RL Filter Calculator
This RL Filter Calculator analyzes ideal first-order series RL networks. Output across the resistor gives a low-pass response, while output across the inductor gives a high-pass response.
Use it for cutoff frequency, time constant, inductive reactance, impedance, phase, component selection, and bounded frequency sweep checks in analog filter and signal-conditioning work.
Engineering tool
RL Filter Calculator
Analyze first-order RL low-pass and high-pass filters, cutoff frequency, time constant, inductive reactance, impedance, phase, component values, and response sweeps.
Total series resistance in the ideal RL model, including source resistance when applicable.
Ideal inductance used in the first-order RL filter.
Frequency where gain, phase, reactance, and impedance are evaluated.
Result console
- Low-pass gain
- 0.70710665
- Cutoff frequency
- 1.591549kHz
- Time constant τ
- 100µs
- XL
- 100.000036Ω
- |Z|
- 141.421382Ω
- Impedance phase
- 45°
- Low-pass gain
- 0.70710665
- Low-pass gain
- -3.0103dB
- Low-pass phase
- -45°
- High-pass gain
- 0.70710691
- High-pass gain
- -3.0103dB
- High-pass phase
- 45°
- Frequency ratio f/fc
- 1.00000036
- Filter state
- Cutoff region
Input R is treated as the total series resistance in the ideal RL model. Real source resistance adds to this value.
The ideal model assumes no additional output load. Finite load impedance can change gain, phase, and cutoff frequency.
Formula reference
RL Filter Formulas
The ideal RL filter model assumes the entered resistance is the total series resistance, an ideal voltage source, no additional load, and an ideal inductor.
ω = 2πfXL = 2πfLZ = R + jωL|Z| = sqrt(R² + (ωL)²)fc = R / (2πL)τ = L / Rfc = 1 / (2πτ)HLP(jω) = R / (R + jωL)|HLP| = 1 / sqrt(1 + (f/fc)²)HHP(jω) = jωL / (R + jωL)|HHP| = (f/fc) / sqrt(1 + (f/fc)²)Gain dB = 20 log10(|H|)Variable definitions
- R
- Total series resistance in ohms
- L
- Inductance in henries
- f
- Analysis frequency in hertz
- ω
- Angular frequency in rad/s
- XL
- Inductive reactance
- fc
- Cutoff frequency
- τ
- RL time constant
Worked Examples
Cutoff frequency
Known: R = 100 Ω, L = 10 mH
fc = 100 / (2π × 0.01) ≈ 1591.55 Hz.
Time constant
Known: R = 100 Ω, L = 10 mH
τ = L/R = 0.01/100 = 100 µs; 1/(2πτ) ≈ 1591.55 Hz.
XL at cutoff
Known: f = fc
XL = 2πfcL = 100 Ω, matching R.
Low-pass at cutoff
Known: f = fc
|HLP| = 1/√2 ≈ 0.7071068, gain ≈ -3.0103 dB, phase = -45°.
High-pass at cutoff
Known: f = fc
|HHP| = 1/√2 ≈ 0.7071068, gain ≈ -3.0103 dB, phase = +45°.
Low-pass below cutoff
Known: f = fc/10
Gain ≈ 0.995037, about -0.0432 dB.
Low-pass above cutoff
Known: f = 10fc
Gain ≈ 0.0995037, about -20.0432 dB.
High-pass below cutoff
Known: f = fc/10
Gain ≈ 0.0995037.
High-pass above cutoff
Known: f = 10fc
Gain ≈ 0.995037.
Solve inductance
Known: R = 1 kΩ, fc = 10 kHz
L = R/(2πfc) ≈ 15.9155 mH.
Solve resistance
Known: L = 10 mH, fc = 1 kHz
R = 2πfcL ≈ 62.8319 Ω.
Impedance at cutoff
Known: R = 100 Ω, XL = 100 Ω
|Z| ≈ 141.421 Ω and impedance phase = 45°.
Frequency unit equivalence
Known: 1000 Hz and 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 rows.
Complementary response
Known: Same ideal RL network
|HLP|² + |HHP|² = 1 for the unloaded series model.
RL Filter
An RL filter is a first-order passive filter. The same series network can behave as low-pass or high-pass depending on Vout location.
Cutoff Frequency
The ideal cutoff frequency is R/(2πL). At cutoff, XL equals R and magnitude is 1/√2.
Time Constant
The transient time constant is τ = L/R, and fc = 1/(2πτ).
Complementary Response
In the ideal unloaded series network, low-pass and high-pass magnitude squares sum to one.
Source Resistance
If a real source resistance is in series, it contributes to effective R and shifts cutoff frequency.
Load Impedance
A finite load connected to the output changes the transfer function and can alter gain, phase, and cutoff.
Real Inductors
Inductor DCR, saturation, core loss, parasitic capacitance, and self-resonance are not modeled in V1.
Frequency Limit
Above self-resonant frequency, an inductor may stop behaving like an ideal inductance.
Common Mistakes
Support reference
FAQ
What is an RL filter?
An RL filter is a first-order passive filter made from resistance and inductance. Its response depends on whether output is measured across the resistor or the inductor.
How do I calculate the cutoff frequency of an RL filter?
Use fc = R / (2πL), where R is total series resistance in ohms and L is inductance in henries.
Is an RL circuit a low-pass or high-pass filter?
It can be either. Output across R gives a low-pass response. Output across L gives a high-pass response.
Why does output across the resistor create a low-pass filter?
At low frequency, inductor reactance is small, so most input voltage appears across R. At high frequency, inductor reactance rises and less voltage appears across R.
Why does output across the inductor create a high-pass filter?
At low frequency, XL is small, so inductor voltage is small. At high frequency, XL becomes large, so a larger share of the input appears across L.
What happens at the cutoff frequency?
At cutoff, XL = R. Both ideal low-pass and high-pass magnitude are 1/√2, or approximately -3.0103 dB. Low-pass phase is -45° and high-pass phase is +45°.
What is the RL time constant?
The RL time constant is τ = L / R. It describes first-order transient response and relates to cutoff by fc = 1 / (2πτ).
How are cutoff frequency and time constant related?
They are reciprocal first-order descriptions: fc = 1 / (2πτ) and τ = L / R.
How do I calculate inductive reactance?
Use XL = 2πfL, where f is frequency in hertz and L is inductance in henries.
What is the roll-off of an RL filter?
An ideal first-order RL filter rolls off at about 20 dB per decade beyond the transition region.
How does inductor DCR affect an RL filter?
Inductor DCR adds effective series resistance, which shifts cutoff frequency and changes practical voltage division. This V1 calculator treats the entered R as total series resistance.
Why does inductor self-resonance matter?
A real inductor has parasitic capacitance. Above its self-resonant frequency, it may no longer behave like an ideal inductance, so ideal RL filter equations can become misleading.
Planned Engineering Guides
Planned guide
RL Filters Explained
Planned guide
RL Low-Pass vs High-Pass Filters
Planned guide
Inductive Reactance Explained
Planned guide
RL Time Constant
Planned guide
Real-World Inductor Losses
Planned Filter Calculators
LC Filter Calculator
PWM Low-Pass Filter Calculator
Related Calculators
Filter Q Factor & Bandwidth Calculator
Analyze filter Q, bandwidth, center frequency, and fractional bandwidth.
AvailableRLC Filter Calculator
Analyze second-order RLC resonance, Q, bandwidth, impedance, and response.
AvailableInductive Reactance Calculator
Calculate ideal inductive reactance and angular frequency.
AvailableRL Time Constant Calculator
Calculate RL transient time constant and current response.
AvailableLC Resonance Calculator
Calculate LC resonant frequency or solve L and C for resonance.
Engineering Disclaimer
This calculator uses an ideal first-order RL filter model for engineering estimates. It does not model inductor DCR separately, saturation, core loss, parasitic capacitance, self-resonance, finite source/load impedance, EMI behavior, or measured response.