If a pure sine-wave signal is applied to the input of an ideal voltage comparator (with no hysteresis), what general waveform shape appears at the comparator’s output?

Introduction:
A comparator is a decision-making device: it compares an input voltage to a reference and switches its output to one of two saturation levels depending on the sign of the difference. This question checks whether you recognize that “thresholding” a sine produces a two-level output (a rectangular/square wave).

Given Data / Assumptions:

• Ideal comparator, very high gain, rail-to-rail saturation.
• Reference at 0 V (or any fixed V_ref); input is a clean sine wave that crosses the reference each cycle.
• No hysteresis unless stated; edges are idealized.

Concept / Approach:
Whenever the input exceeds the reference, the output saturates “high”; when the input falls below the reference, it saturates “low.” As a result, the output toggles between two constant levels, forming a rectangular waveform whose duty cycle depends on the reference level and input symmetry.

Step-by-Step Solution:
Apply sine wave v_in(t) to the comparator with threshold V_ref.For v_in > V_ref, output → +V_sat; for v_in < V_ref, output → −V_sat.Crossings occur twice per cycle; the output is high for the portion of the cycle above the threshold and low otherwise.Thus, the waveform is rectangular (often called square if 50% duty cycle).

Verification / Alternative check:
Oscilloscope tests in lab confirm that thresholding a sine produces fast transitions to fixed levels. Adding hysteresis (Schmitt trigger) improves noise immunity but retains the rectangular nature.

Why Other Options Are Wrong:

• Ramp/sawtooth/triangle: Produced by integrators or ramp generators, not by simple thresholding.
• Sine wave: That is the input, not the comparator’s two-level output.

Common Pitfalls:

• Expecting a “perfect square”; real comparators have finite slew and propagation delay.
• Ignoring the effect of V_ref offset, which skews duty cycle away from 50%.

Final Answer:
rectangular wave