Differentiator function — DC output claim: “A differentiator circuit can convert a pulse input into a nearly constant DC output.” Assess the validity of this statement for a standard RC differentiator.

Introduction / Context:
An RC differentiator emphasizes rapid changes in the input signal and suppresses slowly varying components. Designers often use it to detect edges of pulses and to create narrow trigger spikes. The claim that such a circuit produces a nearly constant DC output from a pulse input reverses its intended function and needs to be evaluated critically.

Given Data / Assumptions:

• Simple RC differentiator: series capacitor followed by a resistor to ground with output taken across the resistor.
• Input: a rectangular pulse or a train of pulses.
• Small-signal, linear, time-invariant behavior; no active elements.

Concept / Approach:
Differentiation is mathematically v_out ∝ dv_in/dt. For a rectangular pulse, dv/dt is large at the rising and falling edges and nearly zero during the flat top. Consequently, the differentiator outputs a positive spike at the rising edge and a negative spike at the falling edge, with almost zero output between edges (apart from small exponential tails). There is no mechanism to produce a steady DC level from a constant input segment in a passive RC differentiator.

Step-by-Step Solution:

Verification / Alternative check:
Scope captures of an RC differentiator fed by a pulse train show symmetric positive/negative spikes bracketing each pulse, with the mean output near zero. This is standard edge-detection behavior used in timing and trigger circuits.

Why Other Options Are Wrong:

• Correct: Contradicts the fundamental purpose of a differentiator.
• Valid only with a very large capacitor / very low frequency: Changing RC alters spike width, not the fact that steady DC is rejected.

Common Pitfalls:
Confusing differentiators with integrators or low-pass filters that can produce average/DC components; overlooking that the differentiator’s transfer magnitude increases with frequency and tends to zero at DC.

Final Answer:
Incorrect.