High-frequency period calculation: What is the period (time for one cycle) of a 16 MHz sine wave?

Introduction:
Converting between frequency and period is fundamental in signal processing, microcontroller timing, and communications. The period is the reciprocal of frequency: higher frequency means shorter period.

Given Data / Assumptions:

• Frequency f = 16 MHz = 16 * 10^6 Hz.
• Ideal single-tone sine wave.
• We need T in seconds (or nanoseconds).

Concept / Approach:

The relationship is T = 1 / f. After computing T in seconds, convert to nanoseconds by multiplying by 10^9. This quick conversion is widely used for clock signals in digital electronics.

Step-by-Step Solution:

Verification / Alternative check:

Check by multiplication: 16 * 10^6 Hz * 62.5 * 10^-9 s = 1.0 (dimensionless), confirming consistency. Also, 8 MHz would be 125 ns; doubling frequency halves period, aligning with 16 MHz → 62.5 ns.

Why Other Options Are Wrong:

• 196 ns / 31.25 ns / 19.9 ns / 6.25 ns: Do not equal 1 / 16 MHz; some correspond to other frequencies (e.g., 32 MHz → 31.25 ns).

Common Pitfalls:

• Misplacing decimal points during unit conversion between microseconds and nanoseconds.
• Confusing MHz (10^6) with kHz (10^3) or GHz (10^9).

Final Answer:

62.5 ns