# Classical Physical Explanation for Turn Ratio in Transformer

Hello. I'm trying to understand why, in terms of Maxwell's Equations, the ratio of the number of turns in a transformer converts an input voltage to an output voltage. EE explanations only seem to go as deep as this article: http://en.wikipedia.org/wiki/Transformer#Basic_principles

They state that the ratio of the input voltage to output voltage is determined by the number of turns in the primary and secondary coil. But why? What's actually happening to various field lines to change voltages?

## Answers and Replies

Drakkith
Staff Emeritus
Science Advisor
Have you studied electromagnetic induction?

Yes, but not in the usual way.

I'm familiar with maxwell's equations and all of that notation, I'm just trying to analyze this part in those terms.

I'm looking for someone to explain in terms of the mechanisms of induction, preferably with calculus.

Is there a way I can further refine the question to get more help?

Hello. I'm trying to understand why, in terms of Maxwell's Equations, the ratio of the number of turns in a transformer converts an input voltage to an output voltage. EE explanations only seem to go as deep as this article: http://en.wikipedia.org/wiki/Transformer#Basic_principles

They state that the ratio of the input voltage to output voltage is determined by the number of turns in the primary and secondary coil. But why? What's actually happening to various field lines to change voltages?

An alternating current will create magnetic and electric field components around the wire. Magnetic field component produced by input is transferred (carried like waveguide) to secondary winding (output) via a ferromagnetic core. Inversely, secondary winding is exposed to magnetic fields carried by ferromagnetic core and induces back a current at open terminals of output. Core is the physical link to carry magnetic fields. Turn ratios determine voltage ratio because at each turn you roll more, you will be exposing more wire length to the magnetic field.

Check out Faraday's law.

The heart of the matter is magnetic flux linkage. Induction is the process where a magnetic field changing in time across some area in space gives rises to a curling electric field along the edge of that area (the electric field lines literally curl around in a circle). If you happen to have a conducting wire loop placed along the edge of that area containing, which by definition contain free charge, the curling electric field will exert a force on the charges, driving a current through the wire. The key is the amount of magnetic field changing across the area spanned by the loop of wire - the magnetic flux linkage. If you increase the area spanned by the loop of wire, but leave everything else the same, you increase the flux linkage, and thus the inductance. But instead of using ever bigger loops of wire to get more induction, you can also stack loops. Two loops of wire sitting next to each other in a uniform changing magnetic field have as much flux linkage as two loops stacked on top of each other. This is a very space saving way to control the area exposed to the field, and thus the flux linkage: coil a wire so that you make a stack of loops. If you have 20 turns on a coil, you are stacking 20 loops, and thus have 20 times the area and the inductance on a single loop.