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

[hardwarefyi]

[jehe]

Output Voltage Equation:

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

Variables:

• V_out : Output voltage of the filter.
• V_in: Input voltage to the filter.
• R: Resistance
• C: Capacitance.
• ω: 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.