Average output of an RC differentiator with repetitive pulses: What is the average (DC) value of the output waveform?

Introduction / Context:RC differentiators are used to emphasize rapid changes (edges) in input signals. When driven by repetitive pulses, the output consists of positive and negative spikes around transitions, with little average value over one period.

Given Data / Assumptions:

• RC differentiator configuration.
• Input is a repetitive pulse train (periodic).
• Capacitor charges and discharges around transitions; steady segments yield near-zero output.

Concept / Approach:A differentiator's output approximates the time-derivative of the input. Over each complete period of a periodic waveform, the average of its derivative is zero, since the waveform returns to the same value every cycle.

Step-by-Step Reasoning:Let v_out ≈ RC * d(v_in)/dtAverage over one period T: (1/T) * ∫_0^T d(v_in)/dt dt = (1/T) * (v_in(T) - v_in(0))For periodic input, v_in(T) = v_in(0) ⇒ average derivative = 0Hence the average output ≈ 0 V

Verification / Alternative check:On an oscilloscope, you typically see equal-area positive and negative spikes at rising and falling edges. Their net area per period is zero, confirming zero average.

Why Other Options Are Wrong:

• Equal to the input or 63% of input: These refer to steady values in charging systems, not a differentiator's average.
• Cannot be determined: It can—by periodicity and calculus.

Common Pitfalls:Confusing differentiators with integrators, or assuming a DC offset from asymmetrical pulses (standard symmetric pulses give zero average in ideal differentiators).

Final Answer:is zero