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Transformer Windings Diameters (G5C16)

The 2019-2023 General License question pool asks about the diameters of transformer windings, comparing primary to secondary:

G5C16: Why is the conductor of the primary winding of many voltage step-up transformers larger in diameter than the conductor of the secondary winding?

A. To improve the coupling between the primary and secondary

B. To accommodate the higher current of the primary

C. To prevent parasitic oscillations due to resistive losses in the primary

D. To ensure that the volume of the primary winding is equal to the volume of the secondary winding

Let’s first briefly describe a transformer, then consider the definition of “step up” transformer, and finally address the windings diameter.

Transformers are used to shift AC voltages from one value to another. For example, a transformer may be used as a component of a station’s power supply to shift the 120 VAC of commercial household power to a value closer to that required by a typical transceiver, perhaps something less than 20 VAC since most modern transceivers are designed to operate at or near 13.8 VDC. (Further voltage regulation and rectification of the ~20 VAC power is performed by other components of the power supply beyond the transformer, as described in General License Course Section 6.5.)

A transformer with a square-shaped common core, primary windings around the left side, secondary windings around the right side.
A transformer has primary and secondary windings on a common core of material.

Physically, a transformer is two windings of conductor (typically wire) that share a common core about which the windings are coiled. A core may be made from powdered iron, silicon steel, other metal alloys, or ferrite material, depending upon the specific performance requirements. An AC voltage is applied to one of the windings called the primary. Being a fine inductor component, the primary produces an alternating polarity magnetic field about itself and within the core material. The secondary winding on the core is also a fine inductor, and by the principle of mutual inductance an identical frequency AC voltage is induced in the secondary by the changing magnetic field of the primary winding. That is, the magnetic flux resulting from the primary winding passes through the secondary winding and induces an EMF (voltage).

Step Up / Step Down: The voltage induced in the secondary by the primary is a function of the number of turns in each of the two coils. The ratio of the voltages between the two windings is equal to the ratio of the number of turns in the coils, or

Es/Ep = Ns/Np

where N is the number of turns for each respective winding indicated by lower case 's' or 'p.'

So, if we want to “step down” the voltage from a higher to a lower value, as in the power supply example cited above, we would design our secondary to have fewer windings than our primary. And specifically, we would compute the secondary voltage as

Es = Ep (Ns/Np)

Given a primary voltage, such as 120 VAC, a ratio of the windings may be selected to result in a desired secondary output AC voltage. An example of this computation may be found in General License Course Section 6.5, associated with question G5C06, and discussed in our transformer windings article on question G5C06.

You should see now that a “step up” transformer could also be engineered, changing the primary voltage to a higher value in the secondary by selecting a ratio of windings in which the secondary has a greater number of turns than the primary.

By the law of conservation of energy, the power (P=IE) across the windings of the transformer must be conserved. Thus, the product of current and voltage in the primary must equal the product of current and voltage in the secondary, or

Ip x Ep = Is x Es

Let’s consider a step up transformer case, as the question alludes to. Suppose we seek to step up 12 VAC to 120 VAC by selecting a secondary-to-primary turns ratio of 10:1, perhaps absolute turns of primary = 500 and secondary = 5000. By the conservation of energy equation above this means that the current in the primary (Ip) will have to be 10 times greater than the current in the secondary (Is). For our step up example:

(12V)(50A) = (120V)(5A) = 600W [Primary = Secondary]

Windings Diameter: From the example above it is easy to see that the primary winding in a step up transformer must handle greater current than the secondary. As such, the primary winding conductor must be rated for the required current. Generally, this means the diameter of the wire from which the primary is constructed must be of a sufficient diameter for the expected current, and this diameter will necessarily be greater than the diameter required by the secondary to handle its lower current value.

The answer to General License question G5C16, “Why is the conductor of the primary winding of many voltage step up transformers larger in diameter than the conductor of the secondary winding? is “B. To accommodate the higher current of the primary.”

-- Stu WØSTU


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