Series Resonance in Crystal

Question

I am trying to understand the sentence "to give the crystal maximum control of the loop gain...". Assuming by maximum control it is saying to maximize the feedback factor, which in series resonance case should be: $$\beta=\frac{R_{load}}{R_{load} + R_{source} + R_s},R_s=ISR$$

But if we want to maximize beta, we should increase the load resistance. For example, say ISR (Internal Series Resistance) is 10 ohms, if we assume load and series resistance to be 100 ohms each, then beta is 100/(100 + 100 + 10) = 0.476

But if we take load and source resistance to be 10 ohms each, then beta is 10 / (10 + 10 + 10) = 0.333

Clearly increasing the load resistance is going to increase my loop gain, but the statement is claiming the opposite. So what this sentence meant when it said to give the crystal maximum control of the loop gain I have to reduce the values of my source and load resistances.

Answer 1

Add 47pF capacitors from both ends of the Crystal to GND. You now have a PI filter. Make Rload 100Kohm, to have minimal effect on the crystal behavior. Make Rsource variable, from 10 ohms to 1Kohm.

Now perform analyses. Or run sims, with tiny time steps. And inject a single edge into bottom of the left-most 47pF cap, to kickstart the oscillation