RC high pass filter
Calculator and formulas for calculating the parameters of an RC high pass filter
This function calculates the properties of a high-pass filter consisting of a resistor and a capacitor. The output voltage, attenuation and phase shift 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]
\(\displaystyle U_C\) = Voltage at the Capacity [V]
Formulas for the RC high pass
Calculate the voltage ratio
The output voltage U2 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 XC is known
\(\displaystyle U_2=U_1 ·\frac{R}{\sqrt{R^2 + X_C^2}}\)
\(\displaystyle X_C=\frac{1}{2 π · f ·C}\)
Attenuation in decibels
At the resonance frequency, the damping is 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
\(\displaystyle V_u=20·lg\left(\frac{ω · R · C} {\sqrt{1 + (ω · R · C)^2}}\right)\)
Phase shift
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.
\(\displaystyle φ=acos \left(\frac{U_2}{U_1} \right) = \left(\frac{U_a}{U_e} \right)\)
\(\displaystyle φ= arctan \left(\frac{1}{ω · R ·C}\right)\)
Cutoff frequency
At the cutof frequency fg bzw. ωg the value of the amplitude-frequency response (i.e. the magnitude of the transfer function) is 0.707, which corresponds to -3dB.
\(\displaystyle 0.707= \frac{1}{\sqrt{2}}\)
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
\(\displaystyle I=\frac{U}{Z} \)
Capacitor voltage
\(\displaystyle U_C=X_C ·I \)
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
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