Topology swap thought experiment — starting with a classic RC integrator (series resistor feeding a capacitor to ground, output across the capacitor), if the positions of the components are swapped (series capacitor feeding a resistor to ground, output across the resistor), what does the new circuit implement?
-
ARL differentiator
-
BRC differentiator
-
CRL integrator
-
DRC integrator
-
EPure low-frequency attenuator only
Answer
Correct Answer: RC differentiator
Explanation
Introduction / Context:First-order RC networks can be arranged to emphasize integration (slow change) or differentiation (edge emphasis). An “RC integrator” typically has a series resistor and a shunt capacitor with the output taken across the capacitor. Swapping the positions of R and C and taking the output across the resistor yields the complementary high-pass behavior associated with an RC differentiator.
Given Data / Assumptions:
- Original circuit: series R, capacitor to ground, output across C.
- Modified circuit: series C, resistor to ground, output across R.
- High-impedance measurement so loading is negligible; small-signal linear behavior.
Concept / Approach:In the differentiator arrangement (series C, shunt R, output across R), the capacitor passes rapid changes (high-pass action) while the resistor converts the changing current to a voltage. The output magnitude is therefore proportional to the rate of change of the input within the useful bandwidth, producing edge spikes to steps/pulses. Conversely, the integrator (series R, shunt C, output across C) accumulates charge and emphasizes low-frequency content (low-pass action).
Step-by-Step Solution:
Identify original: low-pass RC with V_out at the capacitor → integrator behavior for τ ≫ signal width.Swap series/shunt positions: now a high-pass RC with V_out at the resistor.Recognize differentiator behavior: output highlights edges and fast changes.Conclude the new circuit is an RC differentiator.Verification / Alternative check:Frequency response: integrator has gain ∝ 1/ω at high frequencies (low-pass), while differentiator has gain ∝ ω at low frequencies (high-pass within limits). Swapping elements flips the response class.
Why Other Options Are Wrong:
- RL differentiator / RL integrator: incorrect component family.
- RC integrator: describes the original, not the swapped configuration.
- “Pure attenuator only”: while both topologies can attenuate, the key function here is differentiation.
Common Pitfalls:Confusing where the output is taken; with RC differentiator it must be across the resistor, not the capacitor.
Final Answer:RC differentiator.