Calculator and formulas for calculating the parameters of an RC low pass
This function calculates the properties of a low-pass filter consisting of a resistor and a capacitor. The output voltage, attenuation and phase rotation are calculated for the given frequency.
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\(\displaystyle C\) = 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]
\(\displaystyle U_R\) = Voltage at the restistor [V]
The output voltage U2 of an RC low pass is calculated according to the following formula.
\(\displaystyle U_2=U_1 ·\frac{1} {\sqrt{1 + (2 · π · f · R · C)^2}}\)
or easier if XC is known
\(\displaystyle U_2=U_1 ·\frac{X_C}{\sqrt{R^2 + X_C^2}}\)
\(\displaystyle X_C=\frac{1}{2 π · f ·C}\)
At the resonance frequency, the damping is 3 dB. If the input and output voltage are known, the attenuation for all frequencies 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.
\(\displaystyle V_u=20·lg\left(\frac{1} {\sqrt{1 + (2 · π · f · R · C)^2}}\right)\)
or simply shown
\(\displaystyle V_u=20·lg\left(\frac{1} {\sqrt{1 + (ω · R · C)^2}}\right)\)
In an RC low pass, the output voltage lags the input voltage by 0 ° - 90 °, depending on the frequency. At the resonance frequency, the phase shift is -45 °. At low frequencies, it tends to 0. At high frequencies, the phase shift in the direction of -90 °. The phase shift can be calculated using the following formula.
\(\displaystyle φ=acos \left(\frac{U_2}{U_1} \right))\)
\(\displaystyle φ= arctan (ω · R ·C)\)
At the limit frequency fg bzw. ωg the value of the amplitude-frequency response (ie the magnitude of the transfer function) is 0.707. This corresponds to -3 dB.
\(\displaystyle 0.707= \frac{1}{\sqrt{2}}\)
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