Periodic Steady State analysis for class C amplifier
In high Q oscillators, it is very difficult to change the amount of energy which is involved in the oscillation.

Take a simple low-Q RLC oscillator like this one:



In this type of circuit the Q of the LC tank (mainly L1 and C1) is not very high. Something like a Q of 100 should be achievable at RF frequencies. On a chip or for very high frequencies Q might be much lower like Q = 10.

Having a low-Q tank means that if there was no active circuit to keep the oscillation going, the oscillation would die out after only a few cycles (of the oscillation frequency). The task of the active circuit is to pump energy into the tank to keep the oscillation going.

You can easily simulate such circuits, also in a PSS simulation, because the oscillator is quick to respond (within a few cycles) to any changes.

Not let's look at a high-Q oscillator like this Crystal oscillator:



As the tank it uses a Crystal which can be modeled as a high-Q RLC tank like this:



A crystal behaves as a very low-loss (and therefore high-Q) RLC tank. This is modeled by having a model with a very small C1 (a few femto Farad) and a very large L1 (a few milli Henry). It is not uncommon for Crystals to have a Q factor in the order of 100000 (100k). Compare that to a factor Q = 100 which is already quite good for a circuit only using capacitors and inductors.

This makes for a very high Q tank and the result of this is that it takes many cycles for changes to take place regarding the signals in the tank. It is like the energy is "trapped" inside the tank (the energy alternates between C1 and L1) and only small portions of energy can be added or removed from the tank in each cycle.

The result is that it is very impractical to simulate very high-Q oscillators using a PSS simulation or even a transient simulation. Many cycles need to be simulated to simulate for example the startup behavior. For a 25 MHz crystal oscillator I worked on, the startup time was measured to be around 10 ms so that means that you would need to simulate more than 250000 (250k) cycles to simulate this.

What I do as a workaround is make a lower-Q version model of the Crystal with for a example a Q of 1000. Then I do my time simulations (transient or PSS) using this model. I can still use the high-Q model in an AC analysis to determine loopgain and frequency response though.