Resistor-Capacitor (RC) Filter
Calculated Cutoff Frequency (ƒc):
1591.55 Hz
Resistor-Inductor (RL) Filter
Calculated Cutoff Frequency (ƒc):
1591.55 Hz
Circuit Diagram
Frequency Response (Bode Plot)
Core Concepts
Understand the fundamental principles behind low-pass filters.
What is a Low-Pass Filter?
A low-pass filter is an electronic circuit that allows signals with a frequency lower than a specific cutoff frequency to pass through it, while attenuating (reducing the amplitude of) signals with frequencies higher than this cutoff frequency. In essence, it blocks high frequencies and lets low frequencies pass, which is useful for removing noise from a signal or for audio applications like subwoofers.
The Cutoff Frequency (ƒc)
The cutoff frequency is the point at which the filter begins to work. Specifically, it's the frequency at which the output signal's power is reduced to half the power of the input signal. This is also known as the -3dB point. Frequencies below ƒc are passed with little to no attenuation, while frequencies above ƒc are progressively attenuated at a specific rate (the "roll-off").
RC Filter Explained
The RC low-pass filter uses a resistor and a capacitor. At low frequencies, the capacitor has a high impedance, so most of the input voltage appears at the output. As the frequency increases, the capacitor's impedance drops, creating a voltage divider with the resistor that attenuates the output signal. The formula is:
ƒc = 1 / (2 * π * R * C)
RL Filter Explained
The RL low-pass filter uses a resistor and an inductor. At low frequencies, the inductor has a very low impedance, acting almost like a wire, so the input signal passes to the output easily. As frequency increases, the inductor's impedance rises, forming a voltage divider with the resistor that blocks the high-frequency components from reaching the output. The formula is:
ƒc = R / (2 * π * L)
Real-World Applications
Where you'll find low-pass filters in action.
Audio Systems
In audio crossovers, low-pass filters direct low-frequency signals to subwoofers, ensuring they only reproduce bass sounds they are designed for.
Signal Processing
Used to remove high-frequency noise or "hiss" from signals, cleaning up data from sensors or in telecommunications before further processing.
Image Processing
Analogous filters are used in software for image blurring and smoothing, effectively removing high-frequency details or noise from an image.
Assumptions, examples, and cutoff-frequency verification
The calculator uses ideal first-order filter models. For an RC low-pass filter, take the output across the capacitor and use fc = 1/(2πRC), with R in ohms and C in farads. For a series RL low-pass filter, take the output across the resistor and use fc = R/(2πL), with L in henries. At cutoff, the ideal amplitude is about 0.707 of the passband level, or −3.01 dB.
Calculation checks
| Topology | Inputs | Substitution | Expected result |
|---|---|---|---|
| RC, output across C | R = 1 kΩ; C = 0.1 µF | 1/(2π × 1000 × 0.1 × 10−6) | 1,591.55 Hz |
| RL, output across R | R = 100 Ω; L = 10 mH | 100/(2π × 10 × 10−3) | 1,591.55 Hz |
Limits of the result
- The calculation assumes a zero-ohm source and an infinite-impedance load. Include source resistance and load impedance in a real circuit.
- For RC, include capacitor tolerance, temperature/voltage coefficients, and ESR. For RL, include winding resistance and coil parasitic capacitance.
- The formulas describe one passive stage. Cascaded, active, Butterworth, Bessel, and Chebyshev filters require order, Q, and op-amp bandwidth analysis.
With R ±1% and C ±10%, the RC example can have a calculated cutoff of roughly 1,432.54–1,786.25 Hz before loading and parasitics are included.
Verify on a breadboard or PCB
- Apply a low-amplitude sine wave and measure Vin and Vout simultaneously with two oscilloscope channels.
- For RC, measure across the capacitor; for the shown RL circuit, measure across the resistor.
- Sweep around the calculated frequency. The measured cutoff is where |Vout/Vin| ≈ 0.707.
- If it differs, measure the actual R, C, or L and recalculate with source, load, and winding resistance included.
