Transformer theory (was:Re: Another ~1960 computer kit)

From: Philip.Belben_at_pgen.com <(Philip.Belben_at_pgen.com)>
Date: Thu Dec 31 03:48:48 1998

Dave Dameron wrote:

> OFF topic:
> Max wrote:
> There's little need to make coils these days, and wiring electric lights
> isn't very fun when one can play around with things millions of times
more
> complex.
>
> Hey! I've wound several experimental coils this year. Did you wonder
_how_ a
> transformer works? I know the equations to design one, but am asking
> something more fundamental. The secondary winding of a transformer has
> voltage induced in it, but what couples the energy to it from the primary
> winding's magnetic field?
> (Hint: The magnetic field can be zero at the secondary)

As the list's resident electrical (as opposed to electronic) engineer, I
feel I must make a stab at answering this. Especially since my first job
at PowerGen was research on transformers. (Not at this fundamental level
though - I was looking at fault detection systems)

As I see it, when you have a winding linked with a magnetic field, you
induce a voltage in the winding proportional to the rate of change of the
field. If you like to visualise lines of magnetic flux, the voltage is
related to the number of flux lines that actually cut the wires of the
winding, not the flux linked with the winding at any time.

This means, among other things, that (for sinusoidal ac) the flux is zero
when the voltage is at its peak and vice versa.

The transformer, though, is not a differentiator since the magnetic field
is proportional to the integral of voltage in the primary. That is, flux =
integral (Volts in).dt; (Volts out) = d(flux)/dt (assume = means "is
proportional to")

Note also that the flux depends only on voltage, NOT CURRENT. You
associate magnetic fields with currents (well, I do, anyway), and as you
increase the primary current you expect the field to increase. But it
doesn't. An equal and opposite effect from the secondary current exactly
balances this.

This has a number of implications that are quite important for my current
(pun not intended) job, modelling power systems.

1. The equivalent circuit of a transformer has a branch in parallel with
the primary, the magnetising branch. This is an inductance representing
the magnetic field (and it's in parallel, so it depends only on voltage as
above) and a resistance representing "iron losses"

2. No transformer is perfect. There is regulation - inductance and
resistance apparently in series with it. The resistance represents "copper
loss" - the physical resistance of the windings. The inductance represents
flux in each winding that _does not_ link with the other, and therefore is
not backed off by current in the other winding. But in an electrical
system model, the simplest representation of a tranformer is a series
inductance connecting two sides of the transformer. Ironically, this
represents physically the magnetic field that does not connect the two
sides of the transformer!

3. For metering, protection and the rest, you see a lot of current
transformers. One of these consists of a high current, low voltage primary
- usually a bar running through the middle of the toroidal core - and one
or more multi-turn (low current) secondaries. The equation is simple. The
mmf (magnetomotive force = amps * turns) of all the windings add up to zero
(equal and opposite effect of secondary current again). Because the
measuring kit acts as an effective short circuit on the secondary - or
drops a few volts at most - the magnetising current is almost zero, and you
can thus make very accurate measurememnts.

Is this the answer you wanted?

Final note. What do you mean by "the primary winding's magnetic field" as
distinct from that of the secondary? To a good approximation, the magnetic
field is the same at both the primary and the secondary. It may be close
to zero, for reasons I described. But the difference between the mag.
field at the two windings contributes only to the equivalent series
impedance. It is not something to look at when discussing the detailed
operation of the tranformer.

> As for wiring lights, Christmas tree light strings here are now cheap
series
> strings although the bulbs may have some wire turns wrapped around the
leads
> to prevent a open circuit if a bulb burns out. This often don't work, so
the
> entire string is usually thrown away, like many modern ASIC type computer
boards

Aargh! I've not heard of that (throwing the whole string away) before but
I can well believe it.

Philip.
Received on Thu Dec 31 1998 - 03:48:48 GMT