Why do transformers use so many turns?

When you apply voltage to the primary winding of a power transformer, some current will flow, even when the secondary is open circuit. The amount of this current is determined by the inductance of the primary coil. The primary must have a high enough inductance to keep that current reasonable. For 50 or 60 Hz power transformers, this inductance is pretty high, and you typically cannot get there with a small number of turns in the winding.

If you had only 1 turn on an iron core it might have an inductance of (say) 1 uH. When you apply two turns inductance doesn't double, it quadruples. So two turns means 4 uH. "So what?" you may say!

Well, for a given AC voltage applied, the current taken by that two turn winding is one-quarter of the current for a single turn winding. Take note because this is fundamental in understanding core saturation.

What causes core saturation (something that is to be largely avoided)? The answer is the current and the number of turns. It's called magneto motive force and it has dimensions of ampere turns.

So, with two turns and one quarter the current, the ampere turns (magneto motive force) is half that of a single turn winding. So, immediately we can observe that if two turns took the core to the "edge" of saturation, a single turn coil would significantly saturate and be a big problem.

This is the fundamental reason why transformers use many primary turns. If a certain transformer has 800 turns and is at the point of saturation, significantly reducing the turns will saturate the core.

What happens when the core saturates you might ask. Inductance starts to drop and more current is taken and this saturates the core more and well, you should see where this is going.

Note that this answer has not considered anything other than the primary winding; in effect we are just talking about the primary magnetisation inductance - it is this and this alone that can saturate the core. Secondary load currents have no part to play in core saturation.

Also note that transformers used in high speed switching power supplies have relatively few turns; 10 henry at 50 Hz has an impedance of 3142 ohms and 1 mH at 500 kHz has exactly the same impedance. For a core that naturally produces 10 uH for a single turn, to wind 1 mH requires ten turns (remember it's turns squared in the formula for inductance). For the same core at 50 Hz (impractical of course), 10 henry requires 1000 turns.

If you have an iron core for a transformer, one of its specs is "how many turns one winding must have per one volt when the frequency is given". One can't bypass this spec and have fewer turns without having the following consequences

• reduced efficiency
• more unwanted transversal current that only causes losses, but do not anything useful for the voltage transformation process

The transversal current can be made lower by increasing the inductance of the primary winding.

The turns/volt spec is a consequence of the following list of facts which all have a tendency to make the coil inductances smaller:

• the iron material has limited magnetic permeability
• the iron core can't be made of full iron. It's divided to thin insulated layers to keep the eddy currents small enough in the core. The insulation takes its space and that's off from the iron
• the magnetic flux of one winding partially bypasses the iron and the other windings
• too much transversal current causes magnetic saturation in the iron. The saturation radically reduces the magnetic permeability

How one can fight against these by adding more turns? It's because the inductance grows as the square of the number of the turns. One can arque: But the magnetization (=turns x current) grows too! True, but it grows only linearly, so enough turns, then finally the inductance is high enough to outfight the drawbacks.

Exactly, not all drawbacks. The space is limited. Thus more turns means that the wire must be thinner. This increases the resistance and the resistive losses (=heating).

Transformers work by transferring energy via magnetic flux from one side to the other.

Both sides are made up by inductors, the primary inductor creates a magnetic field, the secondary inductor receives it and induces it into the secondary coil.

The inductance determines the ability to create magnetic flux (\$ \Phi \$) from a current and is proportional:

$$ L = { d\Phi \over di } \text{ and } d\Phi = L * di $$

An inductor's inductance is determined by the number of turns (beside the area, or size):

$$ N = { µ N² A \over l } \text{ (simplified, reduced winding-area-length relation) } $$

See Wikipedia on Inductance

A small transformer is usually desirable, so more turns is better than bigger size (simply put).

The inductance has to match the mains frequency. Otherwise the primary winding would either now allow enough electrical and thus magnetical current to flow (for higher frequencies) or is more like a short circuit (for lower frequencies). Both is not desirable.

Lower frequencies require higher inductance (=more turns or bigger cores). This is the reason why switching power supplies, utilizing higher frequencies in the hundrets of kHz - MHz range, use so small transformers while being able to transfer much more power compared to conventional transformers.

A quote from the Wikipedia article on transformers:

The EMF of a transformer at a given flux density increases with frequency.^[16] By operating at higher frequencies, transformers can be physically more compact because a given core is able to transfer more power without reaching saturation and fewer turns are needed to achieve the same impedance.

(Emphasis mine.)

See Wikipedia on Effect of frequency on transformers

So,

• the power the transformer needs to transfer s determined by the current flowing through its coils
• the current the wire has to conduct determines the wire thickness (which plays into the size)
• the size of the coil and the number of turns determine the inductance
• the inductance at a certain frequency determines the ability to transfer energy

Conclusion: you'd need to make the transformer physically bigger to reduce the number of windings. When reducing the number of windings you lower the efficiency and increase the losses. And this is usually not desirable.

Your basic premise is false, so the question can't really be answered.

Transformers come in many many varieties of voltage and current for their inputs and outputs. Some use many turns of thin wire (high voltage, low current). Some use few turns of thick wire (low voltage, high current).

So the answer to "Why do they not...", is "They do" (when it's appropriate).