What is the value of the output voltage in a passive low pass RC filter?

Output Voltage Equation:

V_{out} = V_{in} \left(\frac{1}{1 + j\omega RC}\right)


  • V_out : Output voltage of the filter.
  • V_in: Input voltage to the filter.
  • R: Resistance
  • C: Capacitance.
  • Ī‰: Angular frequency of the input signal (𝜔 = 2𝜋𝑓, where 𝑓 is the frequency in hertz).
  • j: Imaginary unit
j = \sqrt{-1}

Frequency Response:

  • At low frequencies

    H(\omega) \approx 1 \implies V_{out} \approx V_{in}

    The output voltage is approximately equal to the input voltage, meaning low frequencies pass through with little attenuation.

  • At high frequencies

    H(\omega) \approx \frac{1}{j\omega RC} \implies V_{out} \approx \frac{V_{in}}{j\omega RC}

    The output voltage decreases, meaning high frequencies are attenuated.

This filter is widely used in electronics for signal conditioning, noise reduction, and smoothing signals.

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