In a series RC low-pass filter, at low frequencies the output is approximately:

In a series RC low-pass filter, at low frequencies the output is approximately:

• A. The output magnitude is approximately equal to the input and phase shift is near 0 degrees
• B. The output magnitude is significantly attenuated and phase shift near -90 degrees
• C. The output magnitude is approximately equal to the input but with phase near -90 degrees
• D. The output magnitude is greater than the input with phase near 0 degrees

Answer: (A)

In a series RC low-pass filter, the capacitor’s impedance sets how much of the input gets to the output. At very low frequencies, the capacitor presents a large impedance, so almost no current flows through the resistor. With little current, the voltage drop across the resistor is tiny, leaving nearly the entire input voltage appearing across the capacitor. That makes the output magnitude essentially equal to the input. The math behind this is a transfer function H(jω) = Zc/(R + Zc) = 1/(1 + jωRC); as ω → 0, H → 1 and the angle of H tends to 0°, so the output is in phase with the input. So the output magnitude is approximately the input and the phase shift is near 0 degrees.

In a series RC low-pass filter, the capacitor’s impedance sets how much of the input gets to the output. At very low frequencies, the capacitor presents a large impedance, so almost no current flows through the resistor. With little current, the voltage drop across the resistor is tiny, leaving nearly the entire input voltage appearing across the capacitor. That makes the output magnitude essentially equal to the input. The math behind this is a transfer function H(jω) = Zc/(R + Zc) = 1/(1 + jωRC); as ω → 0, H → 1 and the angle of H tends to 0°, so the output is in phase with the input. So the output magnitude is approximately the input and the phase shift is near 0 degrees.