Equipment designed to work with one frequency power will not necessarily work with another frequency.
- Transformers designed to work with 60Hz will have lower ratings when working at 50Hz (Important for power distribution and individual devices)
- The speed (RPM) of AC motors is tied directly to the power line frequency.
- AC Wall clocks wouldn't work :)
The combination of 50Hz and 60Hz would cause generators to fight eachother
- See the plot of both 50Hz and 60Hz superimposed from Wolfram
- The blue plot shows the difference. Where the function is large, the generators are fighting eachother (Big Boom!)
I will define jitter specifically as the cycle to cycle jitter, so the time variation from one cycle to the next compared to a perfect cycle period. This is a common jitter definition and will allow me to explain the relationship between that and phase noise.
Note that a cycle to cycle jitter measurement is a delay and subtract to a phase noise or equivalently a time measurement process. You compare the time in one edge to the time in the previous edge and subtract to get the cycle to cycle jitter. Also note that time is related to phase as follows:
$$T_e = \phi_e\frac{T_p}{2\pi}$$
Where
$$T_e = \text{time error in seconds} $$
$$\phi_e = \text{phase error in radians} $$
$$T_p = \text{cycle time of one clock period} $$
A delay and substract process is a first order highpass filter with a corner at 1/T where T is the length of the delay in seconds. You can intuitively see this if you consider the lower and higher frequency offsets for phase noise. The lowest frequency offsets represent phase fluctuations vs time that are moving very slowly, so slowly in fact that after our finite delay of one cycle, the fluctuation has not changed (therefore same error in the next cycle); when we subtract to measure the cycle to cycle jitter the error will be zero. Faster fluctuations however will be uncorrelated, and so in fact will double in rms value consistent with adding (or subtracting) equal and uncorrelated noise sources.
This is shown in the figure below, and this high pass filter is effectively what is applied to the phase noise power spectral density in the process of measuring cycle to cycle jitter. Thus if you take the single-sided phase noise power spectral density $S_{\phi}(f)$, apply this effective single pole filter (along with the +3 dB factor!) and then integrate the resulting power spectral density, you will get a resulting variance. The square root of this variance after converting to time error using the first formula I gave will equal your rms cycle to cycle jitter!
Mathematically everything I described would be as follows:
$$\tau_{rms}=\frac{T_p}{2\pi} \sqrt{2\int_{f_L}^{f_H} S_\phi(f)\left(\frac{1}{s+\frac{1}{T}} \right)^2 df} $$
Where in practical applciations $f_L$ is typically 2 decades less than the corner frequency set by 1/T and $f_H$ is the measurement bandwidth of the system.
Best Answer
That sort of generator uses DDS, or Direct Digital Synthesis
It keeps track of the phase of the required output in a register, and outputs the cosine of the phase.
To use nice round numbers, let's say you have a 10 MHz clock, and want to generate 1.000000 MHz. Each 100 ns clock cycle, your phase register gets incremented by 0.1 of a cycle. If you want to generate 1.000 000 001 MHz, then each clock you'd increment by 0.100 000 000 100 of a cycle.
Frequency resolution is cheap, you just give your phase register enough LSBs. In this case, mHz resolution with a 10 MHz clock, you'd need 10 digits if the sums were done in decimal, or as more likely at least 34 bits if they were done in binary. With binary arithmetic, sometimes the master clock will be a nice 'binary' frequency to get nice Hz resolution. With cheaper generators the designers often just throw another load of LSBs at the phase register, and have very fine resolution of a nasty binary Hz fraction, which is 'fine enough'. My low cost generator has μHz!
Only the top few MSBs, typically 10 to 16 depending on the quality (cost) of the output, get to drive the phase -> cosine converter. As a result, the phase at your output is never more accurate than a few parts per thousand. However, the output phase error is non-cumulative, and over time, the waveform will keep the correct average rate of change of phase (aka frequency) with respect to the clock, and to any other channels being generated by the same clock.
So the frequencies are precise, the phases approximately so. It's this approximation to phase that means that DDS outputs have phase noise spurious outputs. These cannot be seen on an oscilloscope, but will be visible on any modest spectrum analyser.