Electronics
RC Low Pass and High Pass Filter: Cutoff Frequency, Design and Calculator
An RC filter uses a resistor and a capacitor to pass certain frequencies while blocking others. The low pass filter passes low frequencies. The high pass filter does the opposite.
Low Pass Filter
High Pass Filter
Cutoff Frequency
RC Circuit
3 dB Point
RC filters are the simplest frequency-selective circuits in electronics. They require only two components yet appear in almost every electronic system from audio equalisation to power supply noise suppression.
Hello everyone, today we are going to learn about the RC low pass filter and high pass filter.
We will understand how a resistor and a capacitor work together to create a frequency-selective circuit. We will cover the cutoff frequency formula and how to calculate it for any combination of R and C values.
We will also learn what the 3 dB point means, how the phase angle changes with frequency, and the difference between the low pass and high pass configurations.
Two worked examples are included, plus a live calculator so you can design your own RC filter for any application.
We will understand how a resistor and a capacitor work together to create a frequency-selective circuit. We will cover the cutoff frequency formula and how to calculate it for any combination of R and C values.
We will also learn what the 3 dB point means, how the phase angle changes with frequency, and the difference between the low pass and high pass configurations.
Two worked examples are included, plus a live calculator so you can design your own RC filter for any application.
RC Low Pass and High Pass Filter: How Each Circuit Works
RC Low Pass Filter
The resistor is in series; the capacitor is to ground. At low frequencies it passes the signal. At high frequencies it pulls the output toward ground. Output is taken across the capacitor.
RC High Pass Filter
The capacitor is in series; the resistor is to ground. At high frequencies the signal passes through. At low frequencies the capacitor blocks the signal. Output is taken across the resistor.
Cutoff Frequency Formula for RC Low Pass and High Pass Filter
The cutoff frequency is the same formula for both the low pass and high pass RC filter. It depends only on the resistor value and the capacitor value:
fc = 1 / (2 x pi x R x C)
fc = cutoff frequency in Hz | R = resistance in Ohms | C = capacitance in Farads | pi = 3.14159
At the cutoff frequency, the output voltage drops to 0.707 times the input voltage. This is the 3 dB point.
The low pass filter passes the signal below this frequency. The high pass filter behaves in the opposite direction.
The phase angle changes with frequency. For a low pass filter, the output lags the input by up to 90 degrees. At the cutoff frequency, the phase lag is exactly 45 degrees.
For a high pass filter, the output leads the input by up to 90 degrees, with a 45-degree lead at the cutoff frequency.
Rearranging to Find R or C
When designing a filter for a specific cutoff frequency, you can rearrange the formula to find the required R or C value:
R = 1 / (2 x pi x fc x C)
Use when capacitor value is already chosen. Solve for the required resistor value.
C = 1 / (2 x pi x fc x R)
Use when resistor value is already chosen. Solve for the required capacitor value.
Frequency Response: What Happens at Each Frequency Range
Frequency vs fc
LPF output
HPF output
What is happening in the circuit
Much below fc
Full signal
Blocked
Capacitor acts as open circuit. LPF: signal passes to output. HPF: signal cannot cross the series capacitor.
At 0.1 x fc
99.5%
10%
LPF passes almost all signal. HPF passes only 10% of input amplitude. Decade below cutoff.
At fc (3 dB point)
70.7%
70.7%
Both filters output 70.7% of input voltage. Xc = R. Phase shift is 45 degrees. Half the input power is passed.
At 10 x fc
10%
99.5%
LPF passes only 10% of input. HPF passes almost all signal. Decade above cutoff.
Much above fc
Blocked
Full signal
Capacitor acts as short circuit. LPF: output pulled to ground. HPF: signal passes through series capacitor to output.
RC Filter Cutoff Frequency Calculator
RC Low Pass and High Pass Filter Calculator
Enter any two values to calculate the third, plus gain and phase at any frequency
Cutoff frequency fc--
Capacitive reactance Xc at test frequency--
Output voltage ratio (Vout / Vin)--
Gain in dB--
Phase shift at test frequency--
Filter region--
Two Worked Examples for RC Filter Design
Example 1: Low Pass Filter 1 kHz cutoff, audio noise suppression
Requirement:
Design a low pass filter with fc = 1000 Hz to remove high-frequency noise from an audio signal.
Choose a standard capacitor value: C = 10 nF (0.01 microfarad)
Step 1: Calculate required R
R = 1 / (2 x pi x fc x C)
R = 1 / (2 x 3.14159 x 1000 x 10 x 10^-9)
R = 1 / (62.83 x 10^-6) = 15,915 Ohms
Use nearest standard value: 15 kOhm or 16 kOhm
Step 2: Verify cutoff with 15 kOhm
fc = 1 / (2 x 3.14159 x 15000 x 10 x 10^-9)
fc = 1 / 942.5 x 10^-6 = 1061 Hz (close enough)
Step 3: Gain and phase at 5 kHz (5x cutoff)
Xc = 1 / (2 x pi x 5000 x 10 x 10^-9) = 3183 Ohms
Gain = Xc / sqrt(R^2 + Xc^2) = 3183 / sqrt(15000^2 + 3183^2)
Gain = 3183 / 15334 = 0.208 (20.8% of input, minus 13.6 dB)
Design a low pass filter with fc = 1000 Hz to remove high-frequency noise from an audio signal.
Choose a standard capacitor value: C = 10 nF (0.01 microfarad)
Step 1: Calculate required R
R = 1 / (2 x pi x fc x C)
R = 1 / (2 x 3.14159 x 1000 x 10 x 10^-9)
R = 1 / (62.83 x 10^-6) = 15,915 Ohms
Use nearest standard value: 15 kOhm or 16 kOhm
Step 2: Verify cutoff with 15 kOhm
fc = 1 / (2 x 3.14159 x 15000 x 10 x 10^-9)
fc = 1 / 942.5 x 10^-6 = 1061 Hz (close enough)
Step 3: Gain and phase at 5 kHz (5x cutoff)
Xc = 1 / (2 x pi x 5000 x 10 x 10^-9) = 3183 Ohms
Gain = Xc / sqrt(R^2 + Xc^2) = 3183 / sqrt(15000^2 + 3183^2)
Gain = 3183 / 15334 = 0.208 (20.8% of input, minus 13.6 dB)
Example 2: High Pass Filter 100 Hz cutoff, DC blocking for sensor input
Requirement:
Design a high pass filter with fc = 100 Hz to block DC offset from a sensor signal.
Choose a standard resistor: R = 10 kOhm
Step 1: Calculate required C
C = 1 / (2 x pi x fc x R)
C = 1 / (2 x 3.14159 x 100 x 10000)
C = 1 / (6,283,185 x 10^-6) = 159 nF
Use nearest standard value: 150 nF or 180 nF
Step 2: Verify cutoff with 150 nF
fc = 1 / (2 x 3.14159 x 10000 x 150 x 10^-9)
fc = 1 / 9.42 x 10^-3 = 106 Hz (close enough)
Step 3: Gain at 20 Hz (below cutoff)
Xc = 1 / (2 x pi x 20 x 150 x 10^-9) = 53,052 Ohms
Gain = R / sqrt(R^2 + Xc^2) = 10000 / sqrt(10000^2 + 53052^2)
Gain = 10000 / 54,034 = 0.185 (18.5% of DC component blocked by 81.5%)
Design a high pass filter with fc = 100 Hz to block DC offset from a sensor signal.
Choose a standard resistor: R = 10 kOhm
Step 1: Calculate required C
C = 1 / (2 x pi x fc x R)
C = 1 / (2 x 3.14159 x 100 x 10000)
C = 1 / (6,283,185 x 10^-6) = 159 nF
Use nearest standard value: 150 nF or 180 nF
Step 2: Verify cutoff with 150 nF
fc = 1 / (2 x 3.14159 x 10000 x 150 x 10^-9)
fc = 1 / 9.42 x 10^-3 = 106 Hz (close enough)
Step 3: Gain at 20 Hz (below cutoff)
Xc = 1 / (2 x pi x 20 x 150 x 10^-9) = 53,052 Ohms
Gain = R / sqrt(R^2 + Xc^2) = 10000 / sqrt(10000^2 + 53052^2)
Gain = 10000 / 54,034 = 0.185 (18.5% of DC component blocked by 81.5%)
RC Low Pass vs High Pass Filter: Full Comparison
| Parameter | Low Pass Filter | High Pass Filter |
|---|---|---|
| Component order | R in series, C to ground | C in series, R to ground |
| Output taken across | Capacitor | Resistor |
| Passes | Low frequencies (f below fc) | High frequencies (f above fc) |
| Blocks | High frequencies (f above fc) | Low frequencies (f below fc) and DC |
| Phase at fc | 45 degree lag | 45 degree lead |
| Gain at fc | 0.707 of input (minus 3 dB) | 0.707 of input (minus 3 dB) |
| Cutoff frequency | fc = 1 / (2 x pi x R x C) | fc = 1 / (2 x pi x R x C) |
| Typical applications | Noise removal, anti-aliasing before ADC, audio treble cut | DC blocking, audio bass cut, AC coupling between stages |
Tip: For sharp frequency selectivity, cascade multiple RC stages or use an active filter.
A single RC stage rolls off at 20 dB per decade (6 dB per octave) beyond the cutoff frequency. This is called a first-order filter. Cascading two identical RC stages gives a second-order response at 40 dB per decade but also shifts the effective cutoff frequency. For sharper filtering in instrumentation and audio applications, use an active filter built around an op-amp, which provides steeper roll-off without the loading and frequency shift problems of cascaded passive stages.
A single RC stage rolls off at 20 dB per decade (6 dB per octave) beyond the cutoff frequency. This is called a first-order filter. Cascading two identical RC stages gives a second-order response at 40 dB per decade but also shifts the effective cutoff frequency. For sharper filtering in instrumentation and audio applications, use an active filter built around an op-amp, which provides steeper roll-off without the loading and frequency shift problems of cascaded passive stages.
Watch: RC Filter Cutoff Frequency Explained
RC Filter Questions Engineers and Students Ask
What is the cutoff frequency of an RC filter?
The cutoff frequency is the 3 dB point where output drops to 70.7% of input. It is calculated as fc = 1 / (2 x pi x R x C).
What is the difference between a low pass and high pass RC filter?
In a low pass filter, the resistor is in series and the capacitor is to ground. In a high pass filter, the capacitor is in series and the resistor is to ground.
What is the 3 dB point in an RC filter?
The 3 dB point is where the output power is half the input power. The output voltage is 0.707 times the input. It is also called the cutoff frequency or half-power frequency.
What is the roll-off rate of an RC filter?
A single RC stage rolls off at 20 dB per decade beyond the cutoff frequency. This is a first-order response. For steeper roll-off, cascade multiple stages or use an active filter.
Can an RC filter remove DC from a signal?
A high pass RC filter blocks DC and very low frequencies, called AC coupling. Choosing a low cutoff frequency such as 1 Hz allows all signal frequencies through while blocking DC offset.
Related Articles on This Site
- Capacitor Types Explained
- Impedance and Reactance in AC Circuits
- Phase Angle in AC Circuits
- How Decoupling Capacitors Work
- Capacitor Working Principle
External References
- RC Low Pass Filter Tutorial | Electronics Tutorials
- RC High Pass Filter Tutorial | Electronics Tutorials
What We Learn Today
- The cutoff frequency formula is fc = 1 / (2 x pi x R x C) and is the same for both the RC low pass filter and the RC high pass filter. At fc, the output voltage is 70.7% of the input (the 3 dB point) and the phase shift is exactly 45 degrees. The component order determines which filter type results: R series and C to ground gives a low pass filter. C series and R to ground gives a high pass filter.
- The frequency response rolls off at 20 dB per decade beyond the cutoff frequency for a single RC stage. One decade below the cutoff, the high pass filter passes only 10% of the input. One decade above the cutoff, the low pass filter passes only 10% of the input.
- To design an RC filter for a specific cutoff frequency, choose a standard capacitor value then calculate R = 1 / (2 x pi x fc x C), or choose a standard resistor value then calculate C = 1 / (2 x pi x fc x R). Use the nearest standard component value and verify the resulting cutoff frequency matches the requirement.
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