 #26
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OK, Electrician, time for me to eat crow.
You were right, the equations are the same. And what I wrote in post #17 was trash.
I forgot about a little thing called 'stability':
An op amp circuit consisting of resistors only will obey the 'golden rule' if and only if the net feedback factor is negative. Always providing the amp is 'fully compensated', not saturated by an excessively large input and the op amp gain is infinite (and the offset voltage and current are zero, blah blah ...).
The feedback factor, usually written as β, is the fraction of the op amp's output fed back to its input. β is a positive number if the feedback is negative.
You can have both positive and negative feedback in a circuit and the golden rule still applies, providing the net feedback is negative. I'm attaching a sketch as a simple example.
Your circuit in fact does have both positive (via the 84K resistor) and negative (via the 100K) feedback. I will compute β_{} and β_{+} and the net β = β_{}  β_{+} in a while. I suggest you try this also. Here β_{+} stands for the positivefeedback factor.
If you reverse the op amp inputs, β_{} becomes β_{+}, β_{+} becomes β_{}, and the circuit is unstable and the 'golden rule' does not apply.
So sorry about this. You are to be congratulated for sticking to your guns and insisting on knowing what's going on!
You were right, the equations are the same. And what I wrote in post #17 was trash.
I forgot about a little thing called 'stability':
An op amp circuit consisting of resistors only will obey the 'golden rule' if and only if the net feedback factor is negative. Always providing the amp is 'fully compensated', not saturated by an excessively large input and the op amp gain is infinite (and the offset voltage and current are zero, blah blah ...).
The feedback factor, usually written as β, is the fraction of the op amp's output fed back to its input. β is a positive number if the feedback is negative.
You can have both positive and negative feedback in a circuit and the golden rule still applies, providing the net feedback is negative. I'm attaching a sketch as a simple example.
Your circuit in fact does have both positive (via the 84K resistor) and negative (via the 100K) feedback. I will compute β_{} and β_{+} and the net β = β_{}  β_{+} in a while. I suggest you try this also. Here β_{+} stands for the positivefeedback factor.
If you reverse the op amp inputs, β_{} becomes β_{+}, β_{+} becomes β_{}, and the circuit is unstable and the 'golden rule' does not apply.
So sorry about this. You are to be congratulated for sticking to your guns and insisting on knowing what's going on!
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