# Understanding Basic Transformer Theory

Discussion in 'Homework Help' started by Dennis H, Dec 12, 2014.

1. ### Dennis H Thread Starter New Member

Dec 12, 2014
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I am trying to explain basic operation of a plain vanilla power transformer and I'm not sure I get what's going on here. I've clicked and clicked and clicked and this is what I've come up with. If anybody that understands this stuff could tell me if this is correct or not I would be greatly appreciative.

Basic principles of operation of a single phase power transformer. Assume in the initial condition that the primary is connected to a constant voltage AC source and there is nothing connected across the output of the secondary – infinite impedance. The current in the primary is being controlled by Ohm’s Law. V=IR where: V is the applied voltage, I is the resultant current and R is the impedance. The impedance of the coil is the vectoral sum of the DC Resistance of the copper and the XL – the Inductive Reactance. XL is a restriction to the flow of current that is being caused by the counter electromotive force, a force that counters the building and collapsing field surrounding the primary windings and by the counter magnetomotive force, a force that counters the building and collapsing field in the magnetic core.
The field in the core is inducing a voltage in the secondary windings. There is a voltage, but because there is no load, there is no current. Now let’s see what happens when we connect a load. Because a current is now flowing in the secondary, like the current in the primary, the current in the secondary is creating a field. According to Lenz’s Law, this field is in opposition to the field that created it, the magnetic field in the core. Because the field in the secondary is opposing the field in the core, the net counter field seen by the primary decreases. As such the inductive reactance of the primary has been lowered and so more current is flows in the primary. These fields work continuously and inseparably to maintain this balance. The net field in the core is always the same – the field that was there before any current was flowing in the secondary.

2. ### crutschow Expert

Mar 14, 2008
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Sounds correct to me.
Does it make sense to you?

3. ### Dennis H Thread Starter New Member

Dec 12, 2014
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Does it make sense? Well I'm good with a fair amount of it. Before you put a load on the secondary I feel really comfortable. Put a load on the secondary and the current induced follows Lenz's Law - check. Why the current goes up in the primary aaahhh not so much. "Because the field in the secondary is opposing the field in the core, the net counter field seen by the primary decreases. As such the inductive reactance of the primary has been lowered and so more current flows in the primary." This is the part that makes me say REALLY and wonder if my statement is completely true or just kind of close.

4. ### crutschow Expert

Mar 14, 2008
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The magnetizing current and core flux of a transformer is determined by the input voltage and frequency and the primary turns. This is a constant, and there is no load current component in the equation for that flux.

When the current increases in the secondary, the direction of the current is opposite to that of the primary (since a positive voltage at the primary is current into the transformer and a positive voltage at the secondary is current out of the transformer. The secondary current thus reduces the core flux. Since the core flux must remain constant for a given input voltage and frequency, the input current must correspondingly increase to counter the reduction from the secondary current and maintain the core flux. Thus change in the secondary current is always balanced by a change in the primary current.

Does that help?

5. ### Dennis H Thread Starter New Member

Dec 12, 2014
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Hey thanks a lot for your help. I'm totally good with the idea that the current in the secondary has a field that is in opposition to the flux that was there before the secondary started conducting. The only gap I'm down to is the specific mechanism that makes the primary current go up.

Are my two sentences:

"Because the field in the secondary is opposing the field in the core, the net counter field seen by the primary decreases. As such the inductive reactance of the primary has been lowered and so more current flows in the primary."

Completely true or just kind of close?

Again thanks for your help and patience.

6. ### crutschow Expert

Mar 14, 2008
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I would go for "kind of close".
Certainly the impedance of the primary is reduced but that's the real part of the impedance (the reflected load impedance), not the magnetizing current inductive part, so I don't think that equates to the inductive reactance being less.
But I don't know if there's a better way to explain it.

7. ### Dennis H Thread Starter New Member

Dec 12, 2014
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Hey thanks again for the help. I'm going to have to try to do some further research and now have some key words I can Google. I'm determined to get to the bottom of this and say it simply yet completely and perfectly correct. I think I need to know the name of the stuff the primary sees after there's flow in the secondary. The stuff that wasn't there when the primary was magnetizing the core only. Thanks again

Feb 17, 2009
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9. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Perhaps it is possible to reason that the mysterious "stuff" at the primary, when current is switched on in the secondary, is purely a fundamental property that arises from the physical circumstances and whatever laws govern the observed phenomena. This might lead to a conclusion that the classical view may not offer a complete (or rather satisfying) explanation. Perhaps one could suggest the notion that, "to every action there is an equal and opposite reaction", may have to suffice.

Consider an ideal transformer comprising two identical, perfectly coupled windings each of (say)1000 turns. Each winding has a self inductance of 1H and zero resistance. There is no leakage inductance nor does the magnetic circuit saturate at any flux density. The ideal case is hopefully a useful one, since if one can't explain transformer operation for an ideal situation then that problem would be true of the non-ideal situation.

Suppose the primary winding is energised at some instant (call it t=0 seconds if you like) by an ideal DC voltage source of 1V. One second later, let a 1 ohm resistor be switched across the secondary winding terminals. What do we "observe" in terms of the various current and voltage conditions?

At the instant the primary is energised, one can reason that primary current rises linearly from zero amps at the rate of 1A per second. We can also similarly reason that the magnetic flux mutually & completely linking the primary and secondary windings is rising linearly at the rate of 0.001 weber per second.

According to Faraday's Law, the linearly increasing magnetic flux will induce a constant emf in the secondary winding of exactly 1V.

At the instant when the 1 ohm load is switched onto the secondary we have to account for several things:

1. The linearly rising primary current commensurate with the primary exciting voltage.
2. The secondary voltage.
3. The secondary current.
4. The magnetic flux conditions before and after the secondary load is connected.
5. The primary component current arising due to the connection of load.

At the t=1 second point, the primary current will have risen to 1A due the 1V DC primary exciting voltage acting alone.
Does the secondary voltage change when the load is connected?
Provided the rate of magnetic flux change at that time is the same as that before the load connection, then the secondary voltage will not change. If the mutual flux had somehow changed instantaneously, then we would anticipate (by Faraday's Law) an infinite voltage transient in both primary and secondary voltages. But this cannot be physically justifiable, as the primary voltage is constrained by the ideal 1V DC source. The rate of change of the resulting mutual flux must therefore be exactly the same as it was before the secondary load was connected.

However, the (instantaneous?) secondary current transition from 0 to 1A at t=1 second, will give rise to a flux which (one presumes) exactly opposes the increasing primary induced exciting flux. Had we waited 2 seconds before connecting the load, then one would have only partial oppostion of flux, given the primary current would have then been 2A rather than 1A.

I have stated that the flux must be maintained at a constant rate of rise. The only possible way that we can account for this when the load is connected, is to assume that a component of current in the primary must instantaneously arise to cancel the flux produced by the secondary current of 1A. Therefore, at the instant the load is applied at t=1 second, the primary current would jump from 1A to 2A. Again, had we delayed the load connection to t=2 seconds, the primary current would have jumped instantaneously from 2A to 3A.

So what "stuff" caused this transition in primary current to happen? I don't believe there is any "stuff" as such. The physical system is constrained by conditions which must be satisfied - otherwise a physical impossibility in the classical sense, must be accounted for.

10. ### crutschow Expert

Mar 14, 2008
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That "stuff" is the varying magnetic flux the flows in the core and through the windings, and is always there when AC voltage is being applied to the primary. That flux generates the back emf to counter the input voltage. When secondary current flows, the flux is reduced, resulting in a corresponding reduction of the back emf in the primary. The primary current then increases until the flux is again high enough to counter the applied primary voltage.

11. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Over what time scale would this "transient" state for flux equalization evolve in an ideal transformer?

12. ### Dennis H Thread Starter New Member

Dec 12, 2014
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WOW thanks. lots of reading to do for sure. t_n_k I'll draw that one out and get to the bottom of this. Today's an epic travel day for me.

13. ### crutschow Expert

Mar 14, 2008
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For an ideal transformer I would guess, at the speed of light.
Edit: And since an ideal transformer would have zero dimensions, then it would happen instantly.

Last edited: Dec 15, 2014
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14. ### t_n_k AAC Fanatic!

Mar 6, 2009
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I'm also guessing for a real transformer we would still be looking at very small time scales.
Could we measure the phenomenon somehow in a real situation? I'm genuinely unsure. Presumably it would be difficult to separate the load induced flux adjustment response from other (dominant?) responses due to the non-ideal transformer parameters.
This leads me to ask (having regard to the OP's noble objective) if we can then ever fully describe transformer function without resorting to a potentially unverifiable assertion - whether valid or not. Perhaps the OP isn't really that fussy - provided the explanation appears logical.

The OP might enjoy this

http://videolectures.net/mit802s02_lewin_lec16/