If you've ever wondered how houses and buildings use the electricity from power plants, you should learn about the transformers in power grid distributions which convert high-voltage currents to the ones you use in household appliances. These transformers use simple designs across most types of transformers, but can vary greatly in how much they change input voltage based on how they're built.

## Transformer Winding Formula

The transformers that power grid distributions systems use follow simple designs that use coil wound around a magnetic core in different areas.

These coils of wire take incoming current and change the voltage according to the **transformer turns ratio**, which is

for the number windings of the primary coil and secondary coil *N _{p}* and

*N*, respectively, and the voltage of the primary coil and the secondary coil

_{s}*V* and

_{p}*V*, respectively.

_{s}This **transformer winding formula** tells you the fraction by which a transformer changes incoming voltage and that the voltage of the winds of a coil is directly proportional to the number of windings of the coils themselves.

Keep in mind that, although this formula is referred to as "ratio," it is actually a fraction, not a ratio. For example, if you had one winding in the primary coil and four windings in the secondary coil of a transformer, this would correspond to a fraction of 1/4, meaning that the transformer cuts the voltage by a value of 1/4. But the ratio 1:4 means that, for one of something, there are four of something else, which doesn't always mean the same thing as a fraction.

Transformers can increase or decrease voltage, and are known as **step-up** or **step-down** transformers depending on which action they perform. This means the transformer turns ratio will always be positive, but can vary between being greater than one for step-up transformers or less than one for step-down transformers.

The transformer winding formula only holds true when the angles of primary and secondary windings are in phase with one another. This means that, for a given alternating current (AC) power supply that switches back and forth between forward and reverse current, the current in both the primary and secondary windings are in sync with one another during this dynamic process.

There may be some transformers with a transformer turns ratio of 1 that do not change voltage, but, instead, are used to split different circuits from one another or to slightly change the resistance of a circuit.

## Transformer Design Calculator

You can understand the properties of transformers to determine what a transformer design calculator would take into account as a method of determining how to construct transformers themselves.

Though the primary and secondary windings on a transformer are separate from one another, the primary winding induces a current in the secondary windings through a method of inductance. When an AC power supply is sent through the primary windings, current flows through the turns and creates a magnetic field through a method called mutual inductance.

## Transformer Winding Formula and Magnetism

**Magnetic field** describes in what direction and how strong magnetism would act on a moving charged particle. The maximum value of this field is *dΦ/dt* , the rate of change of **magnetic flux** *Φ* over a small period of time.

Flux is a measurement of how much magnetic field flows through a specific surface area such as a rectangular area. In a transformer, the magnetic field lines are sent outward from the magnetic coil around which the wires are wound.

The magnetic flux links both of the windings together, and the magnetic field's strength depends on the amount of current and the number of windings. This can give us a **transformer design calculator** that takes into account these properties.

Faraday's law of inductance that describes how magnetic fields are induced in materials dictates that the voltage by either windings induced

for either primary windings or secondary windings. This is usually referred to as the induced electromotive force (*emf*).

If you were to measure the change in magnetic flux over a small period of time, you could obtain a value of *dΦ/dt* and use it to calculate the *emf*. The general formula for magnetic flux is

for magnetic field *B*, surface area of the plane in the field *A* and the angle between the magnetic field lines and the direction perpendicular to the area *θ*.

You can account for the geometry of the windings around the magnetic core of the transformer to measure flux askat

for an AC power supply where *ω* is the angular frequency (*2πf* for frequency *f*) and *Φ*_{max} is the maximum flux. In this case, frequency *f* refers to the number of waves that pass a given location each second. Engineers also refer to the product of current times the number of turns of windings as "**ampere-turns**," a measure of the coil's magnetizing force.

## Transformer Winding Calculator Examples

If you wanted to compare the experimental results of how the windings of transformers affect their use, you can compare the observed experimental properties to those of a transformer winding calculator.

The software company Micro Digital offers an online Transformer Winding Calculator for calculating Standard Wire Gauge (SWG) or American Wire Gauge (AWG). This lets engineers manufacture wires with the appropriate thickness so they can carry wire charges necessary for their purposes. The transformer calculator turns tells you the individual voltage through each turn of the winding.

Other calculators like the one from the manufacturing company Flex-Core let you calculate the wire size for different practical applications if you enter in the burden rating, the nominal secondary current, the wire length between the current transformer and meter and the input burden of the meter.

The current transformer creates an AC voltage supply in its secondary winding that's proportional to the current in the primary winding. These transformers reduce high voltage currents to lower values using an easy method of monitoring the actual electrical current. The burden is the resistance of the measuring instrument itself to the current sent through it.

Hyperphysics offers an online Transformer Power Calculation interface that lets you use as transformer design calculator or as a transformer resistance calculator. To use it, you need to input a supply voltage frequency, a primary winding inductance, secondary winding inductance, primary winding number of coils, secondary winding number of coils, secondary voltage, primary winding resistance, secondary winding resistance, secondary winding load resistance and mutual inductance.

The mutual inductance *M* accounts for the effect that change in load on secondary coil can exert on the current through the primary with an emf:

for change in current through the primary coil *ΔI _{1}* and change in time

*Δt*.

Any online transformer winding calculator makes assumptions about the transformer itself. Make sure you know how each website calculates the values it claims to do so that you can understand the theory and principles behind transformers in general. How close they are to the transformer winding formula that follows from the physics of a transformer depends on these properties.

References

- Micro Digital: Transformer Winding Calculator
- Bright Hub Engineering: How to Make a Transformer
- Flex-Core: Current Transformer Secondary Wire Sizing Calculator
- Electronics Tutorials: The Current Transformer
- Magnelab: What does CT Burden Mean?
- Lumen: Magnetic Flux, Induction, and Faraday’s Law
- Hyperphysics: Transformer Power Calculation
- Hyperphysics: Mutual Inductance

About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.