What is Cutoff Frequency?

Cutoff frequency (fc), also known as the corner frequency or -3dB point, is the frequency at which the output power of a filter circuit is reduced to half (-3dB) of its input power. At this frequency, the voltage gain is reduced by a factor of 1/√2 (approximately 0.707).

The cutoff frequency is a critical parameter in RC and RL filters for:

RC Low Pass Filters: Allow low frequencies to pass, attenuate high frequencies
RC High Pass Filters: Block low frequencies, allow high frequencies to pass
RL Low Pass Filters: Use inductance instead of capacitance for filtering
RL High Pass Filters: Inductive high pass filtering

Understanding cutoff frequency is essential for circuit design, audio processing, signal conditioning, and EMI/RFI filtering.

Cutoff Frequency Formulas

The cutoff frequency depends on the filter type and components used in the circuit.

fc = \frac{1}{2\pi RC}

RC Low Pass / High Pass Filter: Where fc is cutoff frequency in Hz, R is resistance in ohms, and C is capacitance in farads.

fc = \frac{R}{2\pi L}

RL Low Pass / High Pass Filter: Where fc is cutoff frequency in Hz, R is resistance in ohms, and L is inductance in henries.

fc = \frac{1}{2\pi \tau} \text{ where } \tau = RC

Alternative Formula (RC - Time Constant): Where τ (tau) is the RC time constant in seconds.

\phi = -45° \text{ (for first-order filters)}

Phase Shift at Cutoff Frequency: At the cutoff frequency, the phase shift is -45 degrees.

How to Use the Cutoff Frequency Calculator

This calculator helps you determine the cutoff frequency of filter circuits or calculate required component values.

Select Filter Type: Choose between RC Low Pass, RC High Pass, RL Low Pass, or RL High Pass filters.
Enter Component Values: Input resistance (R) in Ω, kΩ, or MΩ, and either capacitance (C) or inductance (L) with appropriate units.
Click Calculate from Components: The calculator will compute the cutoff frequency and display step-by-step calculations.
Calculate Component Values: Alternatively, enter desired cutoff frequency and one component value, then click "Calculate Component" to find the other component value needed.
Review Results: View detailed calculation steps showing the mathematical process and final cutoff frequency value.

Understanding -3dB Point

The -3dB point is the standard definition for cutoff frequency in filter design. At this frequency:

Power is reduced to 50% of the input power (Pout = 0.5 × Pin)
Voltage magnitude is reduced to 70.7% of input (Vout = 0.707 × Vin)
This equals -3 decibels in logarithmic terms (20 log₁₀(0.707) ≈ -3dB)
The phase shift is exactly -45° for first-order filters

Above the cutoff frequency, signals are progressively attenuated at a rate of 20dB per decade for first-order filters.

RC Filter Applications

RC filters (using resistors and capacitors) are widely used in:

Audio Processing: Removing high-frequency noise from analog signals
Power Supplies: Filtering ripple from rectified AC voltage
Signal Conditioning: Preparing sensor signals for analog-to-digital conversion
EMI/RFI Suppression: Protecting circuits from electromagnetic interference
Tone Controls: In audio amplifiers and equalizers

RC circuits are preferred for lower frequencies because capacitors are more practical and affordable than inductors at low frequencies.

RL Filter Applications

RL filters (using resistors and inductors) are common in:

Power Electronics: Filtering high-frequency switching noise from power supplies
RF Circuits: Radio frequency circuit applications
Motor Control: Protecting motor control circuits from switching transients
High-Frequency Applications: More practical than RC for frequencies above several MHz

RL circuits are preferred at higher frequencies where inductors become more practical and capacitive coupling is less desirable.

Practical Example

Example: Design an RC low pass filter with a cutoff frequency of 1 kHz and a 10 kΩ resistor.

Solution:

Use formula: fc = 1 / (2πRC)
Rearrange: C = 1 / (2π × fc × R)
Substitute: C = 1 / (2π × 1000 × 10000)
Calculate: C = 1 / (62,831,853) = 15.9 nanofarads

You would use a 10 kΩ resistor and a 15.9 nF capacitor (standard value: 16 nF) to achieve approximately 1 kHz cutoff frequency.

What is the difference between cutoff frequency and corner frequency?

Cutoff frequency and corner frequency are the same thing—both refer to the -3dB point where the output power is reduced to half of the input power.

Why is the cutoff frequency called the -3dB point?

Because 20 log₁₀(0.707) = -3.01 dB, and 0.707 is the voltage ratio at the cutoff frequency. This is a standard logarithmic measure used in electronics.

Do RC and RL filters have the same cutoff frequency formula?

No. RC filters use fc = 1/(2πRC), while RL filters use fc = R/(2πL). However, both follow the same principle of defining the -3dB point.

Can I use this calculator for higher-order filters?

This calculator is designed for first-order filters. Higher-order filters have more complex transfer functions and may have multiple cutoff frequencies.

What happens above the cutoff frequency in a low pass filter?

Above the cutoff frequency, the signal is attenuated at approximately 20 dB per decade (or 6 dB per octave) for a first-order filter, depending on the filter order.

How do I choose between RC and RL filters?

For low frequencies (< 10 kHz), use RC filters—capacitors are smaller and cheaper. For high frequencies (> 1 MHz), RL filters are often more practical.

What is the phase shift at the cutoff frequency?

At the cutoff frequency, the phase shift is -45 degrees for both RC and RL first-order filters, regardless of filter type.

Can I design a filter without knowing the cutoff frequency?

Yes, but cutoff frequency is a fundamental parameter. Knowing it helps determine component values and ensure proper signal filtering and protection.

Cutoff Frequency Calculator