by Joe Evans, Ph.D
December 17, 2011

Last of four parts

Last month, we studied the properties and effects of resistive, inductive and capacitive loads in an AC circuit. This month, we will take self induction a step further and apply it to that very simple machine that is at the heart of AC power—the transformer.

As I mentioned in Part One, (Pumps & Systems, June 2010)a unique quality of AC power is that its voltage can be changed easily and in either direction—up or down. This allows us to generate power at some voltage and step it up to a higher voltage for long distance transmission. This decreases losses due to heat and significantly reduces the wire size. Once it reaches its point of use, voltage can be reduced to a useable intensity. The key element in this process is the transformer, and the key to its operation is a phenomenon known as mutual induction.

Mutual Induction

If two coils of wire are placed near each other (see Figure 1), an alternating current flowing in one will create a magnetic field that induces a voltage and current in the one nearby, even though they are not in direct contact. This occurs because the lines of flux associated with the magnetic field extend well beyond the coil that created them. This property is called mutual inductance or mutual induction, and it is the basis of the transformer. The transformer gets its name from the process of transforming electrical energy into magnetic energy and then back to electrical energy. The coil that produces the magnetic field is called the primary (input) and the coil that intercepts that field is called the secondary (output).

Figure 1 


Figure 1

Although some transformers consist of coils separated by an air gap, most use insulated wire wound about a laminated iron core (see Figure 2). The iron core increases transformer efficiency by directing nearly all the flux produced by the primary through the secondary coil. The laminations reduce eddy current losses that would be much higher in a solid core design. Depending on the design and capacity, transformer efficiency can range from 20 to 99 percent. Larger ones—for example those designed for power distribution applications—operate at 98 percent or better. Another important property of the transformer is electrical isolation. Since the primary and secondary coils are not in contact, the power source is isolated from the point of use.

Figure 2 

Figure 2

Voltage, Current and the Turns Ratio

According to Faraday's law, voltage produced in the secondary of a transformer depends on the voltage in the primary and the number of turns (loops) in the primary and secondary coils. This may sound a little complicated, but this relationship can be stated very simply with something called the turns to voltage ratio. The equation below—where V is voltage, N is the number of turns, p is the primary and s is the secondary—explains this relationship:

Vs = (Ns / Np) x Vp

Secondary voltage is directly proportional to the product of the turns ratio and primary voltage. If Ns is greater than Np, then the voltage in the secondary coil is greater than that of the primary coil, and the transformer is called a step-up transformer. If the opposite is true, we have a step-down transformer. For example, suppose a transformer has a primary with 1,000 turns and a secondary with 100 turns. Based on the equation above, the turns ratio is 1/10 or 0.1. If the voltage feeding the primary is 1,200 V then the secondary voltage will be 120V.
However, what about current? How do we calculate its change? The transformer is an intelligent machine because it automatically adjusts the current to keep power (in watts) constant. A slight modification of the original equation explains this relationship:

Is = (Np / Ns) x Ip

In the equation above, current (I) replaces voltage and the turns ratio is reversed. When fewer turns are in the secondary, a transformer steps down voltage, but it increases current and, therefore, keeps power constant. In the case of our step-down transformer example above, if the primary is fed by 1,200 V at 1 A, then the secondary would provide 120 V at 10 A. Both volt / amp combinations provide 1,200 W of power.

Winding Configurations

Transformers allow an extremely flexible secondary output and are not limited to a single secondary winding. Figure 3 shows an example of a typical power supply transformer. The primary is fed by 110 V and induces three individual secondary coils providing 5 V, 6.3 V and 700 V. The 700 V coil shows another feature of the transformer. A “tap” placed at the center of the coil provides two 350-V outputs in addition to its full voltage output. Multiple taps may also be placed within a single coil.

Figure 3 

Figure 3