Active High-Pass Filter Calculator
This Active High-Pass Filter Calculator estimates the ideal cutoff frequency, time constant, passband gain, and cutoff-point magnitude for a first-order RC high-pass network followed by an op-amp stage.
Use it for first-pass AC coupling, DC blocking, audio signal conditioning, sensor interfaces, and active buffer or non-inverting gain designs where the ideal first-order model is appropriate.
Engineering tool
Active High-Pass Filter Calculator
Calculate first-order active high-pass filter cutoff frequency, time constant, passband gain, and magnitude at the -3 dB point.
RC high-pass filter resistor used to set cutoff frequency.
RC high-pass filter capacitor used to set cutoff frequency.
Cutoff frequency (fc)
1.591549 kHz
High-pass roll-off below fc: +20 dB/decade, about +6 dB/octave
Result console
- Cutoff frequency (fc)
- 1.591549kHz
- Passband gain
- 1V/V
- Passband gain
- 0dB
- Time constant (τ)
- 100µs
- Magnitude at cutoff
- 0.707107V/V
- Relative cutoff level
- -3.0103dB
- Filter resistor R
- 10kΩ
- Filter capacitor C
- 10nF
Result is valid for the ideal first-order active high-pass filter model.
Formula reference
Active High-Pass Filter Formula
The ideal first-order active high-pass filter model uses an RC cutoff network and an optional non-inverting op-amp gain stage.
fc = 1 / (2 × π × R × C)τ = R × CUnity-gain buffer mode: Av = 1Non-inverting gain mode: Av = 1 + (Rf / Rg)Gain(dB) = 20 × log10(Av)Magnitude at fc = Av / √2Variable definitions
- fc
- Ideal -3 dB cutoff frequency
- R
- Filter resistor
- C
- Filter capacitor
- τ
- Time constant
- Av
- High-frequency passband gain
- Rf
- Feedback resistor in non-inverting gain mode
- Rg
- Ground resistor in non-inverting gain mode
Variable Description
- Filter resistor R
- The resistor in the RC high-pass network. Increasing R lowers cutoff frequency.
- Filter capacitor C
- The capacitor in the RC high-pass network. Increasing C lowers cutoff frequency.
- Cutoff frequency fc
- The ideal -3 dB frequency where output magnitude is Av divided by √2.
- Time constant τ
- The RC product. It describes the first-order transition between attenuation and passband behavior.
- Passband gain Av
- The high-frequency op-amp gain. It is 1 in buffer mode or 1 + Rf/Rg in gain mode.
- Magnitude at cutoff
- The expected output magnitude at fc relative to the input, equal to passband gain divided by √2.
Worked Examples
Example 1: Unity-Gain Active High-Pass Filter
- Mode
- Unity-Gain Buffer
- R
- 10 kΩ
- C
- 10 nF
fc = 1 / (2 × π × R × C); τ = R × C
fc = 1 / (2 × π × 10,000 × 10 × 10^-9) ≈ 1.5915 kHz; τ = 100 µs
Passband Gain = 1 V/V, Gain = 0 dB, Magnitude at fc ≈ 0.707 V/V
Signals well below the cutoff are attenuated, while higher-frequency signals approach unity gain.
Example 2: Non-Inverting Active High-Pass Filter
- Mode
- Non-Inverting Gain
- R
- 4.7 kΩ
- C
- 100 nF
- Rf
- 10 kΩ
- Rg
- 10 kΩ
fc = 1 / (2 × π × R × C); Av = 1 + Rf/Rg
fc ≈ 338.63 Hz; τ = 470 µs; Av = 1 + 10 kΩ / 10 kΩ = 2 V/V
Gain ≈ 6.02 dB, Magnitude at fc ≈ 1.414 V/V
The op-amp gain raises the high-frequency passband magnitude, while the RC values set the ideal first-order cutoff.
First-order active high-pass filter
This V1 calculator models only a first-order RC high-pass network with an op-amp buffer or non-inverting gain stage.
Cutoff frequency
The cutoff frequency is the ideal -3 dB transition point between low-frequency attenuation and high-frequency passband behavior.
-3 dB point
At fc, magnitude is Av/√2, which is about -3.01 dB relative to the passband gain.
Passband gain
Unity mode uses Av = 1. Non-inverting mode uses Av = 1 + Rf/Rg.
Time constant
The time constant τ equals R × C and is tied to the high-pass transition frequency.
Roll-off rate
Below the cutoff region, a first-order high-pass filter changes at about 20 dB/decade or 6 dB/octave.
DC blocking
High-pass filters are often used to block DC offsets while passing AC signal content.
AC coupling
The RC network can couple changing signals between stages while rejecting slow baseline shifts.
Sensor interface
High-pass filtering can remove drift or low-frequency offsets, but it may also remove useful slow sensor information.
Audio applications
First-order high-pass filters are common for rumble reduction, coupling networks, and simple crossover estimates.
Gain-bandwidth product limitation
The ideal RC formula does not include op-amp gain-bandwidth product. Verify the op-amp frequency response with the selected passband gain.
Slew rate limitation
Large high-frequency output signals may be limited by op-amp slew rate even if the RC calculation is correct.
Common Mistakes
Mixing up high-pass and low-pass behavior
The same cutoff equation appears in both first-order filters, but the frequency response is opposite.
Assuming no output exists below cutoff
A first-order high-pass filter attenuates low frequencies progressively rather than eliminating them abruptly.
Confusing µF and nF
A 100 nF capacitor is 0.1 µF. Unit mistakes can move cutoff frequency by orders of magnitude.
Forgetting unit conversion
Convert kΩ, nF, µF, and pF consistently before checking manual calculations.
Ignoring op-amp bandwidth
The op-amp must support the selected passband gain and frequency range.
Ignoring tolerance effects
Resistor and capacitor tolerance shift the actual cutoff frequency in production hardware.
Support reference
FAQ
What is an active high-pass filter?
An active high-pass filter combines an RC high-pass network with an op-amp stage. It attenuates low frequencies and passes higher frequencies with the selected passband gain.
How is cutoff frequency calculated?
For the first-order model used here, cutoff frequency is fc = 1 / (2 × π × R × C), where R is the filter resistor and C is the filter capacitor.
What happens below the cutoff frequency?
Signals below fc are progressively attenuated. A first-order high-pass filter does not completely remove all lower-frequency content.
What is the difference between active and passive high-pass filters?
A passive RC high-pass filter uses only passive components. An active high-pass filter adds an op-amp stage for buffering, gain, and impedance isolation.
How does gain affect the circuit?
In this first-order model, the RC network sets cutoff frequency while the non-inverting op-amp stage sets the high-frequency passband gain.
Can this calculator be used for audio crossover design?
It can estimate a first-order high-pass corner frequency, but complete audio crossover design may require driver impedance, acoustic response, higher-order slopes, and component tolerance analysis.
What is the roll-off rate of a first-order high-pass filter?
A first-order high-pass filter rises toward the passband at about 20 dB per decade, or about 6 dB per octave, below the cutoff region.
Why must op-amp bandwidth be checked?
The op-amp must support the desired passband gain and frequency range. Real designs should check gain-bandwidth product, slew rate, output swing, and datasheet limits.
Related Engineering Guides
Dedicated active filter guides are planned for this topic cluster. These guide topics are reserved for future publication and are shown without links until the pages exist.
Planned Engineering Guide
Active High-Pass Filter Basics
Planned guide covering active high-pass filter operation, AC coupling, passband gain, and impedance isolation.
Planned Engineering Guide
Understanding Cutoff Frequency
Planned guide explaining -3 dB cutoff, magnitude ratio, roll-off, and practical measurement interpretation.
Planned Engineering Guide
AC Coupling Design
Planned guide covering DC blocking, bias paths, input impedance, startup transients, and signal-chain coupling.
Planned Engineering Guide
Choosing RC Values for High-Pass Filters
Planned guide covering resistor and capacitor selection, tolerance, leakage, dielectric behavior, and noise.
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Engineering Disclaimer
This calculator uses an ideal first-order active high-pass filter model for estimation and education. It does not model real op-amp gain-bandwidth product, slew rate, input bias current, output swing, input offset voltage, noise, layout parasitics, startup transients, source impedance, load impedance, or component tolerance. Real designs should verify the op-amp frequency response and datasheet limits before hardware release.