Tracking (servo) ADC behavior at a steady input: “When the analog input to a tracking A/D converter is constant, the digital output will oscillate around the true code.” Evaluate this behavior.

Introduction / Context:Tracking (a.k.a. servo or up/down) ADCs adjust their output code one LSB at a time to follow the input. Understanding their steady-state behavior clarifies why they are simple but relatively slow to acquire large step changes and why they show code toggling even for constant inputs near decision thresholds.

Given Data / Assumptions:

• Tracking ADC that increments/decrements a DAC until Vdac matches Vin within 1 LSB.
• Constant, noise-free Vin (practically, small noise exists).
• Ideal quantizer with finite resolution.

Concept / Approach:In a tracking ADC, a comparator evaluates (Vin − Vdac). If positive, the logic increments the code; if negative, it decrements. With a constant Vin not exactly at a quantization center, the loop hunts between the nearest two adjacent codes. Even with a centered value, thermal/comparator noise usually produces occasional toggling (limit-cycle behavior). Hence, the digital output “oscillates” by ±1 LSB around the best representation.

Step-by-Step Solution:

Verification / Alternative check:Loop analysis reveals a limit cycle when the error cannot be reduced below 0.5 LSB. Simulations or bench tests show a square-wave-like flipping between two codes for DC inputs near thresholds.

Why Other Options Are Wrong:

• Incorrect: Would imply perfect static holding, which contradicts the algorithm.
• Only true with noisy references: Noise amplifies the effect but is not required for the basic limit cycle.
• Ambiguous: Resolution does not eliminate ±1 LSB hunting; it sets the step size.

Common Pitfalls:Expecting rock-solid constant codes from tracking ADCs; overlooking the need for output averaging or hysteresis to stabilize readouts.

Final Answer:Correct