Power companies in the United States supply a nominal line voltage of 115 V rms at a frequency of 60 Hz. The actual voltage coming out of a power outlet may vary from 105 V to 125 V rms, depending on the time of day, locality, and other factors. Recall that the relation between the rms value and the peak value of a sine wave is given by
Vrms = 0.707Vp (4-1)
This equation says that the rms voltage equals 70.7 percent of the peak voltage. Recall what rms value means. This is the equivalent dc voltage that would produce the same amount of power over one complete cycle.
Basic Equation
Line voltage is too high for most of the devices used in electronics equipment. This is why a transformer is commonly used in almost all electronics equipment. This transformer steps the ac voltage
down to lower levels that are more suitable for use with devices like diodes and transistors.
Figure 4-1 shows an example of a transformer. The left coil is called the primary winding and the right coil is called the secondary
winding. The number of turns on the primary winding is N1, and the
number of turns on the secondary winding is N2. The vertical lines
between the primary and secondary windings indicate that the turns are wrapped on an iron core.
Figure 4-1 Figure 4-2
Unloaded Transformer Loaded Transformer
With this type of transformer, the coefficient of coupling k
approaches one, which means tight coupling exists. In other words, all the flux produced by the primary winding cuts through the secondary winding. The voltage induced in the secondary winding is given by V N N V 2 2 1 1 (4-2)
The voltages in this equation may be either rms or peak voltages. Just be consistent and use rms for both, or peak for both.
Step-Up Transformer
When the secondary winding has more turns than the primary winding, more voltage is induced in the secondary than in the primary. In other words, when N2/N1 is greater than one, the
transformer is referred to as a step-up transformer. If N1 = 100
turns and N2 = 300 turns, the same flux cuts through three times as
many turns in the secondary as in the primary winding. This is why the secondary voltage is three times as large as the primary voltage.
Step-Down Transformer
When the secondary winding has fewer turns than the primary winding, less voltage is induced in the secondary than in the
primary. In this case, the turns ratio, N2:N1, is less than one, and the
transformer is called a step-down transformer. If N1 = 100 turns
the secondary as in the primary winding, and the secondary voltage is half the primary voltage.
Effect on Current
Figure 4-2 shows a load resistor connected across the secondary winding. Because of the induced voltage across the secondary winding, a current exists. If the transformer is ideal (k = 1 and no power is lost in the windings or the core), the output power equals the input power:
P2 = P1
or
V2I2 = V1I1
We can rearrange the foregoing equation as follows:
I I V V 1 2 2 2
But Eq. (4-2) implies that V2/V1 = N2/N1. Therefore,
I1 I2 N2 N1 or I N N I 1 2 1 2 (4-3)
An alternative way to write the foregoing equation is
I N N I 2 1 2 1 (4-4)
Notice the following. For a step-up transformer, the voltage is stepped up but the current is stepped down. On the other hand, for a step-down transformer, the voltage is stepped down but the current is stepped up.
Example 4–1
Suppose the voltage from a power outlet is 120 V rms. What is the peak voltage?
Solution
Using algebra, we can rewrite Eq. (4-1) in this equivalent form:
V p Vr m s
0 7 0 7.
Now, substitute the rms voltage and calculate the peak voltage:
V p 1 2 0 0 7 0 7 1 7 0 V V .
This tells us that the sinusoidal voltage out of the power outlet has a peak value of 170 V.
Example 4–2
A step-down transformer has a turns ratio of 5:1. If the primary voltage is 120 V rms, what is the secondary voltage?
Solution
Divide the primary voltage by 5 to get the secondary voltage:
V2 1 2 0 5 2 4 V V Example 4–3
Suppose a step-down transformer has a turns ratio of 5:1. If the secondary current is 1 A rms, what is the primary current?
Solution With Eq. (4-3), I1 1 5 0 2 A A .
As a check on this answer, use your common sense as follows, This is a step-down transformer, which means the current is stepped up going from primary to secondary, equivalent to saying the current is stepped down as we go from the secondary to the primary. This means the primary current is five times smaller than the secondary current. Whenever possible, you should check that your answers are logical because it is easy to make a mistake with equations.