# Magnetic Ckt/Power Transmission Q's

#### jegues

Joined Sep 13, 2010
733
See figure attached for questions.

Question 1: I would argue that this statement is true. If we think of the equivalent circuit model for a given magnetic circuit the air gap is modeled as a resistor which is a purely linear device. This implies that in the context of magnetic circuits, the airgap is to be thought of as something with linear attributes.

Question 2: Electricity is transmitted at high voltages to reduce the energy lost in long distance transmission. Transformers make these high voltages possible, they can step up and step down the voltages as desired. Thus without transformers creating such high voltages, we would have less efficient power transfer over long distances.

Question 3: Excitation with sinusoidal voltage implies the presence of a sinusoidal flux. The flux/current relationship on the other hand, will be nonlinear in saturation. As we increase the voltage, the point on the flux/current curve passing through the "knee point" and enters saturation, where the current will exhibit non-linear effects. Theses non-linear effects account for the distortion we are seeing on the output waveform.

I had a tough time trying to answer some of these questions, so I'm fairly certain some of the stuff I've said is incorrect or can be better explained.

Are my explanations correct? Are only portions of it correct? What would be a better way of answering the question/explaining such a phenomenon? Is there anything else I could mention?

I'd love to hear what your answers to the questions above would have been.

Thanks again!

#### steveb

Joined Jul 3, 2008
2,436
See figure attached for questions.

Question 1: I would argue that this statement is true. If we think of the equivalent circuit model for a given magnetic circuit the air gap is modeled as a resistor which is a purely linear device. This implies that in the context of magnetic circuits, the airgap is to be thought of as something with linear attributes.

Question 2: Electricity is transmitted at high voltages to reduce the energy lost in long distance transmission. Transformers make these high voltages possible, they can step up and step down the voltages as desired. Thus without transformers creating such high voltages, we would have less efficient power transfer over long distances.

Question 3: Excitation with sinusoidal voltage implies the presence of a sinusoidal flux. The flux/current relationship on the other hand, will be nonlinear in saturation. As we increase the voltage, the point on the flux/current curve passing through the "knee point" and enters saturation, where the current will exhibit non-linear effects. Theses non-linear effects account for the distortion we are seeing on the output waveform.

I had a tough time trying to answer some of these questions, so I'm fairly certain some of the stuff I've said is incorrect or can be better explained.

Are my explanations correct? Are only portions of it correct? What would be a better way of answering the question/explaining such a phenomenon? Is there anything else I could mention?

I'd love to hear what your answers to the questions above would have been.

Thanks again!
Your answers seem correct to me and I would have answered similarly. However, I find open ended questions like these difficult and you never know when the professor has a particular aspect of the answer he is looking for, that you may not have thought about.

One thing that bothers me about the first question is it's not clear to me how to judge when something is more nonlinear. Nonlinear is the state of not being linear and if something is not linear then it is hard to say if one thing is more nonlinear. However, I'd guess that the measure most people would use is the second derivative found in the linearization process. The DC offset tells you the operating point, while the first derivative gives you the linear equivalent AC response. Thus, it seems that the second derivative is a possible measure of how "nonlinear" something is. But, be cautious because not all nonlinear systems are linearizable in this way, and even linearizable systems might have zero second derivative and non-zero higher order derivatives. Thus, the statement that something is more nonlinear than another can be nonsense, unless a measure or metric is put in place to define it. For example, there are definitions of "harmonic distortion" that make the question quantifiable.

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#### jegues

Joined Sep 13, 2010
733
Your answers seem correct to me and I would have answered similarly. However, I find open ended questions like these difficult and you never know when the professor has a particular aspect of the answer he is looking for, that you may not have thought about.

One thing that bothers me about the first question is it's not clear to me how to judge when something is more nonlinear. Nonlinear is the state of not being linear and if something is not linear then it is hard to say if one thing is more nonlinear. However, I'd guess that the measure most people would use is the second derivative found in the linearization process. The DC offset tells you the operating point, while the first derivative gives you the linear equivalent AC response. Thus, it seems that the second derivative is a possible measure of how "nonlinear" something is. But, be cautious because not all nonlinear systems are linearizable in this way, and even linearizable systems might have zero second derivative and non-zero higher order derivatives. Thus, the statement that something is more nonlinear than another can be nonsense, unless a measure or metric is put in place to define it. For example, there are definitions of "harmonic distortion" that make the question quantifiable.
I had asked the professor about the first question regarding the airgap being either linear or nonlinear and the explanation he gave is somewhat like this,

First he mentioned about how the reluctance of the air gap will dominate the reluctance of the core. This becomes obvious if you were to make the calculations for both. (Or simply recognize that the relative permeability of air is 1)

After that he went on saying that air is a very bad magnetic medium, and that it won't saturate, (There is no saturation region on the $$i \quad vs \quad \phi$$ curve) thus we only observe linear behaviour.

Any insight with this? Can someone explain this any clearer?