Value of loop gain for steady state oscillations

Question

I was reading on a book (High-Frequency Oscillator Design for Integrated Transceivers, J. van der Tang, Dieter Kasperkovitz, Arthur H.M. van Roermund) this paragraph about the start-up condition for an oscillator:

Let's consider for instance a common base Colpitts Oscillator (biasing network for the base is not shown):

Now, I may do a small signal analysis of this circuit at open loop, find the expression of the loop gain, and size the components in order to make its absolute value greater than one. But, which is the mechanism that will reduce it once the oscillator has started? Is it automatic? How can I size the components in order to make it exactly equal to 1?

Answer 1

Non linearities in the transistor will inevitable make the loop gain equal to 1 at some peak to peak amplitude and, the natural impact of this is that the amplitude is difficult to precisely predict (not normally a big deal). The second impact is that the sine wave output will be naturally flattened on one or both peaks and, again, this is often not regarded as a big problem.

So, in short, the sine wave amplitude builds (because loop gain is greater than 1) and, as clipping starts to impact the sine wave shape, loop gain falls to exactly unity.