Calculate RC High Pass Filter

Calculator and formulas for calculating the parameters of an RC high pass filter

Calculate RC High Pass

RC High Pass Filter

This function calculates the properties of a high pass filter made from a resistor and capacitor. The output voltage, attenuation and phase shift are calculated for the given frequency.

Results
Reactance XC:
Output voltage U₂:
Attenuation [dB]:
Phase angle φ:
Cutoff frequency f₀:
Impedance Z:
Voltage UC:
Current I:
Time constant τ:

RC High Pass Circuit

RC High Pass Circuit
Symbol Explanations
C = Capacitance [F]
R = Resistance [Ω]
U₁ = Input voltage [V]
U₂ = Output voltage [V]
XC = Capacitive reactance [Ω]
φ = Phase angle [°]
Z = Input impedance [Ω]
I = Current [A]
UC = Voltage across capacitor [V]
High Pass Characteristics
  • Passes high frequencies
  • Attenuates low frequencies
  • -3dB at cutoff frequency
  • +20dB/decade rise
  • Phase shift 0° to +90°
Cutoff Frequency
\[f_c = \frac{1}{2\pi RC}\]

At the cutoff frequency, the attenuation is -3dB.

RC High Pass - Theory and Formulas

RC High Pass Fundamentals

An RC high pass filter is a first-order filter that passes high frequencies and attenuates low frequencies. The output is taken across the resistor. At low frequencies, the capacitor has high resistance, at high frequencies it has low resistance.

Important Formulas

Voltage Ratio
\[U_2 = U_1 \cdot \frac{2\pi fRC}{\sqrt{1 + (2\pi fRC)^2}}\]

or simpler with XC:

\[U_2 = U_1 \cdot \frac{R}{\sqrt{R^2 + X_C^2}}\]
Reactance
\[X_C = \frac{1}{2\pi fC}\]

The capacitive reactance decreases with increasing frequency.

Attenuation and Phase

Attenuation in dB
\[A = 20 \cdot \log_{10}\left(\frac{U_2}{U_1}\right)\]

or directly:

\[A = 20 \cdot \log_{10}\left(\frac{\omega RC}{\sqrt{1 + (\omega RC)^2}}\right)\]
Phase Shift
\[\phi = \arccos\left(\frac{U_2}{U_1}\right)\]

or:

\[\phi = \arctan\left(\frac{1}{\omega RC}\right)\]

Cutoff Frequency and Characteristic Values

Cutoff Frequency
\[f_c = \frac{1}{2\pi RC}\]

At fc: Attenuation = -3dB, Phase = 45°

Impedance
\[Z = \sqrt{X_C^2 + R^2}\]

Total impedance of the circuit

Time Constant
\[\tau = RC\]

Characteristic time of the circuit

Frequency Response

Frequency Response Characteristics
  • Low frequencies (f ≪ fc): Strong attenuation, Phase → +90°
  • Cutoff frequency (f = fc): -3dB attenuation, Phase = +45°
  • High frequencies (f ≫ fc): No attenuation, Phase → 0°
  • Roll-off rate: +20dB/decade above fc
  • Transfer function: H(jω) = jωRC/(1 + jωRC)

Practical Applications

AC Coupling:
• Amplifier coupling
• DC blocking
• Audio inputs
• Signal transmission
High Frequency Filters:
• RF amplifiers
• Communication systems
• Noise filters
• Anti-hum filters
Differentiators:
• Edge detectors
• Pulse generators
• Trigger circuits
• Time derivatives

Design Guidelines

Important Design Aspects
  • Cutoff frequency selection: Should be well below the lowest frequency to be transmitted
  • Capacitance choice: Larger C → lower fc, but larger components
  • Resistance choice: Trade-off between input impedance and signal level
  • Loading effects: Following stage should be high impedance
  • Tolerances: Component variations affect cutoff frequency

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Capacitor functions

Series connection with capacitors  •  Series connection with 2 capacitors  •  Reactance Xc of a capacitor  •  Time constant of an R/C circuit  •  Capacitor charging voltage  •  Capacitor discharge voltage  •  R/C for the charging voltage  •  Series circuit R/C  •  Parallel circuit R/C  •  Low pass-filter R/C  •  High pass-filter R/C  •  Integrator R/C  •  Differentiator R/C  •  Cutoff-frequency R,C  •  R and C for a given impedance  •