Ripple factor vs. form factor in rectifiers In rectifier circuits, the ripple factor RF and the form factor FF are related by which expression?
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ARF = (FF^2 − 1)^0.5
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BRF = FF
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CRF = FF − 1
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DRF = (FF − 1)^0.5
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E—
Answer
Correct Answer: RF = (FF^2 − 1)^0.5
Explanation
Introduction / Context:Ripple factor (RF) measures the AC ripple content relative to the DC component at a rectifier output, while form factor (FF) is the ratio of RMS value to average value of the output waveform. Their relationship is frequently tested in exams.
Given Data / Assumptions:
- V_rms denotes RMS value of output.
- V_dc denotes average (DC) value of output.
- AC component RMS is V_ac_rms where V_ac_rms^2 = V_rms^2 − V_dc^2.
Concept / Approach:
By definition, RF = V_ac_rms / V_dc and FF = V_rms / V_dc. Substituting V_ac_rms in terms of V_rms and V_dc yields a direct algebraic relation between RF and FF.
Step-by-Step Solution:
FF = V_rms / V_dc → V_rms = FF * V_dc.V_ac_rms^2 = V_rms^2 − V_dc^2 = (FF^2 − 1) * V_dc^2.RF = V_ac_rms / V_dc = sqrt(FF^2 − 1).Verification / Alternative check:
For pure DC (no ripple), FF = 1 and RF = 0, which satisfies RF = sqrt(1 − 1) = 0.
Why Other Options Are Wrong:
Other options contradict the squared relationship derived from RMS-DC decomposition.
Common Pitfalls:
Confusing average and RMS definitions or forgetting that the AC component is orthogonal to the DC component in power calculation.
Final Answer:
RF = (FF^2 − 1)^0.5