About 10 years ago I bought Gardner's "Phaselock Techniques" (3rd edition). Expensive (>100 $), but worth every cent if you want to work with PLLs.
You can either follow his maths in the earlier chapters, or go to chapter 11, "Loop Filters".
I quote:
"Only a type 1 PLL can be realized with a passive filter,..."
He then goes on to explain that a more desirable PLL is type 2 (0 phase error), which needs a second-order loop response, hence the active filter.
He also writes about early misconceptions on how to analyze the PD output stage, which still plague the 4046 data sheets and application notes (they've never been revised).
Hope this helps. Cheers.