Step-down chopper (buck chopper) average output voltage A step-down (buck) chopper is fed from a DC source of magnitude V. If the switch on-time and off-time per cycle are Ton and Toff respectively, identify what V * (Ton / (Ton + Toff)) represents.

Introduction / Context:DC–DC step-down (buck) choppers reduce the average output voltage by switching a DC source on and off with duty ratio control. Understanding the relationship between duty ratio and average output is fundamental for power electronics design and control.

Given Data / Assumptions:

• Input DC voltage = V (constant).
• Switch on-time = Ton; off-time = Toff; switching period T = Ton + Toff.
• Ideal switch and diode; continuous conduction assumed for the average relation.

Concept / Approach:

The average of a periodic waveform equals the area under one period divided by the period. The chopper applies V to the load during Ton and 0 V during Toff (ignoring the inductor freewheel path for the idealized average calculation), hence the average equals V multiplied by the duty ratio D = Ton/T. This relation is independent of the specific R, L, or E in the load for the average value, provided steady-state averaging is valid.

Step-by-Step Solution:

Verification / Alternative check:

Inductor volt-second balance in continuous conduction also yields V_out = D * V for a buck converter.

Why Other Options Are Wrong:

(b) RMS requires squaring and is not simply V * D. (c) The expression is the average regardless of load type under standard buck operation. (d) Not applicable since it clearly represents the average.

Common Pitfalls:

Confusing average with RMS; forgetting that ripple filters do not change the average relation V_out = D * V.

Final Answer:

Average output voltage