Frequency counters: sampling interval vs. measurement quality How does the sampling (gate) interval of a frequency counter affect the displayed result?

Introduction / Context:
Digital frequency counters count the number of input cycles within a fixed gate time (sampling interval). The choice of this interval affects resolution, precision, and update rate of the displayed frequency.

Given Data / Assumptions:

• Counter measures cycles within a sampling window Tgate.
• Displayed frequency f_meas ≈ N / Tgate, where N is counted cycles.
• Timebase is accurate and stable.

Concept / Approach:
For a given input frequency, increasing Tgate allows more cycles to be counted, reducing the relative quantization error (±1 count). The fractional resolution improves approximately as 1 / N, so longer gate times give finer precision, albeit with slower updates.

Step-by-Step Solution:

Verification / Alternative check:
Observe the stability of the last digits: with a 1 s gate, a 10 MHz signal yields N ≈ 10,000,000; with 0.1 s, N ≈ 1,000,000, so the least significant digits vary more.

Why Other Options Are Wrong:

• Directly/Inversely with sampling interval: These do not specify what aspect; the key relationship is precision improving with longer gate time.
• Less precision with longer interval: Opposite of true behavior.

Common Pitfalls:
Confusing precision with accuracy; accuracy depends on the timebase oscillator, while precision (resolution) depends on gate time.

Final Answer:
More precision with longer sampling interval