RC differentiator topology: In a basic RC differentiating circuit, the output is taken across the resistor (R), producing a high-pass, edge-emphasizing response. True or false?

Introduction / Context:
RC networks can approximate time differentiation when the time constant is chosen properly relative to the input wave shape. Correct node selection determines whether the circuit differentiates or integrates.

Given Data / Assumptions:

• Series RC circuit driven by a source.
• Output measured across the resistor.
• Assume τ = R*C is small compared with the significant time scales of the input pulse width.

Concept / Approach:

Taking the output across R yields H(jω) = jωRC / (1 + jωRC), a first-order high-pass response. In the time domain, for τ much smaller than the input waveform period, Vout ≈ τ * dVin/dt, which emphasizes rapid changes (edges) and suppresses slow variations (DC).

Step-by-Step Solution:

Verification / Alternative check:

Apply a step input. The output is a narrow positive spike on the rising edge and a negative spike on the falling edge, characteristic of differentiation. Scope traces confirm high-pass behavior and edge emphasis.

Why Other Options Are Wrong:

• Answering “False” would imply the resistor node does not provide differentiation; however, moving the output to the capacitor node produces the opposite (integration/low-pass).

Common Pitfalls:

Using too large τ so that the circuit no longer approximates d/dt; forgetting that real differentiators amplify noise and may require limiting networks to maintain stability.

Final Answer:

True