(jω)
- voltage transfer function
Worked Examples
Characteristic frequency
Known: L = 10 mH, C = 1 µF
f0 = 1/(2π√LC) ≈ 1591.55 Hz.
Characteristic impedance
Known: Same values
Z0 = √(L/C) = √(0.01 / 1e-6) = 100 Ω.
Reactance identity at f0
Known: Same values at f0
XL ≈ XC ≈ 100 Ω, matching √(L/C).
Butterworth load
Known: L = 10 mH, C = 1 µF
RL = √(L/C)/√2 ≈ 70.710678 Ω.
Butterworth low-pass at f0
Known: RL ≈ 70.710678 Ω
|H| ≈ 0.70710678 and gain ≈ -3.0103 dB.
Q = 1 at f0
Known: RL = 100 Ω
|H| ≈ 1 and gain ≈ 0 dB, so f0 is not the general -3 dB point.
Q = 2 at f0
Known: RL = 200 Ω
|H| ≈ 2 and gain ≈ +6.0206 dB, indicating response peaking.
Low-pass far below f0
Known: f << f0
Gain approaches 1 in the ideal low-pass passband.
Low-pass far above f0
Known: f >> f0
Gain approaches 0 and rolls off toward 40 dB/decade.
High-pass far below f0
Known: f << f0
Gain approaches 0 below the high-pass transition.
High-pass far above f0
Known: f >> f0
Gain approaches 1 in the ideal high-pass passband.
Solve inductance
Known: C = 1 µF, f0 ≈ 1591.55 Hz
L ≈ 10 mH.
Solve capacitance
Known: L = 10 mH, f0 ≈ 1591.55 Hz
C ≈ 1 µF.
Unit equivalence
Known: 1 mH and 1000 µH
Both convert to the same internal inductance and produce the same result.
Log sweep
Known: 100 Hz to 100 kHz, 50 points
The calculator generates 50 finite ordered response rows.
Butterworth -3 dB
Known: Q = 1/√2
The computed low-pass -3 dB frequency is approximately f0.
Non-Butterworth -3 dB
Known: Q ≠ 1/√2
The actual -3 dB frequency is calculated and is not forced to equal f0.
Characteristic identity
Known: At f0
XL(f0) ≈ XC(f0) ≈ √(L/C).
LC Filter
LC filters are second-order passive networks. The same L and C values can behave differently depending on topology and termination.
Characteristic Frequency
The ideal natural frequency is 1/(2π√LC), but that does not make it the universal -3 dB cutoff.
Loaded Q
For the defined output-node shunt load model, Q = RL√(C/L). Load resistance directly changes damping and peaking.
Butterworth Damping
Q = 1/√2 is the Butterworth reference for this simplified second-order model.
Peaking
Q above 1/√2 can produce gain peaking near the characteristic frequency. High Q is not automatically desirable.
Source Effects
The V1 model assumes an ideal voltage source with Rs = 0. Real source impedance adds damping and changes response.
Load Effects
Load resistance is the output-node shunt termination. It is not a vague circuit resistance and should match the defined topology.
Real Components
Inductor DCR, core loss, capacitor ESR, ESL, self-resonance, and PCB parasitics are not modeled in V1.
Common Mistakes
Support reference
FAQ
What is an LC filter?
An LC filter is a second-order passive network that uses an inductor and capacitor to shape frequency response. Depending on topology, it can act as a low-pass or high-pass filter.
How do I calculate the frequency of an LC filter?
The ideal LC natural frequency is f0 = 1 / (2π√LC), where L is in henries and C is in farads. This calculator reuses the project LC resonance utility for that calculation.
Is LC resonant frequency the same as cutoff frequency?
Not always. For the loaded second-order model used here, f0 equals the -3 dB frequency only at the Butterworth condition Q = 1/√2. Other Q values move the actual -3 dB point.
How does an LC low-pass filter work?
The V1 low-pass model uses a series inductor feeding an output node where the capacitor and load resistance are connected in parallel to ground.
How does an LC high-pass filter work?
The V1 high-pass model uses a series capacitor feeding an output node where the inductor and load resistance are connected in parallel to ground.
What is the characteristic impedance of an LC network?
For ideal L and C values, characteristic impedance is Z0 = √(L/C). At the natural frequency, XL and XC both equal this value.
How does load resistance affect an LC filter?
For the defined loaded topology, Q = RL√(C/L). Higher load resistance raises Q and can create peaking; lower load resistance increases damping.
How do I calculate the Q factor of a loaded LC filter?
For this simplified output-node shunt load model, Q = RL√(C/L). Equivalent forms are Q = RL/(ω0L) and Q = ω0RLC.
What is a Butterworth LC response?
In this model, the Butterworth damping reference occurs when Q = 1/√2. The response is maximally flat and f0 matches the -3 dB frequency.
Why can an LC filter have peaking?
When Q rises above 1/√2, the second-order response can exceed unity near the characteristic frequency. High Q is useful in some selective networks but can cause ringing and tolerance sensitivity.
What is the roll-off of a second-order LC filter?
An ideal LC low-pass ultimately rolls off at about 40 dB per decade above its passband. An ideal LC high-pass rises at about 40 dB per decade below its passband.
How do inductor DCR and capacitor ESR affect the result?
Real DCR, ESR, ESL, core loss, source impedance, PCB parasitics, and self-resonance change damping, gain, Q, and usable frequency range. This V1 calculator does not model those parasitics.
What is the difference between this calculator and the LC Resonance Calculator?
The LC Resonance Calculator solves the ideal L-C natural frequency relationship. This LC Filter Calculator adds topology, load resistance, transfer function response, Q, damping, actual -3 dB frequency, peaking, and sweep tables.
Planned Engineering Guides
Planned guide
LC Filters Explained
Planned guide
LC Low-Pass Filter Design
Planned guide
LC High-Pass Filter Design
Planned guide
LC Resonance vs Cutoff Frequency
Planned guide
Understanding LC Filter Q
Planned guide
Real-World LC Filter Losses
Planned Filter Calculators
Butterworth Filter Calculator
Pi Filter Calculator
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Engineering Disclaimer
This calculator uses an ideal loaded LC filter model for engineering estimates. It assumes an ideal voltage source and finite output-node shunt load resistance. It does not model source resistance, inductor DCR, core loss, capacitor ESR, capacitor ESL, component tolerance, self-resonance, PCB parasitics, or measured response. Use SPICE and lab measurement for critical designs.