Hi Tesla, I did not mean that your simplification was not correct.

My doubts were poited to the 50k Resistor and the definition of the loop gain.

Anylyzing the loop gain of your circuit gives, of course, the same result as given in one of my earlier posts:

LG=(1+R4/R3)*R6/(R5+R6)*R1/(R1+R2)=....=+1.713

Because we are speaking about the outer (overall) loop, I have opened the loop for injection of a test signal at the non-inv. terminal of the most left opamp. All local loops remain closed. This approach is in accordance with system theory for multi-loop systems.

Added (edit):

I will repeat that you modification (simplification) is correct - it is a clever idea!

And I also see your motivation to show what happens when we open also the local (negative) gain determining loop.

I know what you intend to show:

For defining the

However, in this case it is really a problem to compute the overall loop gain (as your formula shows).

This is a classical problem for all high-gain loops because this definition does not allow the commonly used simplification (infinite open-loop gain).

Therefore, it is a classical approach to keep all local loops closed (unfortunately, this is not always possible).

However, it is not necessary to find the exact loop gain value. For our purpose it is sufficient to verify the condition for stability: (k+)< (k-)

But in the present case (values as in the original question) we have k+=0.57 and k-=0.5

My doubts were poited to the 50k Resistor and the definition of the loop gain.

Anylyzing the loop gain of your circuit gives, of course, the same result as given in one of my earlier posts:

LG=(1+R4/R3)*R6/(R5+R6)*R1/(R1+R2)=....=+1.713

Because we are speaking about the outer (overall) loop, I have opened the loop for injection of a test signal at the non-inv. terminal of the most left opamp. All local loops remain closed. This approach is in accordance with system theory for multi-loop systems.

Added (edit):

I will repeat that you modification (simplification) is correct - it is a clever idea!

And I also see your motivation to show what happens when we open also the local (negative) gain determining loop.

I know what you intend to show:

For defining the

**feedback factor**this way, the faktor k is - as shown in your expression (post#38) - a sum of two factors with different sign (k+ and k-).However, in this case it is really a problem to compute the overall loop gain (as your formula shows).

This is a classical problem for all high-gain loops because this definition does not allow the commonly used simplification (infinite open-loop gain).

Therefore, it is a classical approach to keep all local loops closed (unfortunately, this is not always possible).

However, it is not necessary to find the exact loop gain value. For our purpose it is sufficient to verify the condition for stability: (k+)< (k-)

But in the present case (values as in the original question) we have k+=0.57 and k-=0.5

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