Part of Analogue and filter calculators
AC Coupling Capacitor Calculator
Size a coupling capacitor from cutoff frequency and the effective resistance seen by the capacitor.
Inputs
Select which value to calculate from the first-order RC cutoff relationship.
Results
RC high-pass filtering attenuates frequencies below cutoff. For AC coupling, use the effective resistance seen by the capacitor, including bias and input resistances.
Use an AC coupling capacitor to block DC while passing the wanted signal band
An AC coupling capacitor forms a first-order high-pass network with the resistance around the receiving input. The design task is not just choosing a capacitor: it is choosing a cutoff frequency, identifying the effective resistance, and checking settling, leakage, bias, and signal swing.
Amplifier inputs
Pass the wanted AC signal into a biased op-amp or comparator input while blocking DC offset.
Sensor and audio paths
Set the low-frequency corner low enough to preserve wanted content without excessive settling time.
DC offset removal
Remove upstream DC bias before a stage with its own defined common-mode or bias point.
Equations and model
The calculator uses the same first-order high-pass cutoff equation, but this page frames it around AC-coupling design decisions.
Coupling cutoff
The first-order high-pass corner formed by the coupling capacitor and effective resistance.
Capacitor value
Use a target low-frequency corner and effective resistance to choose capacitance.
Settling time scale
The same network also determines startup settling and recovery after large signal steps.
fc - Low-frequency cutoff
Unit: hertz (Hz)
The frequency where the ideal coupled amplitude is about -3 dB from the passband.
R - Effective resistance
Unit: ohms (Ω)
The resistance seen by the capacitor, including bias resistors, input resistance, and relevant source or termination resistance.
C - Coupling capacitor
Unit: farads (F)
The series capacitor that blocks DC while passing the wanted AC signal band.
τ - Settling time constant
Unit: seconds (s)
The recovery time scale after startup, bias movement, or large transients.
Worked example
This example is covered by the shared analogue calculation test suite.
Design question: An AC-coupled signal feeds a 100 kΩ biased input. Choose a capacitor for a 16 Hz low-frequency corner.
Inputs: R = 100 kΩ, fc = 16 Hz.
Capacitance: C = 1 / (2π × 16 Hz × 100 kΩ) = 99.5 nF.
Practical first choice: 100 nF gives a cutoff very close to 16 Hz with the assumed 100 kΩ effective resistance.
Time constant: τ = R × C ≈ 9.95 ms, so startup and recovery behaviour should also be checked.
Finding the effective resistance
Most AC-coupling mistakes come from using the wrong resistance in the cutoff equation.
Receiving side
- Input resistance may be explicit or hidden inside a device model.
- Bias resistors often appear in parallel from the capacitor viewpoint.
- Terminations can dominate the effective resistance.
Source side
- Source impedance can contribute depending on topology.
- DC bias conditions on both sides affect startup transients.
- Large coupling capacitors may create inrush or pop/click behaviour.
Assumptions and limitations
First-order approximation
The model assumes one dominant coupling capacitor and one effective resistance. More complex bias networks may need circuit simulation.
Capacitor details matter
Tolerance, leakage, voltage coefficient, dielectric absorption, polarity, and distortion can matter depending on signal level and application.
Bias and headroom are separate
The cutoff calculation does not confirm input common-mode range, clipping margin, or amplifier bias stability.
Related calculators and next checks
Follow the next check based on whether the concern is frequency response, settling, amplifier bias, or related first-order filters.
RC high-pass filter calculator
Use for the general first-order high-pass version of the same equation.
RC time constant calculator
Check startup settling, recovery time, or charge/discharge behaviour.
Op-amp gain calculator
Use when the coupling capacitor feeds an amplifier input or bias network.
RC low-pass filter calculator
Use for the complementary first-order low-pass case.
Analogue and filter hub
Follow related RC, filter, coupling, and analogue workflows.
FAQ
What resistance should I use for an AC coupling capacitor?
Use the effective resistance seen by the capacitor. This may include input resistance, bias resistors, termination, and source resistance depending on the circuit topology.
Is bigger capacitance always better?
Not always. A larger capacitor lowers the cutoff, but can increase size, leakage, cost, startup settling time, inrush stress, and distortion if the dielectric is poorly chosen.
Why does startup settling matter?
The coupling capacitor must charge to the bias point after power-up or after a large transient. The RC time constant can create recovery delays or audible/measurement pops if it is too long.
Engineering reference
Equations, assumptions, and design guidance
Solves the ideal first-order RC high-pass cutoff relationship.
Equations and variables
fc = 1 / (2 * pi * R * C)tau = R * C- fc
- Cutoff frequency (Hz)
- R
- Resistance (ohm)
- C
- Capacitance (F)
Assumptions and limitations
Assumptions
- The source and load impedances do not shift the effective resistance.
- The capacitor is ideal across the frequency range of interest.
Limitations
- Component tolerance, capacitor ESR/ESL, op-amp input impedance, and source/load interaction are not included in this nominal solve.
Worked example and design use
1 kOhm and 100 nF filter
Inputs: R = 1 kOhm, C = 100 nF
Outputs: fc is about 1.59 kHz, tau = 100 us
Design guidance
- For AC coupling, use the effective resistance seen by the capacitor, including bias and input resistances.
- Check R and C tolerances when cutoff placement is critical.