Flipped voltage follower analysis

[mirror_pole]

Hello guys,

im analysing the simple flipped voltage follower current mirror :
(Fig.3a on the third page)

I tried to analyse the closed loop transfer function by applying Rosenstark method and got confused. From the picture node x is the input and node y the output. If i chose Transistor M2 to be the independant source I get G,infinity=0 . Does this mean the "ideal" gain equals 0 in this case or did i missunderstand something? Is this maybe somehow connected to ideal properties of transimpedance amplifiers, since it is the case here?

If i chose M1 to be the independant source i get a G,infinity which is frequency dependant. From my professors script i read that in this case one cannot use the return ratio T(s) to make a statement concering step response and i would really like to know why. He says that G,infinity has to be a real number.

In this paper the loop gain is calculated by cutting this loop and applying a V,test at the gate of M2. This is actually the same thing if you calculate T(s) with Rosenstark by making M2 the independant source (and in this case G,infinity is 0, so a real number). So does this mean from this calculation i can make a statement concerning open loop poles and zeros on the basis of T(s)?

Im really confused about the use of rosenstark with multiple dependand sources because i dont know exactly what return ratio i can use. Maybe someone is experienced enough to help me here with my thoughts.

I would be really gratefull.


edit: thinking about it it maybe makes sense why G,infinity=0 . If i think about M2 as the feedback network here i can say that the current through M1 is the error term and idealy it has to be as low as possible. So in the ideal case the error current is zero which means that there is no voltage drop at the output and therefore G,infinity is zero. Does it makes sense?

 

[sutapanaki]

Here is a possible way of derivation. I first did it for a simple diode connected transistor, treated as a feedback circuit. Then it is very similar to that also for your circuit.

 

[mirror_pole]

Hey sutapanaki,

Thanks your your answer! Your calculation is right and it does make sense because if u asume large loop gain the closed loop gain is determined by the feedback factor which is 1/gm in this case. i did the same calculation some time ago but now im trying to solve it with all the capacitances.

The problem i have with this method where u cut the feedback loop and apply a test voltage is that i dont know the best "spot" to cut the feedback loop (carefull with loading effects etc)
Thats why i prefere Rosenstark method to calculate T(s) because you dont ask yourself this question in first place.
But if you compare Rosenstarks calculation for T and the method for cuttin the loop interestingly there is a similarity that the best "spot" to cut the loop is at the gate of a transistor.

My main problem is that if i do the calculation for T with Rosenstark by making the Source of M1 independant i get a different result if i do it the other way around (making Source of M2 independant). Solving the Y matrix with nodal analysis results in 2 different denominators and the question is which T is corrent. That means which T(s) should i consider to make an assumption about the open loop poles of the system?

Considering this paper https://ieeexplore.ieee.org/document/1487657 they calculate the loop gain by making the Source of M2 independant. Intuitively i would do the same but this is not an exact answer.