buddypoor
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Hello SHELDON, Thanks for your answer. Sorry, but I am afraid that you are mistaken. I think that you misunderstand the Middlebrook method.
I don't think so. Please, look at the attached pdf-file. I have tried to explain the background of Middlebrooks method using a simple example - and I think I have shown that it is, indeed, an open-loop simulation. But, that's no surprise. It's only logical - the gain of an open loop cannot be determined in a closed-loop configuration. That would be a contradiction!
The loop remains closed for the measurement. A signal is injected into the loop and you measure the return ratio.
No, that`s not the case. In principle, it is impossible to simulate the loop gain when the loop remains closed! It is evident that the loop gain is identical to a ratio of two voltages - an output voltage caused by an input voltage. That means, you need two ac decoupled nodes for injection of the input and measurement of the output - whereby the output voltage must be caused only by the gain of the open loop! That is the reason I have asked you twice: How and where do you intend to inject such a voltage into a closed loop?
If you look at the other measurement techniques: VCVS-based, two-port, Tian's method, in all cases the loops are closed. In some cases the signals are injected inside the loop but this does not mean that the loop is open.
The answer is given in the attachement. Perhaps the loops look as they were closed - but they aren't. A phase shift of 180 degrees causes inversion and results in oscillation so phase margin is defined relative to a 180 degree phase shift.
No, speaking of the loop gain the PM is defined relative to zero resp. 360 deg. The margin is defined relative to 180 deg only if you speak about the simple product of all loop elements - i.e. without consideration of the inversion due to negative feedback (as it is often done in control systems). However, the term loop gain must include the minus sign. Thus, the reference to 360 deg.
You need to calculate the system transfer function,
For which purpose? It is not needed for loop gain determination. More than that, it is not possible to derive an expression for the loop gain from the closed-loop transfer function without knowing the contribution of the amplifier in advance.
Each method of measuring the loop gain: Middlebrook, Tian, VCVS, two-port places different requirements on where the signal is injected and the measurements are made.
Yes, no doubt about it. Otherwise, all these methods would be more or less identical. However, all are open-loop based. Maybe, its not easy to realize by simple visual inspection (as in case of Middlebrook). __________________
Sorry, for the long answer. But I think - in particular for beginners, who may follow this discussion - it is important to (a) know the exact definitions of the parameters and (b) their meanings and (c) how they can be measured/simulated.
Greetings, regards. Comments are welcome.
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