I once experimented with the 567 tone decoder which uses a PLL. It isn't the same as the 4046 but my observations might be of use.
I hoped I could use the 567 to reject off-frequencies. I hoped it would extract only the center frequency and turn it into clean DC pulses.
It didn't work that way. I got nothing resembling my original input signal.
The output only went high as long as it could detect the center frequency was dominant. The amplitude had to be at least .4V peak-to-peak.
I tried varying the input signal up and down a few cycles. The output became jittery.
It went high for a few cycles, then low for a few cycles. The cause was that the input was getting in and out of phase with the internal PLL.
When the difference got to be more than a few Hz, output went to zero continuously.
I found that what I needed was a narrow bandpass filter. I chose a bi-quad design, using 3 op amps. It worked well.
if I use the Comparator II, its center frequency depends on the R1 and C1, is there any formula to calculate the f0 using R1 and C1 exactly ?
You'll want to use a potentiometer to tune to the proper frequency. My data books show a 500k pot in the examples.
The formula is F = 1 / RC according to one book. Another has 1.1 / RC.