Question E4B01:
Which of the following factors most affects the accuracy of a frequency counter?  

Choices:  
A: Input attenuator accuracy  
B: Time base accuracy  
C: Decade divider accuracy  
D: Temperature coefficient of the logic    

Correct Answer is  B: Time base accuracy  

To measure frequency, a counter counts cycles during a precisely timed gate. The timing for that gate comes from the counter’s time base (its reference oscillator).

1) Why “Time base accuracy” is correct
- The measured frequency is computed as:
  $$f_{meas} = \frac{N}{T_g}$$
  where $N$ is the number of input cycles counted in gate time $T_g$.
- Any fractional error in the time base directly appears in $T_g$, so the fractional frequency error is essentially the same as the time base error:
  $$\frac{\Delta f}{f} \approx \frac{\Delta T_g}{T_g} \equiv \epsilon_{time\ base}$$
- Therefore, the accuracy of the counter is dominated by the time base accuracy (e.g., OCXO/TCXO/GPSDO quality).

2) Why the other choices are incorrect
- Input attenuator accuracy: Affects signal amplitude, not the timing of edges being counted. As long as the signal triggers reliably, amplitude scaling doesn’t change the count.
- Decade divider accuracy: Digital dividers divide by exact integers. They do not introduce “accuracy” error; they only pass along the time base’s characteristics.
- Temperature coefficient of the logic: While temperature can affect propagation delay and max frequency, digital counting remains exact edge-by-edge. The dominant accuracy term is still the oscillator reference, not logic temperature drift.

3) Useful formulas and rules of thumb
- Fractional accuracy tracks the time base:
  $$\frac{\Delta f}{f} \approx \epsilon_{time\ base}$$
  For a time base of ±1 ppm: 
  $$\Delta f \approx f \times 1\times10^{-6}$$
  Example: at 100 MHz, ±1 ppm → ±100 Hz.
- Resolution (not accuracy) from gate time:
  $$\Delta f_{res} \approx \pm \frac{1}{T_g}$$
  With $T_g = 1\ \text{s}$, resolution is 1 Hz. Increasing $T_g$ improves resolution but not the fundamental accuracy set by the time base.
- Best practice: Use an external 10 MHz reference (OCXO/GPSDO) to improve counter accuracy.