# Transformers

Discussion in 'Electronic Design' started by Danny, Apr 12, 2004.

1. ### DannyGuest

Hi

I was told a while ago, 'the input current to a transformer is dependent
upon the output current taken by the load', first of all, is this true??

If it is true, then what is the realtionship between the two? because
surely, when there is no load there is definitely a current through the
primary coil, that is what was puzzeling me.

Dan

2. ### John WoodgateGuest

I read in sci.electronics.design that Danny <[email protected]
Yes, but a bit misleading. It is *dependent*, but the primary current
isn't zero when the secondary current is zero. This is called an
'affine' relationship, not 'proportional'.
Some current is needed in the primary coil to produce the magnetic field
in the core. Surprisingly, this is called 'magnetizing current'. It
actually has two parts; one part, Ifield, which is 90 degrees lagging
the applied voltage, actually makes the magnetic field, while a smaller
part (you hope), Iloss, is in phase with the applied voltage and is due
to the eddy-current and hysteresis losses in the core.

If we call the total primary current Ip, the secondary current Is, the
turns ratio n and the magnetizing current Im, then:

Ip = Im + nIs,

where the currents are phasors (vectors in old-speak). Note that if the
secondary current is MORE than the primary current, n is LESS than 1.

If we split Im into its parts:

Im = sqrt{(Ifield)^2 + (Iloss)^2)}.

Is is not in-phase with the secondary voltage unless the load is a pure
resistance.

3. ### John JardineGuest

Yes it is true.
And yes, there is always a small current flowing through the primary.
This 'always-present' primary current is there simply cos' the primary looks
like a big inductor (say 10H if a mains type) sitting across the incoming ac
supply.
Any secondary load currents can be looked at as acting independantly of this
constant but small "magnetising" current. And -no-, this magnetising current
isn't a constant power waste as it's mostly running out of phase with the
incoming voltage. The few real watts of heat that you feel as the
transformer just sits there doing nothing is caused by the resistance of the
primary wire turns (in series with the reactance of that 10H) and some small
losses (hysteresis/eddy) in the transformer steel.
For example... 60Hz, 110Vac supply with a 10H, 1000 ohms transformer
primary.
Primary reactance is 2 X Pi X 60Hz X 10H = 38k ohms.
Resulting 'Magnetising' current must be 110Vac divided by this 38kohms =
30ma (lossless as out of phase with incoming)
This 30ma is also going through the 1000 ohms winding resistance which gives
a real power loss (I^2.R) of 30ma X 30ma X 1000ohms = 0.7watts. The steel
losses aren't calculable but guess at equal to the wire loss. Say a total of
1.4 Watts
regards
john

4. ### Reg EdwardsGuest

I was told a while ago,

=========================

Never listen to old wives.

5. ### BFoelschGuest

Just wanted to add that the magnetizing current is a practicality, not a
theoretical necessity. If you use the standard definition of a "perfect
transformer," which is to say a transformer with infinite primary and
secondary inductance, but a finite ratio of primary to secondary inductance,
the magnetizing current approaches zero. That does not detract from what
anyone else has said, however.

6. ### John PopelishGuest

An ideal (perfect) transformer has no primary current when the
secondary current is zero, and under all load conditions, a primary
current that is related instantaneously ot the secondary current
strictly by the inverse of the turns ratio.

Real transformers have several differences. Add to the above model, a
fixed inductor in parallel with the primary that represents the open
circuit inductance of the windings on the core geometry and material
that have magnetize the core twice (once in each direction) during an
AC cycle. This component of the primary current is inductive, so it
would lag the applied voltage by 90 degrees if the primary had no
resistance. But the actual resistance of the primary reduces this lag
by a bit. So we have a series RC in parallel with the ideal
transformer primary.

So the primary current is larger than what is expected from an ideal
transformer and lags the secondary current a bit. These effects are  