# Transformer turns ratio relationship

### Transformer Basic Operation

Part (A) of the figure shows a transformer whose primary consists of ten turns of This proportion also shows the relationship between the number of turns in. The amount of voltage induced in each turn of a transformer secondary winding will be the same as the voltage across each turn of the primary. TRANSFORMER THEORY Transformers Turns Ratio Each winding of a The turns ratio will establish the proper relationship between the primary and.

If any three of the quantities in the above formulas are known, the fourth quantity can be calculated.

### TURNS AND VOLTAGE RATIOS

A transformer has turns in the primary, 50 turns in the secondary, and volts applied to the primary Ep. What is the voltage across the secondary E s? There are turns of wire in an iron-core coil. If this coil is to be used as the primary of a transformer, how many turns must be wound on the coil to form the secondary winding of the transformer to have a secondary voltage of one volt if the primary voltage is five volts? The ratio of the voltage 5: Sometimes, instead of specific values, you are given a turns or voltage ratio.

In this case, you may assume any value for one of the voltages or turns and compute the other value from the ratio. For example, if a turn ratio is given as 6: The transformer in each of the above problems has fewer turns in the secondary than in the primary.

- Impedance Ratio

As a result, there is less voltage across the secondary than across the primary. The ratio of a four-to-one step-down transformer is written as 4: A transformer that has fewer turns in the primary than in the secondary will produce a greater voltage across the secondary than the voltage applied to the primary. A transformer in which the voltage across the secondary is greater than the voltage applied to the primary is called a STEP-UP transformer. The ratio of a one-to-four step-up transformer should be written as 1: Notice in the two ratios that the value of the primary winding is always stated first.

The magnetic field produced by the current in the secondary interacts with the magnetic field produced by the current in the primary. This interaction results from the mutual inductance between the primary and secondary windings. It is also the means by which energy is transferred from the primary winding to the secondary winding. The inductance which produces this flux is also common to both windings and is called mutual inductance. Figure 11 shows the flux produced by the currents in the primary and secondary windings of a transformer when source current is flowing in the primary winding.

When a load resistance is connected to the secondary winding, the voltage induced into the secondary winding causes current to flow in the secondary winding.

This current produces a flux field about the secondary shown as broken lines which is in opposition to the flux field about the primary Lenz's law. Thus, the flux about the secondary cancels some of the flux about the primary. With less flux surrounding the primary, the counter emf is reduced and more current is drawn from the source.

The additional current in the primary generates more lines of flux, nearly reestablishing the original number of total flux lines. The ampere-turn I X N is a measure of magneto motive force; it is defined as the magnetomotive force developed by one ampere of current flowing in a coil of one turn.

The flux which exists in the core of a transformer surrounds both the primary and secondary windings. Since the flux is the same for both windings, the ampere-turns in both the primary and secondary windings must be the same. When power is then reapplied, the residual field will cause a high inrush current until the effect of the remaining magnetism is reduced, usually after a few cycles of the applied AC waveform. On transformers connected to long, overhead power transmission lines, induced currents due to geomagnetic disturbances during solar storms can cause saturation of the core and operation of transformer protection devices.

The higher initial cost of the core material is offset over the life of the transformer by its lower losses at light load.

These materials combine high magnetic permeability with high bulk electrical resistivity.

## Transformer

For frequencies extending beyond the VHF bandcores made from non-conductive magnetic ceramic materials called ferrites are common. Toroidal cores[ edit ] Small toroidal core transformer Toroidal transformers are built around a ring-shaped core, which, depending on operating frequency, is made from a long strip of silicon steel or permalloy wound into a coil, powdered iron, or ferrite.

The closed ring shape eliminates air gaps inherent in the construction of an E-I core. The primary and secondary coils are often wound concentrically to cover the entire surface of the core. This minimizes the length of wire needed and provides screening to minimize the core's magnetic field from generating electromagnetic interference.

### Impedance Ratio

Toroidal transformers are more efficient than the cheaper laminated E-I types for a similar power level. Other advantages compared to E-I types, include smaller size about halflower weight about halfless mechanical hum making them superior in audio amplifierslower exterior magnetic field about one tenthlow off-load losses making them more efficient in standby circuitssingle-bolt mounting, and greater choice of shapes. The main disadvantages are higher cost and limited power capacity see Classification parameters below.

Because of the lack of a residual gap in the magnetic path, toroidal transformers also tend to exhibit higher inrush current, compared to laminated E-I types.

Ferrite toroidal cores are used at higher frequencies, typically between a few tens of kilohertz to hundreds of megahertz, to reduce losses, physical size, and weight of inductive components. A drawback of toroidal transformer construction is the higher labor cost of winding. This is because it is necessary to pass the entire length of a coil winding through the core aperture each time a single turn is added to the coil.

As a consequence, toroidal transformers rated more than a few kVA are uncommon. Small distribution transformers may achieve some of the benefits of a toroidal core by splitting it and forcing it open, then inserting a bobbin containing primary and secondary windings. The air which comprises the magnetic circuit is essentially lossless, and so an air-core transformer eliminates loss due to hysteresis in the core material.

A large number of turns can be used to increase magnetizing inductance, but doing so increases winding resistance and leakage inductance.

## Module 11.1

Air-core transformers are unsuitable for use in power distribution. Air cores are also used for resonant transformers such as Tesla coils, where they can achieve reasonably low loss despite the low magnetizing inductance. Windings are usually arranged concentrically to minimize flux leakage. Cut view through transformer windings.

High-frequency transformers operating in the tens to hundreds of kilohertz often have windings made of braided Litz wire to minimize the skin-effect and proximity effect losses.