RC integrator topology: In a standard RC integrator circuit, across which component is the output voltage taken?

Introduction / Context:
Identifying where to measure the output in canonical RC networks is fundamental. For an integrator, the capacitor voltage represents the time integral of the input (scaled by RC), so the output is taken across the capacitor.

Given Data / Assumptions:

• Classic passive RC integrator: series resistor R, capacitor C to ground.
• Small-signal, linear operation; frequency content where integration is a good approximation.
• No active elements (e.g., op-amps) in this basic form.

Concept / Approach:
The impedance of a capacitor is Xc = 1/(2 * pi * f * C). At higher frequencies, the capacitor impedance is small, causing most of the input to appear across R (output small). At lower frequencies (within integrator operation range), the capacitor voltage follows the integral of the input's slope changes, hence observed across C.

Step-by-Step Reasoning:
Integrator connection: Vin → R → node → C → ground.Vout is at the node between R and C, i.e., across the capacitor.This configuration shapes fast edges into smaller, smoothed responses consistent with integration.

Verification / Alternative check:
Small-signal transfer function: Vout/Vin = 1 / (1 + j * 2 * pi * f * R * C). For frequencies where |j * 2 * pi * f * R * C| ≫ 1, Vout ≈ (1 / (j * 2 * pi * f * R * C)) * Vin, which is proportional to 1/f and represents integration behavior.

Why Other Options Are Wrong:

• Resistor: That would be a differentiator's output node in the simple RC form.
• Diode or source: Not part of the standard passive RC integrator output definition.

Common Pitfalls:
Confusing integrator and differentiator topologies; remember: integrator → output across C, differentiator → output across R.

Final Answer:
capacitor