**Magnetic lines of flux between two aligned coils of wire when one of the coils carries fluctuating or alternating current.**

When two wires are near each other and one of them carries a fluctuating current, a fluctuating current is induced in the other wire. This effect is known as electromagnetic induction. All ac transformers work according to the _{pri}nciple of electromagnetic induction. If the first wire carries sine-wave ac of a certain frequency, then the induced current is sine-wave ac of the same frequency in the _{sec}ond wire. The closer the two wires are to each other, the greater is the induced current, for a given current in the first wire. If the wires are wound into coils and placed along a common axis (above figure), the induced current will be greater than if the wires are straight and parallel. Even more coupling, or efficiency of induced-current transfer, is obtained if the two coils are wound one atop the other.

_{pri}mary and _{sec}ondary

The two windings, along with the core on which they are wound, constitute a transformer. The first coil is called the _{pri}mary winding, and the _{sec}ond coil is known as the _{sec}ondary winding. These are often spoken of simply as the _{pri}mary and the _{sec}ondary. The induced current in the _{sec}ondary creates a voltage between its end terminals. In a step-down transformer, the _{sec}ondary voltage is less than the _{pri}mary voltage. In a step-up transformer, the _{sec}ondary voltage is greater than the _{pri}mary voltage. The _{pri}mary voltage is abbreviated E_{pri}, and the _{sec}ondary voltage is abbreviated E_{sec}. Unless otherwise stated, effective (rms) voltages are always specified.

The windings of a transformer have inductance, because they are coils. The required inductances of the _{pri}mary and _{sec}ondary depend on the frequency of operation, and also on the resistive part of the impedance in the circuit. As the frequency increases, the needed inductance decreases. At high resistive impedances, more inductance is generally needed than at low resistive impedances.

#### Turns Ratio

**The _{pri}mary voltage (E_{pri}) and _{sec}ondary voltage (E_{sec}) in a transformer depend on the number of turns in the _{pri}mary winding (T_{pri}) versus the number of turns in the _{sec}ondary winding (T_{sec}).**The

_{pri}mary-to-

_{sec}ondary turns ratio in a transformer is the ratio of the number of turns in the

_{pri}mary, T

_{pri}, to the number of turns in the

_{sec}ondary, T

_{sec}. This ratio is written T

_{pri}:T

_{sec}or T

_{pri}/T

_{sec}. In a transformer with excellent

_{pri}mary-to-

_{sec}ondary coupling, the following relationship always holds:

E

_{pri}/E

_{sec}= T

_{pri}/T

_{sec}

That is, the

_{pri}mary-to-

_{sec}ondary voltage ratio is always equal to the

_{pri}mary-to-

_{sec}ondary turns ratio (above figure ).

#### Problem 1

**Suppose a transformer has a _{pri}mary-to-_{sec}ondary turns ratio of exactly 9:1. The ac voltage at the _{pri}mary is 117 V rms. Is this a step-up transformer or a step-down transformer? What is the voltage across the _{sec}ondary?**This is a step-down transformer. Simply plug in the numbers in the preceding equation and solve for E

_{sec}, as follows:

**E**

117/E

1/E

E

= 13.0 V rms

_{pri}/E_{sec}= T_{pri}/T_{sec}117/E

_{sec}= 9.001/E

_{sec}= 9.00/117E

_{sec}= 117/9.00= 13.0 V rms

#### Problem 2

**Consider a transformer with a _{pri}mary-to-_{sec}ondary turns ratio of exactly 1:9. The voltage at the _{pri}mary is 121.4 V rms. Is this a step-up transformer or a step-down transformer? What is the voltage at the _{sec}ondary?**

This is a step-up transformer. Plug in numbers and solve for E

_{sec}, as follows:

**121.4/E**

E

E

= 1093 V rms

_{sec}= 1/9.000E

_{sec}/121.4 = 9.000E

_{sec}= 9.000 × 121.4= 1093 V rms

Sometimes the

_{sec}ondary-to-

_{pri}mary turns ratio is given, rather than the

_{pri}mary-to-

_{sec}ondary turns ratio. This is written T

_{sec}/T

_{pri}. In a step-down unit, T

_{sec}/T

_{pri}is less than 1. In a step-up unit, T

_{sec}/T

_{pri}is greater than 1. When you hear someone say that such-and-such a transformer has a certain “turns ratio,” say 10:1, be sure of which ratio is meant, T

_{pri}/T

_{sec}or T

_{sec}/T

_{pri}! If you get it wrong, you’ll have the

_{sec}ondary voltage wrong by a factor of the square of the turns ratio.

#### Ferromagnetic Cores

**Schematic symbols for transformers. At A, air core. At B, laminated iron core. At C, ferrite or powdered iron core.**

If a ferromagnetic substance such as laminated iron or powdered iron is placed within the pair of coils, the extent of coupling is increased far above that possible with an air core. But this improvement in coupling is obtained at a _{pri}ce. Some energy is invariably lost as heat in the core. Also, ferromagnetic cores limit the maximum frequency at which a transformer will work well. The schematic symbol for an air-core transformer consists of two inductor symbols back-toback (above figure A). If a laminated iron core is used, two parallel lines are added to the schematic symbol (above figure B). If the core is made of powdered iron, the two parallel lines are broken or dashed (above figure C).

In transformers for 60-Hz utility ac, and also for low audio-frequency (AF) use, sheets of an alloy called silicon steel, glued together in layers, are often employed as transformer cores. The silicon steel is sometimes called transformer iron. The reason layering is used, rather than making the core from a single mass of metal, is that the magnetic fields from the coils cause currents to flow in a solid core. These eddy currents go in circles, heating up the core and wasting energy that would otherwise be transferred from the _{pri}mary to the _{sec}ondary. Eddy currents are choked off by breaking up the core into layers, so that currents cannot flow very well in circles.

A rather esoteric form of loss, called hysteresis loss, occurs in all ferromagnetic transformer cores, but especially laminated iron. Hysteresis is the tendency for a core material to be sluggish in accepting a fluctuating magnetic field. Laminated cores exhibit high hysteresis loss above the AF range, and are therefore not good above a few kilohertz.

At frequencies up to several tens of megahertz, powdered iron works well for RF transformers. This material has high magnetic permeability and concentrates the flux efficiently. High permeability cores minimize the number of turns needed in the coils, and this minimizes the loss that occurs in the wires.