In article ,
Winston wrote:

Joseph Gwinn wrote:
(...)

But I need to point one thing out: A transformer feeding a resistive
load like a hot wire is not an inductive load unless the transformer in
question has extremely large leakage inductance (transformers in
tombstone welders would qualify).

This is a puzzlement for me, Joe.

Just now I modeled a 1:1 transformer in SPICE
and loaded the output with a selection of
different resistances.

While driving the input with 60 Hz, I noticed
that the primary voltage peaked before the
primary current did at about ~89 degrees
separation with the secondary loaded at 1
ohm through 100K ohms.

That all looks inductively reactive to me.

Then there is problem with the spice model. More below.


What did I do wrong? Are you talking about
saturated core mode?

In saturated core mode, the primary inductance of the drive winding
drops to a very low value, because saturated iron has roughly the
permeability of air, and one will see huge current surges when the core
saturates and the inductive reactance drops to near zero. This is not
what I think you are seeing.


Never mind computer modeling systems like spice. Let's talk physics.

As seen from the terminals, the voltages of an ideal single-phase
one-path transformer are all in phase (or inverted in sign). The
relation between voltage and current will depend on what is connected to
the transformer. If all loads are resistive, then currents will be in
phase with voltages. If loads are in aggregate reactive, then voltage
and current will get out of phase.

Another way to think about this is to note that no matter how many
windings there are, there is exactly one core, and the net flux through
this core links all windings equally.

Practical transformers very well approximate ideal transformers so long
as:

The inductive reactance of the windings exceeds the impedance of what's
connected to those windings by a factor of at least five or ten.

The stray inductance is insignificant.

The core remains out of saturation.

Eddy currents are reduced to insignificance by lamination of the core or
by use of a ferrite core.

The frequency isn't so high that stray capacitance has a significant
effect.

This is the short form. Transformer design can be a career. But for
all their imperfections, transformers work pretty well.


So, the spice model seems to be giving non-physical results, but
computer models are known for such things, and one must always validate
such models.

War story: Many years ago, I was interested in the physics of xenon
flash lamps. The physical model is pretty simple, a charged capacitor
discharging into an arc, which arc heated the xenon to incandescence,
the resulting light and heat radiation carrying the energy away. This
yields a set of coupled ordinary differential equations that one solves
numerically, time step by time step. I got it all working, and all was
well. Then I changed the duration of the time steps, and more energy
came out as light and heat than was stored in the capacitor. Oops.
Violated the conservation of energy.

Turns out I had made two mathematical mistakes, which mistakes cancelled
one another only for the original step duration.


Joe Gwinn