Phase-locked loop (PLL) fundamentals: For a PLL to initially acquire lock with an input signal, the signal frequency must satisfy which condition?

Introduction:
PLLs synchronize a voltage-controlled oscillator (VCO) to the phase and frequency of an input signal. Two important ranges govern behavior: capture range (for acquisition) and lock range (for tracking once locked). This question distinguishes those concepts and identifies the condition for initial lock acquisition.

Given Data / Assumptions:

• Standard analog PLL with phase detector, loop filter, and VCO.
• Input is a near-sinusoidal signal with slowly varying frequency.
• Loop filter is linear and stable with adequate phase margin.

Concept / Approach:
The capture range is the frequency span within which the loop can pull the VCO into phase lock starting from an unlocked condition. The lock range is typically wider and represents how far the VCO can track the input once locked. Therefore, initial acquisition requires the input frequency to lie within the capture range, not merely the lock range.

Step-by-Step Solution:

Verification / Alternative check:
Loop simulations show that starting outside capture range results in beats at the detector output with no net control voltage convergence; starting inside capture range yields control voltage settling to align VCO and input phases.

Why Other Options Are Wrong:

• Come within the lock range: Lock range applies after acquisition; not sufficient for initial capture.
• Be less/greater than the capture frequency: Capture is a range, not a single frequency inequality.

Common Pitfalls:
Using lock range as a proxy for capture; ignoring loop filter bandwidth and nonlinearity that make capture narrower than lock; forgetting frequency steps can momentarily break lock even within lock range if the step exceeds capture dynamics.

Final Answer:
Come within the capture range.