Differentiator output polarity — falling edge behavior: In a standard RC differentiator (output taken across the resistor), does the output go negative on the falling edge of a positive input pulse?

Introduction / Context:
Polarity of the spikes produced by differentiators matters when designing edge-triggered circuits and pulse shapers. A standard passive RC differentiator places a capacitor in series with the input and a resistor to ground, taking the output across the resistor. Understanding the sign of the output on rising and falling edges is essential for trigger polarity selection.

Given Data / Assumptions:

• Series capacitor, shunt resistor, output across the resistor.
• Input: a positive rectangular pulse returning to zero baseline.
• Ideal, linear behavior; no saturation.

Concept / Approach:
At a rising edge (positive step), current flows through the capacitor into the resistor, dropping voltage across the resistor that is positive at the top node, so the output shows a positive spike. At a falling edge (negative step), current reverses direction; the resistor voltage reverses its polarity, producing a negative spike. Between edges, current decays toward zero and the output returns toward zero as the capacitor charges/discharges.

Step-by-Step Solution:

Verification / Alternative check:
Oscilloscope traces of a differentiator driven by a pulse train show a positive spike at each rising edge and a corresponding negative spike at each falling edge, matching the sign convention presented here.

Why Other Options Are Wrong:

• Incorrect: Ignores the direction reversal of current at the falling edge.
• Conditional options: Duty cycle or exact R/Xc ratio shape spike width/amplitude but not the sign at an ideal instant.

Common Pitfalls:
Taking the output across the capacitor instead of the resistor (which changes interpretation); losing the sign convention on current direction at edges.

Final Answer:
Correct.