# equivalent circuit of a transformer

Discussion in 'Homework Help' started by PG1995, May 14, 2012.

Apr 15, 2011
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2. ### steveb Senior Member

Jul 3, 2008
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It's not a trivial thing to figure out what equivalent circuit best represents an electromagnetic device. You are looking at the end result of years of work by many people. I'm sure some people here can give various good reasons why this circuit is appropriate, but you would probably need to study this very thoroughly to fully understand. There is nothing wrong with asking why, but there is also nothing wrong with grasping the most critical aspects and just accepting the rest as the end result of a lot of research.

Let's take only a small bite out of your question, - the part I personally feel is most critical for you to understand.

Consider only Rp, Lp and Lm. Moving the Rp and Lp as you suggest (between XY) is clearly not a physical representation of a typical coil. The input to the primary transformer should predominantly look like a simple coil, right? Coils are usually expressed as a series connection of a ideal coil and ideal resistor. What you suggest would not be this at all. Also, consider why the input looks like a simple coil, as a first approximation. The self inductance is a result of the flux cutting the primary side circuit. The fact that some of this flux is also cut by the secondary side of the circuit is incidental. The primary side self inductance is a series combination of the leakage inductance (Lp) and the mutual inductance (Lm) because the total flux needed to calculate self inductance is the sum of the leakage flux and the mutual flux. The interaction of primary and secondary are dictated by Lm, but what you see looking into the primary depends on the total self inductance (Lm+Lp).

Last edited: May 14, 2012
3. ### PG1995 Thread Starter Active Member

Apr 15, 2011
753
5
Thank you, Steve.

I understand what you say. Now I'm realizing that most of the time I should just memorize the things and probably understanding would come later. I'm not afraid to study or research this subject thoroughly but you see time is the real problem here. I have still gone through four books to understand the transformer topic. Unfortunately most textbooks have the same approach toward the subject. They just use different diagrams and words but the underlying material is the same. They should at least provide some logical basis for whatever they are saying. Now coming back to the issue of time. In such a limited time one has to cover up many different topics and to make the matter worse, especially in my case, I have really 'bad' instructors, if I may say so. Remember last month when I was asking so many different questions about operational amplifier. Actually I had an exam then and it took me almost two full days to understand some of the material conceptually but on the exam they didn't even ask a single about that stuff; all the questions were about calculations using formulas. Though I was still able to get good marks.

Now I'm feeling that I was wrong in the first place to start this thread because I should have just tried to memorize the equivalent circuit and be done with it and no worries.

Thank you for always being there to help me.

Best regards
PG

4. ### steveb Senior Member

Jul 3, 2008
2,433
469
I don't think you are wrong at all. Curiosity is a great characteristic to have in our field. I would only suggest that you limit your question and not try to understand why all those parasitic components are in particular places, but only try to understand the most dominant and critical pieces, such as the one I highlighted. Once that is firmly under your belt, as time permits, you can go further as needed.

Many things in engineering are learned on an as needed basis. You want to have the fundamentals down cold, and you want to know how to delve into the details when needed, but it is just physically impossible to know everything about everything, - try as we might.

For example, on this very good question that you ask, I've never needed to include all those parasitic components in any real life problem. I've used some of them in different circumstances, but not all. So, basically, I don't know the full answer to your question because I've never needed to know the answer. However, I'm confident that I could delve into the details and get any answer I wanted to get.

PG1995 likes this.