RC low pass filter

Calculator and formulas for calculating the parameters of an RC low pass

RC low pass online calculator


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.


RC low pass calculator

 Input
Resistor
Capacitor
Frequency
Input voltage
Decimal places
 Result
Reactance XC
Output voltage U2
Attenuation dB
Phase shift φ
Cutoff frequency
Impedance Z
Voltage UR
Current I



\(\displaystyle C\) = 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]

Formulas for the RC low pass filter

Calculate the voltage ratio

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

\(\displaystyle U_2=U_1 ·\frac{X_C}{\sqrt{R^2 + X_C^2}}\)
\(\displaystyle X_C=\frac{1}{2 π · f ·C}\)

Attenuation in decibels

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

\(\displaystyle V_u=20·lg\left(\frac{1} {\sqrt{1 + (ω · R · C)^2}}\right)\)

Phase shift

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.


\(\displaystyle φ=acos \left(\frac{U_2}{U_1} \right))\)
\(\displaystyle φ= arctan (ω · R ·C)\)

Cutoff frequency

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.

\(\displaystyle 0.707= \frac{1}{\sqrt{2}}\)

Cutoff frequency formulas

\(\displaystyle ω_g= \frac{1}{R ·C} ⇒\)
\(\displaystyle f_g=\frac{1}{2·π·R·C}\)

\(\displaystyle R=\frac{1}{2·π·f_g·C}\)
\(\displaystyle C=\frac{1}{2·π·f_g·R}\)


Impedance

\(\displaystyle Z=\sqrt{X_C^2 + R^2} \)

Current

\(\displaystyle I=\frac{U}{Z} \)

Restistor voltage

\(\displaystyle U_R=R ·I \)


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