Stopping condition in a counter-ramp ADC: A counter-ramp ADC halts counting at the exact moment when which equality condition is satisfied?

Introduction / Context:
Understanding the stop condition in a counter-ramp ADC is essential to relate the final digital count to the measured analog input. This architecture converts time (the number of clock pulses counted) into amplitude by comparing a generated staircase to the unknown input.

Given Data / Assumptions:

• ADC uses a binary counter, a DAC, and a comparator.
• On each clock pulse, the counter increments, raising the DAC output one LSB.
• Comparator monitors V_in versus V_DAC (staircase).
• Control logic stops the count when the reference meets the input.

Concept / Approach:
As the DAC output climbs in steps, the comparator output flips when V_DAC reaches (or slightly exceeds, per design) V_in. That transition triggers the logic to stop the counter. The captured count is the digital representation of the input and is proportional to the time it took to reach equality.

Step-by-Step Solution:

Verification / Alternative check:
A timing diagram shows comparator output high until the step reaches V_in, then toggling low (or vice versa), coincident with the stop signal. The stop is not tied to a magic 5 V threshold or to hitting the maximum count unless V_in equals full scale.

Why Other Options Are Wrong:

• Counter reaches maximum count: Only true if V_in is full-scale; not the general stop condition.
• Input equals 5 V / DAC equals 5 V: Arbitrary voltage; depends on reference and scaling, not a fixed 5 V.

Common Pitfalls:
Assuming a constant conversion time regardless of V_in; forgetting that conversion time varies with input magnitude in a counter-ramp ADC.

Final Answer:
the input voltage equals the DAC staircase voltage