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## Poynting Theory applied to Txmfrs

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• Taken from the Cornell Education Postings. Consider a transformer wound on a large toroidal core using a high permeability material so that very little
Message 1 of 2 , Sep 27, 2001
Taken from the Cornell Education Postings.

Consider a transformer wound on a large toroidal core using a high
permeability material so that very little magnetic field is outside
the core.That is, there is little leakage reactance. Put a primary
winding along a small length around the circumference of the core.
Put a similar secondary winding on the diametrically opposite of the
primary. Connect the primary to a low impedance ac power source and
the secondary to a variable resistance load.As the load resistance
changes, current in the primary and secondary changes in such a way
as to keep the flux in the core relatively constant.

Using the Poynting theorem, for example, how does power get
transferred from the primary to the secondary? The flux in the core
is not greatly affected by the power. That flux is also longitudinal.
There is no change in the E field. The same voltage is across each
winding at low and high loads.

Suppose you set up a plane symmetrically between the two winding
cutting the core into two halves. If you integrate the Poynting
vector over this plane, I do not see that the E x H to be very
different for high and low resistive loads. There is no physical
current flow across the plane other than displacement current.
**********
One key to the problem is to realize that the leakage reactance of a
transformer is *independent *of the core! The core increases the
magnetizing inductance and coupling coefficient but has NO effect on
the leakage reactance. This is well known to designers of pulse
transformers, for example. Inequivalent circuit diagrams, current
from
the primary to the secondary transfers *through* the leakage
reactance. Most transformer engineers do not think in terms of
Poynting's theorem.

In a transformer as described above, the main portions of the core,
that are not covered by windings, act as two pole pieces. A magnetic
field component fringes between them. It is driven by the bucking
currents flowing in the two windings producing an H field
proportional to the ampere turns in each winding. This H cannot be
reduced byusing a high permeability core material. The core enables
this leakage field to be distributed over a larger volume. Without
this core, the leakage would be local to the individual windings.
This H field produced by opposing currents in the primary and
secondary windings. It provides an H that can be crossed with an E
field to give a power transfer from primary to secondary.

Where does the E field to do this come from? The magnetic field B
through the core is proportional to the voltage across the primary
and secondary and 90 degrees out of phase with this voltage.
Accordingto Faraday's law, this flux produces an E field through the
core hole proportional to the rate of change of flux inside the core.
Thus, this E field is proportional to the voltage in each winding and
90 degrees out of phase with the flux. The result is that the
transverse components of the E and H fields, for resistive loads, are
in phase and contribute to a real transfer of power from primary to
secondary.

I do not know if this description for energy transfer has ever been
presented before.

William Buchman

Last Sunday, at a regular gathering of a local group of people
interested in physics problems, the question of how power gets
transferred between primary and secondary windings. In spite of the
belief that the physics of transfer of power between primary and
secondary was well understood, it was one of our most contentious
gatherings. The explanations included diagrams that have not been
posted here. ( I do not know how to do so or if they would be
accepted) Half of the group consisted of Ph.D.s The rest also had
extensive backgrounds

In addition to the theoretical discussion which showed that high
permeability cores did not prevent external magnetic fields from
being produced. This was also demonstrated experimentally. I was not
the only one present who had thought they understood the physics of
transformers, but who had their understanding revolutionized.

In essence, Poynting's theorem is applied in a region occupied by
leakage flux. Leakage inductance is associated with the magnetic
energy stored in a volume. As that volume decreases, the leakage
inductance decreases. Usually low leakage inductance is a design
goal.
Nevertheless, the fields in this volume are relatively independent of
the volume. When integrated over a surface, however, as required by
the Poynting theorem, the power transfer remains unchanged as leakage
inductance changes.

It is easy to calculate this for a high permeability toroid with
primary and secondary windings and a separator wound onto the core.
Poynting's theorem describes power transfer in detail and is
independent of the spacing.

To my knowledge, transformer designers and engineers just do not use
Poynting's theorem to describe the operation of transformers. A
reference to such use of Poynting's theorem would be appreciated.

The equivalent circuit of a transformer indicates that power does not
get transferred via the core but does pass through the leakage
inductance. Onceone has the equivalent circuit, the actual physics
involved tends to be ignored.

One error in a previous post was the statement that leakage
inductance is aproperty of winding geometry and not affected by the
core. For ordinary transformers, that is just a good approximation.
Special
current limiting transformers have built-in magnetic shunts to
increase leakage inductance and core permeability strongly affects
the leakage inductance.

William Buchman
• Hi, I like to think that my earlier postings on the Poynting vector in transformers has caused some people to experiment and rethink. Cyril ... From:
Message 2 of 2 , Sep 30, 2001
Hi,
I like to think that my earlier postings on the Poynting vector in
transformers has caused some people to experiment and rethink.

Cyril

----- Original Message -----
From: <dtb1000@...>
To: <MEG_builders@yahoogroups.com>
Sent: Friday, September 28, 2001 3:53 AM
Subject: [MEG_builders] Poynting Theory applied to Txmfrs

> Taken from the Cornell Education Postings.
>
> Consider a transformer wound on a large toroidal core using a high
> permeability material so that very little magnetic field is outside
> the core.That is, there is little leakage reactance. Put a primary
> winding along a small length around the circumference of the core.
> Put a similar secondary winding on the diametrically opposite of the
> primary. Connect the primary to a low impedance ac power source and
> the secondary to a variable resistance load.As the load resistance
> changes, current in the primary and secondary changes in such a way
> as to keep the flux in the core relatively constant.
>
> Using the Poynting theorem, for example, how does power get
> transferred from the primary to the secondary? The flux in the core
> is not greatly affected by the power. That flux is also longitudinal.
> There is no change in the E field. The same voltage is across each
> winding at low and high loads.
>
> Suppose you set up a plane symmetrically between the two winding
> cutting the core into two halves. If you integrate the Poynting
> vector over this plane, I do not see that the E x H to be very
> different for high and low resistive loads. There is no physical
> current flow across the plane other than displacement current.
> **********
> One key to the problem is to realize that the leakage reactance of a
> transformer is *independent *of the core! The core increases the
> magnetizing inductance and coupling coefficient but has NO effect on
> the leakage reactance. This is well known to designers of pulse
> transformers, for example. Inequivalent circuit diagrams, current
> from
> the primary to the secondary transfers *through* the leakage
> reactance. Most transformer engineers do not think in terms of
> Poynting's theorem.
>
> In a transformer as described above, the main portions of the core,
> that are not covered by windings, act as two pole pieces. A magnetic
> field component fringes between them. It is driven by the bucking
> currents flowing in the two windings producing an H field
> proportional to the ampere turns in each winding. This H cannot be
> reduced byusing a high permeability core material. The core enables
> this leakage field to be distributed over a larger volume. Without
> this core, the leakage would be local to the individual windings.
> This H field produced by opposing currents in the primary and
> secondary windings. It provides an H that can be crossed with an E
> field to give a power transfer from primary to secondary.
>
> Where does the E field to do this come from? The magnetic field B
> through the core is proportional to the voltage across the primary
> and secondary and 90 degrees out of phase with this voltage.
> Accordingto Faraday's law, this flux produces an E field through the
> core hole proportional to the rate of change of flux inside the core.
> Thus, this E field is proportional to the voltage in each winding and
> 90 degrees out of phase with the flux. The result is that the
> transverse components of the E and H fields, for resistive loads, are
> in phase and contribute to a real transfer of power from primary to
> secondary.
>
> I do not know if this description for energy transfer has ever been
> presented before.
>
> William Buchman
>
> Last Sunday, at a regular gathering of a local group of people
> interested in physics problems, the question of how power gets
> transferred between primary and secondary windings. In spite of the
> belief that the physics of transfer of power between primary and
> secondary was well understood, it was one of our most contentious
> gatherings. The explanations included diagrams that have not been
> posted here. ( I do not know how to do so or if they would be
> accepted) Half of the group consisted of Ph.D.s The rest also had
> extensive backgrounds
>
> In addition to the theoretical discussion which showed that high
> permeability cores did not prevent external magnetic fields from
> being produced. This was also demonstrated experimentally. I was not
> the only one present who had thought they understood the physics of
> transformers, but who had their understanding revolutionized.
>
> In essence, Poynting's theorem is applied in a region occupied by
> leakage flux. Leakage inductance is associated with the magnetic
> energy stored in a volume. As that volume decreases, the leakage
> inductance decreases. Usually low leakage inductance is a design
> goal.
> Nevertheless, the fields in this volume are relatively independent of
> the volume. When integrated over a surface, however, as required by
> the Poynting theorem, the power transfer remains unchanged as leakage
> inductance changes.
>
> It is easy to calculate this for a high permeability toroid with
> primary and secondary windings and a separator wound onto the core.
> Poynting's theorem describes power transfer in detail and is
> independent of the spacing.
>
> To my knowledge, transformer designers and engineers just do not use
> Poynting's theorem to describe the operation of transformers. A
> reference to such use of Poynting's theorem would be appreciated.
>
> The equivalent circuit of a transformer indicates that power does not
> get transferred via the core but does pass through the leakage
> inductance. Onceone has the equivalent circuit, the actual physics
> involved tends to be ignored.
>
> One error in a previous post was the statement that leakage
> inductance is aproperty of winding geometry and not affected by the
> core. For ordinary transformers, that is just a good approximation.
> Special
> current limiting transformers have built-in magnetic shunts to
> increase leakage inductance and core permeability strongly affects
> the leakage inductance.
>
> William Buchman
>
>
>
>
>
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