Measure the open loop gain of an Oscillator

[Pictou]

Hello,
I tried to search how to do it on the forum but every open-loop gain calculation I found were related to amplifier only.

So here is my question, I designed an oscillator (pierce oscillator with quartz) with CMOS transistor. I would like to measure the open-loop gain and phase at the set frequency. My circuit is an amplifier inverter loaded by a quartz with 2 capacitors.
My question is how should I measure the open-loop gain?

For now I used two methods :
1st method :
Opening the loop at the gate of the amplifier, add the same amplifier at the end of the quartz so it can see the same load and measure the gain at the output of the crystal. Used a HB analysis.

2nd method :
Used a stb analysis (middlebrook), however I'm doubtful about that technique as it is used to know if the circuit is stable or not (and I'm using an oscillator which is unstable).


With the 2 methods I have 2 different results on the gain, I don't know which one to believe.

Thank you.

 

[gmont]

if I remember well, middlebrook is a small signal analysis. while the first method you use is large signal. make sure you have a low level signal in HB simulation in order to avoid compression of your "amplifier" .

 

[Pictou]

Thank you, I will try again.

 

[FvM]

I assume the new post is related to your previous thread https://www.edaboard.com/threads/283490/

Curiously you didn't manage till today to post a schematic of your actual design...

Loop gain is usually understood as a small signal quantity, in case of an oscillator we want to determine if the oscillation condition is fulfilled and if the excess gain is low enough to allow stable operation. The amplifier must be biased correctly for loop gain analysis. This is often achieved by an ideal DC feedback over the open loop.

Another straightforward method, that has been often discussed at edaboard inserts a series AC voltage source at an arbitrary place of the loop and measures the achieved vout/vin transfer function. The prerequisite for this method is that the signal flow is mostly unidirectional at this node. If the condition isn't met, e.g. because amplifier S12 is in a similar range as S21, no loop gain can be determined unequivocally.