The 566 is a VCO, that puts out a square wave and a triangle wave, and sure
won't go up to 10.7MHz.
The 565 is an analog PLL, but it's rated for about 500KHz, and will never
make it up to 10.7MHz.
ANd of course, nobody has asked the obvious question, what's the deviation
of this signal? Because it becomes harder to recover a useable signal
when the ratio of signal frequency to deviation gets large. Which is
why it's fine to use 10.7MHz for an FM broadcast band receiver IF, because
the deviation is relatively high, but for narrow deviation a lot of receivers
will bump it down to a lower IF to lower that ratio. A 5KHz deviation
signal at 10.7MHz will cause very little fluctuation in most FM demodulators
while the same signal down at 455KHz will cause a lot of fluctuation.
It's such a common practice that a lot of FM demodulators, of any kind,
intended for narrow deviation use include an oscillator and mixer to
drop the 10.7MHz signal down to 455KHz.
And of course we haven't seen any reasoning on why this has to be a PLL.
Is there a real reason for choosing it, or is the poster simpling grasping
at something without being aware of all that is possible?
For that matter, what's the reasoning for 10.7MHz IF?
If it's a narrow deviation signal, and assuming this isn't going in a
mass production item (after all, someone doing that likely has a better
background than is indicated by such a vague question) one might as
well grab an old cordless telephone at a garage sale or rummage sale,
and extract the IF strip from that. Most of those I've take apart use
one of those older Motorola IF strip ICs that includes that mixer
to drop down to 455KHz, and the phone comes complete with the crystal
to drop from 10.7MHz to 455Khz, and the needed filters.
There are lots of solutions, but the original poster hasn't really described
the problem, so the solutions can't really be offered.
You are correct or more correct than my first note. I have used the 565 to
detect fm at 100khz-200khz ( see national ap note AN146. The 88 to 108mhz to
10.7 is next door at ap note AN147 it uses the Waller 32SN2F1-30.