Stability Circles, S22 = 1 ?

[hakim-djz]

Hi all,

I'm just doing a problem on stability circles for oscillators, and have got S22 = 1.
Well to be honest, the value is like 1.0001576518877

But how would you interpret the stability circle if S22 = 1?

i.e. would the stable region be inside the circle or outside?

 

[BigBoss]

How you could obtain S22=1 in an oscillator ?? It's not defined at all.
Elaborate it a bit more..

 

[hakim-djz]

How you could obtain S22=1 in an oscillator ?? It's not defined at all.
Elaborate it a bit more..

Hi BigBoss,

Right, well the topic I'm covering in my course is oscillators, but this is three-port networks and trying to switch the reference terminal and adding feedback to increase instability. I've attached the question that I'm trying to solve, my schematic and data display.

I've added a inductive feedback of 398 nH, then my |S22| after doing the transformation is 1, which I couldn't
figure out how to explain. Now I did all the calculations in MATHCAD, where the value is 1.0001576518877 using 13 decimal places! Showing that S22 is greater than 1, which would indicate that everything outside the circle is unstable, whereas there's more instability on the output without the feedback. So I'm just confused how to interpret the stability circle on the output, i.e. take it greater than 1 or less than 1, unless there's a definition out there for a magnitude of 1.
As another example question in my notes indicates that there should be increased instability after adding the feedback, but in this case S22 it doesn't?

 

[BigBoss]

Hi BigBoss,

Right, well the topic I'm covering in my course is oscillators, but this is three-port networks and trying to switch the reference terminal and adding feedback to increase instability. I've attached the question that I'm trying to solve, my schematic and data display.

I've added a inductive feedback of 398 nH, then my |S22| after doing the transformation is 1, which I couldn't
figure out how to explain. Now I did all the calculations in MATHCAD, where the value is 1.0001576518877 using 13 decimal places! Showing that S22 is greater than 1, which would indicate that everything outside the circle is unstable, whereas there's more instability on the output without the feedback. So I'm just confused how to interpret the stability circle on the output, i.e. take it greater than 1 or less than 1, unless there's a definition out there for a magnitude of 1.
As another example question in my notes indicates that there should be increased instability after adding the feedback, but in this case S22 it doesn't?

The circles are in the Smith Chart so everything ( every impedance combination) in these circles makes that circuit stable.Outside of the circles is unstable region and every possible impedance combination ( simultaneously) outside of these circles will make the circuit unstable.I cannot see any difficulty..