Calculate R and C for impedance

With this function, the resistor and the capacitor of an RC series circuit (High pass / low pass) can be calculated with a given impedance and cutoff frequency.

Formulas for calculating R and C

At the cutoff frequency, the reactance of the capacitor is identical to the ohmic resistance.

\(\displaystyle Z^2 = R^2 + X_C^2 \)

can be switched to

\(\displaystyle Z^2 = 2 · R^2 \) oder \(\displaystyle Z = \sqrt{2} · R\)

Calculate resistor : \(\displaystyle R=\frac{Z}{\sqrt{2}} \)

Calculate capacitor : \(\displaystyle C=\frac{1}{2·π·f·X_C} ⇒\)   „ \(\displaystyle \frac{1}{2·π·f·R}\)