AC component (ripple) of a rectifier output – RMS value For a rectifier output with measured total RMS value Vrms and DC component Vdc, what is the RMS value of the AC (ripple) component alone?

Introduction / Context:
Rectifier outputs contain a DC component plus ripple (AC component). Quantifying ripple is essential for filter design and performance evaluation. RMS values add in a mean-square sense when components are orthogonal (DC vs AC).

Given Data / Assumptions:

• Total RMS of output voltage = Vrms.
• DC (average) component = Vdc.
• AC component is the residual after removing the DC level.

Concept / Approach:

Because the DC component is constant and the AC component has zero average, the mean of the square of the sum equals the sum of the means of the squares: Vrms^2 = Vdc^2 + (Vac_rms)^2. Therefore, Vac_rms = sqrt(Vrms^2 − Vdc^2).

Step-by-Step Solution:

Verification / Alternative check:

Check limiting cases: If ripple is zero, Vrms = Vdc → Vac_rms = 0. If Vdc = 0 (pure AC), Vac_rms = Vrms, as expected.

Why Other Options Are Wrong:

• Vrms includes DC; not just ripple.
• 0.5 Vrms is arbitrary and incorrect.
• √(Vrms − Vdc) is dimensionally wrong and not based on mean-square addition.

Common Pitfalls:

Subtracting RMS magnitudes directly instead of subtracting power (square) quantities; forgetting that RMS is a quadratic metric.

Final Answer:

(Vrms^2 - Vdc^2)^0.5