Once it is a matrix calculation, it is simple! Excel has matrix features built in as do many hand calculators. Linear algebra is a mainstay of computer science. IIRC, in the book by Smythe, Static and Dynamic Electricity covers such matters. Smythe himself thought that such circuit issues in a book that covered much more complicated issues was out of place.
Bill
-- Fermez le Bush--about two years to go.
Uh, oh! I see that none of my recent posts are appearing here. Gosh, ain't Google Groups great! Guess I'll have to try later and try to re- write what I said. I HATE this work-eating feature of computers and half-baked software!
Just a moment.
Benj (testing)
OK. My investigation to this point shows that Google is actually posting my efforts but is not showing it as posted. In other words you can't read anything I've said IN Google. However, if you have a "real" newsreader, the recent stuff is there.
The bad news is that I haven't got my "free" news service working properly yet and therefore cannot post there with a "spoof" email address. The bottom line is I'm sort of cut off right now.
But I will make a comment or two. Ahem. There is a copy of Terman right on my shelf here and it was one of the FIRST places I looked. Blanket statements about how "easy" it is to derive all this or that Terman "talks about" mutual coupling are total BS. If it's so damn easy then how about YOU just whip it out for us all, OK? We will be forever grateful! As you go on in life, you will one day discover that the most difficult questions to answer are the ones that seem the simplest to ask! I would hardly call the question of parallel coil connections "irrelevant"! I guess all electrical questions are irrelevant. You will recall that the FIRST thing I did was ask if anyone had a reference to a book that had this problem worked out. (That would be "worked out" not "talks about mutual inductance"!) Zero references from Salmon Egg or anyone else!
I have indeed derived the equations shown in Wikipedia (I believe the signs are wrong) but as I've indicated it's not the MATH that is the problem it is the reality of it! The problem has to do with an equivalent circuit for the situation. Any math can be defined valid but if the answers don't match reality it isn't of much electrical value. And the Wikipedia result does appear to agree at least in part with measured data. (The Wikipedia circuit assumes that the changing current in one leg results in a series voltage induced in the other leg)
By the way, the other comment someone made about a power transformer with two different windings is VERY interesting! Yes, that would be similar to what we are talking about although I'm not exactly sure how two different voltage windings would fight each other. I mean if you have a 10 volt winding and you hook it to a 15 volt winding that essentially makes the 10 volt winding have a 5 volt input, right? Which would be reflected back to the primary which then alters the over all output! I'm not sure it actually would smoke the thing. But it might. It's not wise to bet against smoke! If we hooked tow outputs in parallel OUT of phase, it's clear that this would cause the primary to appear with no inductance or as a piece of wire. This is a result apparent in the parallel inductor thing. And yeah, that might result in some heavy currents.
Since 'm sort between a rock and a hard place right now, I'll have to back off until my posts are no longer banned on Google or I fix my terranews setup. But I will keep an eye out for comments.
You are a lost soul an nobody appears to be inclined to rescue you. Life is tough.
Bill
-- Fermez le Bush--about two years to go.
------- Maybe because it is a relatively trivial problem of little interest or use. In the case of parallel wires there is some interest but there is an easy way to deal with it.
----------
---------- Huh? Something missing in your background Sneak up on it. L1=M+e =L2 -plug into the expression and see what happens as e goes to 0. Result is Leq =M. Taking limits is a standard approach in such cases. If M is -ve then the equivalent L =0.
Note that using the T equivalent circuit also gives this without having to sneak up on the problem. What's the big deal? Result is Leq =M =L or Leq=0 Using the equivalent circuit also gives this without having to sneak up on the problem .
Your "formula" apparently ignores Kirchoff's Laws (without which circuit theory is meaningless) and is incorrect because of this.
------- Note that the incorrect Wikipedia approach is actually correct for two coils when L1=L2 for any M It doesn't give the correct answer when L1< >L2 except for M=0 and cannot be extended to more than 2 coils.
-----------
No kidding, Have you looked at the calculations of inductance for finite or infinite wires and the concept of GMR or approximations needed? >
--- Only because you have L1=L2. By the way, reality is not L1=L2=M.
---------- However the T circuit does give the expected result -so again what is the problem. In the case of your transformer - just what is being coupled in the two windings? Your description is questionable. The mutually coupled windings already provide a non-ideal transformer. You can use an ideal transformer but note that the ideal transformer has L1=L2 =M all approaching infinity so the transformer without any load will be an open circuit. Is this what you want? You need a load across one side of it- I suggest M. Hell, you can have a black box with a gremlin in it and a pair of hand crank generators and ammeters if you want -AS LONG AS THE BASIC CIRCUIT EQUATIONS ARE SATISFIED. I suggest that you look at the these equations, given in damn near any text, for coupled windings and make sure that they are satisfied and also that current in coil 1 is only i1 and current in coil 2 is only i2 as in real life- then go for an equivalent circuit 1 and 2 coupled by an ideal transformer, or a T or pi model- lots of ways to skin a cat but make sure you have the right cat to start with.
Generally they all have some form of
v1=L11di1/dt +L12di2/dt v2=L21di1/dt +L22di2/dt
where, (with exceptions in some rotating machines) L12 =L21 =M Look, in the library for some texts such as Krause "Analysis of Electric Machinery" or even Fitzgerald Higgenbotham, Grabel "Basic Electrical Engineering" (a once very popular book, updated many times-used for non-EE students. These are now old but newer circuits and energy conversion texts deal with this stuff. It would also be good for you to look at the magnetic situation involved -i.e. what leads to L11 L22 and L12. The flux relationships leading to these KVL equations are also given in a wide variety of texts.
If you believe, as the preponderance of authors do, that these equations are valid, then both the T circuit and the expression for equivalent inductance follow. If you disagree with these equations- then why do you disagree? I would like to know. If you have a problem with the approach I gave, then question it- I welcome questioning, but do your homework- it is a trivial problem.
You got it! Simple isn't it when you sit down and think about it. It also helps to start with the correct equations as you have.
-----------
You were told, by me and by "donotreply", how to do this. Have you bothered to go back to the basic equations? By the way, look up autotransformers. You seem to have some big holes in your education.
(snip)
(snip)
You'll have, effectively, a lot of shorted turns and thus no inductance. A power transformer has very tight coupling between windings. If you actually did what you said (BTW, dont!), the "two terminal" result would be close to a short circuit. Cheers,. Roger
------------------------ You are absolutely correct.
I looked at this for a particular transformer ( 100KVA, 1000/200V) and the result is that the input current was about 3200A at 200V applied with individual primary and secondary currents of 800 A and 4000A respectively as compared to 1000A/5000A short circuit currents.
Parallel mutual inductances where L1 =L2 or M^2
PolyTech Forum website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.