Calculator and formulas for calculating the parameters of an RC high pass filter
This function calculates the properties of a highpass filter consisting of a resistor and a capacitor. The output voltage, attenuation and phase shift are calculated for the given frequency.

\(\displaystyle C\) = Capacity [F]
\(\displaystyle R\) = Resistance [Ω]
\(\displaystyle U_1\) = Input voltage [V]
\(\displaystyle U_2\) = Output voltage [V]
\(\displaystyle X_C\) = Capacitive reactance [Ω]
\(\displaystyle φ\) = Phase angle [°]
\(\displaystyle Z\) = Input impedance [Ω]
\(\displaystyle I\) = Current [A]
\(\displaystyle U_C\) = Voltage at the Capacity [V]
The output voltage U_{2} of an RC high pass is calculated according to the following formula.
\(\displaystyle U_2=U_1 ·\frac{2 · π · f · R · C} {\sqrt{1 + (2 · π · f · R · C)^2}}\)
or easier if X_{C} is known
\(\displaystyle U_2=U_1 ·\frac{R}{\sqrt{R^2 + X_C^2}}\)
\(\displaystyle X_C=\frac{1}{2 π · f ·C}\)
At the resonance frequency, the damping is 3dB. The damping can be calculated for the different frequencies using the formulas below. If the input and output voltage are known, the attenuation can easily be calculated using the following formula.
\(\displaystyle V_u=20 · lg \left(\frac{U_2}{U_1} \right) \)
If the voltages are not known, the following formula is used.
\(\displaystyle V_u=20·lg\left(\frac{2 · π · f · R · C} {\sqrt{1 + (2 · π · f · R · C)^2}}\right)\)
or simply shown
\(\displaystyle V_u=20·lg\left(\frac{ω · R · C} {\sqrt{1 + (ω · R · C)^2}}\right)\)
In an RC high pass, the output voltage leads the input voltage by 0 °  90 °, depending on the frequency. At the resonance frequency, the phase shift is 45 °. At high frequencies it tends to 0. At low frequencies the phase shift in the direction of + 90 °. The phase shift can be calculated using the following formula.
\(\displaystyle φ=acos \left(\frac{U_2}{U_1} \right) = \left(\frac{U_a}{U_e} \right)\)
\(\displaystyle φ= arctan \left(\frac{1}{ω · R ·C}\right)\)
At the cutof frequency f_{g} bzw. ω_{g} the value of the amplitudefrequency response (i.e. the magnitude of the transfer function) is 0.707, which corresponds to 3dB.
\(\displaystyle 0.707= \frac{1}{\sqrt{2}}\)
