1. Initial capture settings
The optimum settings is to find a balance between large enough sample intervals to achieve high resolution per individual frequency sample, max. 10% of the Frequency deviation.
And small enough Sample intervals to capture enough frequency samples per modulation cycle for good graph visibility.
A rule of thumb is that the number of samples per modulation cycle should be >10, for good graphical view of the modulation signal, and acceptable error of fmax and fmin
Example: 10 kHz modulation frequency (100 us modulation cycle) of a 200 MHz carrier with 200 kHz deviation (0.1% modulation).
Set Sample interval to 10 μs (10% of the modulation cycle). Set Sample Count (N) to 100 (to cover 10 modulation cycles).
Now every frequency sample will have a resolution of (10 ps/10 μs) x 200 MHz = 200 Hz.
This resolution is 1000 times better than the frequency deviation.
Start measurement and view the Timeline graph, which will show10 modulation cycles, with 10 samples per modulation cycle.
To improve the graphical experience, lower Sample Interval to 1 μs (1% of the modulation cycle), and increase Sample Count to 1000.
Now each frequency sample has a resolution of (10ps/1μs) x 200 MHz = 2 kHz. Still with a lot of margin to deviation.
You may want to play around with the Sample Interval and Sample Count setting until you have found your optimum view of the FM signal (no of displayed mod. cycles).
2. Carrier Wave Frequency f0
To determine the carrier wave frequency, just look at fmean which is best approximation of f0.
Ideally the sum of all Sample Intervals should be selected to cover an integer number of modulation periods. This way the positive frequency deviations will compensate the negative deviations during the measurement.
Example: If the modulation frequency is 1 kHz, the Sample Interval 10 μs and N = 1000 will make the Analyzer measure exactly 10 complete modulation cycles. A bad combination of Sample Interval and N would worst case mean that exactly half a modulation cycle is uncompensated for, giving a max. error for a sine modulation of:
f0 – fmean = Δfmax / (sample int.) x N x fmod x π
For very accurate measurements of the carrier wave frequency f0, make an extra measurement session and set Sample Interval as close as possible to an integer number of modulation cycles, and increase the number of samples substantially. A worst case error of half a modulation cycle means far less in a million cycles compared to 10 cycles.
3. Frequency deviation fmax - f0
Read the max, min, and mean frequency values from statistics screen or beneath the graph and calculate fdev as either:
- fmax – fmean
- fmean – fmin
- fp-p/2
These three values should be exactly the same for an ideal sine wave or square wave modulation.
4. Modulation frequency fmod
The modulation frequency is easiest found by visual estimate in the graph on screen by using Cursors. Place one cursor on the beginning of the first modulation cycle and the other – on the end of the last modulation cycle. If the end point time difference between cursors is T seconds and the exact integer number of modulation cycles between cursors is M, the modulation frequency is:
fmod = M/T
5. Errors in fmax, fmin, and fp-p
A too large Sample Interval compared to the modulation cycle time leads to an averaging error that will underestimate the true deviation. A Sample interval corresponding to 10% of the modulation cycle, or 36° of the modulation signal, leads to an error of approx. 1.5%.
If that error is not acceptable, decrease the Sample Interval to make more samples than 10 during the modulation cycle.