# Transformers and flux density

Lots of online discussions on ferrite cored transformer losses might make you think that the core material is in a path in series with the transferred power and that it acts to some extent like an attenuator.

That sort of thinking betrays a lack of understanding of how a transformer works.

If you take a good 50/60Hz 1:1 power transformer, assume no losses, no flux leakage, and ignoring distributed capacitance, you might ask:

1. what is the primary current with nominal voltage applied to the primary and the secondary open circuit;
2. what is the primary current with nominal voltage applied to the primary and rated current flowing in the secondary circuit (resistive load);
3. what is the core flux density in case 2 relative to case 1, much higher, about the same, much lower.

## Flux density in a iron cored transformer

The following expression gives the voltage present on a winding $$E=4.44fNAB_m$$.

where:

E Applied rms voltage
f frequency [Hz]
N turns on the winding where the voltage E is applied
A Magnetic circuit cross-sectional-area enclosed by the winding [m^2]
Bm the maximum flux density [Tesla]

We can rearrange it to make Bm the subject $$B_m=\frac{E}{4.44 f N A}$$.

Readers will observe for that simple model of a transformer, flux density is not a function of load current.

If leakage inductance is taken into account, the applied voltage E is reduced due to the leakage inductance and in fact flux density under load (in a transformer with low leakage inductance) is likely to be slightly less than at no load.

That is not to say transformer losses might not increase significantly with load current, but that it is not due to increased magnetic flux.

Ferrite cored transformers inherit much of this model, though flux leakage may be significantly higher, RF conductor resistance is higher that at 50/60Hz, core materials may be quite lossy at some frequencies (but that does not prevent them being used for a transformer with efficiency acceptable for an application).

Read widely, and think… there is some pretty wooly stuff elaborated on social media.