Also, the PLL diagram seems to show that you have a 1/f^2 loop: 1/f from the SR560 and 1/f from the Hz->rad conversion ??
Well, the diagram I drew is true. I also have been confused by this 1/f^2 issue in our PLL.
As Rana pointed out, the open-loop TF should become 1/f^2 over most of the frequency range, but it still remains 1/f above 5kHz for some reasons.
Need more investigations.
At the beginning I tried phase-locking the VCO to the beat note without any external filters (i.e. SR560 see here), but I never succeeded.
It was because the hold-in range of the PLL was not sufficiently wide, it could stay locked within frequency range of less than +/- 1MHz from the center frequency of 80 MHz.
This is obviously not good, because the beat note typically fluctuates by more than +/- 3MHz in time scale of 1 sec or so.
So I decided to put an external filter, SR560, in order to have a larger DC gain and a higher UGF.
Somehow I unconsciously tuned the SR560 to have a pole at 1Hz with the gain of 2000, which shouldn't work in principle because the open-loop will be 1/f^2.
However I found that the PLL became more robust, in fact it can track the input frequency range of +/- 5MHz.
The open-loop TF is shown above. For comparison I plotted also the open-loop TF wehn it's without the SR560.
I checked the frequency of the VCO output when it was phase-locked to a Marconi, it was healthy (i.e. the same frequency as the input signal from Marconi).