RC low pass filter
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.
|
\(\displaystyle C\) = 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
\(\displaystyle U_R=R ·I \)
Time constant
\(\displaystyle τ=C ·R \)
Capacitor functions
Series connection with capacitorsSeries 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
|
|