Differentiator in steady state — average output: During steady-state operation with a symmetrical pulse train input, is the average output voltage of an RC differentiator approximately zero volts?

Introduction / Context:
RC differentiators respond to changes, not steady levels. For periodic pulse inputs, the output consists of alternating spikes at each transition. Understanding the average (DC) component at the output is important for coupling considerations, measurement offsets, and avoiding unintended biasing of downstream stages.

Given Data / Assumptions:

• Standard RC differentiator with output across the resistor.
• Input is a repetitive pulse train without DC offset.
• Linear, time-invariant operation; steady state reached.

Concept / Approach:
A differentiator ideally has zero gain at DC. For a symmetrical pulse train that rises and falls to the same baseline, the positive spike at each rising edge and the negative spike at each falling edge have equal and opposite areas (charge transfer through the capacitor). Over a complete period, the time-average (integral over one cycle divided by the period) is therefore approximately zero, ignoring minor leakage and parasitic effects.

Step-by-Step Solution:

Verification / Alternative check:
On an oscilloscope with AC coupling disabled, the baseline of the differentiated waveform hovers near 0 V for symmetric pulses. Any small average offset typically points to leakage, unequal edges, or measurement bias, not to inherent DC generation by the ideal differentiator.

Why Other Options Are Wrong:

• Incorrect: Conflicts with the differentiator’s DC blocking property.
• Applies only if duty cycle is 50%: Even with other duty cycles, equal and opposite edge contributions can keep the average near zero as long as the waveform returns to the same baseline each cycle.
• Applies only if there is DC offset: A DC offset at the input would shift the baseline but a pure differentiator does not pass steady DC.

Common Pitfalls:
Assuming unequal spikes due to saturation or slew limits; using a non-symmetric waveform with different high/low levels, which can introduce a small average.

Final Answer:
Correct.