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Power Transformer Question: Why is core magnetic flux maximum at no load?

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killingtime:
[Re-Post as the original disappeared when the forum crashed]

Hi,

Can anyone explain why the magnetic flux in a mains power transformer is highest while in the unloaded state, and why it decreases when a secondary load is applied (and the primary current increases as the load is transferred to it)? There's no problem, just trying to further my understanding of power transformers so I can design one.

I've always understood magnetic fields and flux to vary according to conductor current as many of the equations a afunction of current (discussed further down). Then I stumbled on the article below. It's an interesting read on transformers from the perspective of someone that's done plenty of experimentation. Very little theory on the first page. More of a discussion really, but it all looks correct and confirms many of my actual experiences with Xmrs. Give it a read if you have the time.

https://sound-au.com/xfmr.htm

The piece starts off by asserting that:

"For any power transformer, the maximum flux density is obtained when the transformer is idle."

Well, let's look at a real world example to confirm this. If we take a microwave power transformer, leave the secondary unconnected (unloaded) and drive the primary at mains voltage and frequency (as it was designed), we see a primary current of around 2 to 3 Amps (very poor idle efficiency). That primary current isn't a clean sine wave, and that's because the transformer core (silicon steel) is designed to operate heavily in the saturated region. It's designed this way to save on core steel, copper and weight, a manufacturing win, but at the expense of efficiency. Magnetic saturation in a Xmr or inductor has the same effect as little or no magnetic core at all > inductance drops > impedance drops > current rises. When the core is completely saturated, winding current is only limited by the Ohmic resistance of the copper winding (an electrical short circuit).
Ok so far. Now load the secondary with say 700w. That load is transferred to the primary according to the turns ratio so the primary current goes up as well. If increased Xfmr load also increased core flux then the transformer wouldn't work, as it's already heavily magnetically saturated to start with at idle.

This leads me to believe that flux behaves somewhat independently of load current and is more related to rate of change of primary driving voltage. If correct, then that would explain why Xmr flux goes down at load. The driving voltage hasn't changed (mains) but there are Ohmic voltage losses on the primary winding which go up with the current meaning the Xmr sees a lower primary voltage.

If you need a primer on electromagnetism and equations, Surrey University has a good page with explanations and magnetic duality with the electric world (MMF -> EMF etc).

Scroll down to the part titled "Magnetic Flux" (MF). MF is measured in Webers or Volt Seconds (rate of change of voltage). That's the give away, but it doesn't explain why the flux doesn't increase with current if (using the definitions from the above link):

Φ(flux) = V × T / N  and,
Φ(flux) = I × L / N
V - voltage, T- time, N - coil turns, L - inductance

----------

Magnetic Field Strength: Whenever current flows it is always accompanied by a magnetic field.  The strength, or intensity, of this field surrounding a straight wire is given by:  H = I / (2 π r)
^^^ So magnetic field strength is a function of conductor current (I).

Magnetic Flux Density:  B=μrμ0H
^^^ So Magnetic Flux (Density) B is related to Field Strength and proportional to it according to the permeability of the material it's moving through (μr).

Given the Xmr core size is fixed, if flux density increases, so should the flux. Add retentivity and saturation to this and we end up the 'S' shaped B-H curve. I get this, I just don't see why core flux doesn't increase with current as the Xmr secondary is loaded and current (I) on both windings goes up.

Assuming both flux equations above the ---- line are correct (a university is unlikely to be wrong), the only way flux can decrease with increasing current in an Xmr is if the inductance (L) goes down with increasing current (I) as the Xmr is loaded (N remains constant). Inductance drops due to increased core saturation as the Xmr is loaded? Could this be the answer?

Thanks.

Kleinstein:
The equation  flux = I x L / N only applies to a linear normal inductor. With a transformer one would have to use the difference between primary and secondary current (scaled with the turns number).

In a transformer the flux is kind of forced to follow the votlage. The current than reaches the value needed to cause the needed magentization.

Benta:
For an ideal transformer, core flux is always the same at the same operating voltage/frequency regardless of load current. That's the beautiful thing about transformers.
The flux is maximum at no load is simply because maximum voltage is present at the primary (=minimum resistive voltage drop in the winding).

schmitt trigger:
Exactly as Benta explained.

No or very small IR primary losses, allow the full applied terminal voltage to develop the flux.

james_s:
I thought the back EMF from the secondary "fought" against the flux in the core from the primary, resulting in a lower total flux? Admittedly magnetics is not my specialty.