RL low pass filter

Calculator and formulas for calculating the parameters of an RL low pass filter

RL low pass filter calculator

This function calculates the properties of a low-pass filter consisting of a resistor and a coil. The output voltage, attenuation and phase shift are calculated for the given frequency.

RL low pass filter calculator

Input voltage
Decimal places
Reactance XL
Ouput voltage U2
Attenuation dB
Phase shift φ

\(\displaystyle L\) = Inductance [H]

\(\displaystyle R\) = Resistance [Ω]

\(\displaystyle U_1\) = Input voltage [V]

\(\displaystyle U_2\) = Output voltage [V]

\(\displaystyle X_L\) = Reactance [Ω]

\(\displaystyle f_g\) = Cutoff frequency [Hz]

\(\displaystyle φ\) = Phase angle [°]

Formulas for the RL low pass

Calculate the voltage ratio

The output voltage U2 of an RL low pass is calculated using the following formula.

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

or simply if XL is known

\(\displaystyle U_2=U_1 ·\frac{R}{\sqrt{R^2 + X_L^2}}\)
\(\displaystyle X_L=2 π · f ·L\)

Attenuation in decibels

At the resonance frequency, the damping is 3 dB. It can be calculated for the various 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.

\(\displaystyle V_u=20·lg\left(\frac{R} {\sqrt{R^2 + (2 · π · f · L)^2}}\right)\)

or simply shown

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

Phase shift

In an RL low pass, the output voltage lags behind the input voltage by 0 ° to -90 °, depending on the frequency. At the resonance frequency, the phase shift is -45 °. At low frequencies it tends towards 0. At high frequencies the phase rotates towards -90 °. The phase shift can be calculated using the following formula.

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

Cutoff frequency

At the cutoff frequency fg or ωg the value of the amplitude-frequency response (ie the magnitude of the transfer function) is 0.707, which corresponds to -3dB.

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

Cutoff frequency formulas

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

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