**Introduction**

Amplitude also can be called *magnitude, level, strength* , or *intensity* . Depending on the quantity being measured, the amplitude of an ac wave can be specified in amperes (for current), volts (for voltage), or watts (for power).

**Instantaneous Amplitude**

The *instantaneous amplitude* of an ac wave is the voltage, current, or power at some precise moment in time. This constantly changes. The manner in which it varies depends on the waveform. Instantaneous amplitudes are represented by individual points on the wave curves.

**Average Amplitude**

The *average amplitude* of an ac wave is the mathematical average (or mean) instantaneous voltage, current, or power evaluated over exactly one wave cycle or any exact whole number of wave cycles. A pure ac sine wave always has an average amplitude of zero. The same is true of a pure ac square wave or triangular wave. It is not generally the case for sawtooth waves. If you know calculus, you know that the average amplitude is the integral of the waveform evaluated over one full cycle.

**Peak Amplitude**

*The peak amplitude* of an ac wave is the maximum extent, either positive or negative, that the instantaneous amplitude attains. In many waves, the positive and negative peak amplitudes are the same. Sometimes they differ, however. Figure 13-9 is an example of a wave in which the positive peak amplitude is the same as the negative peak amplitude. Figure 13-10 is an illustration of a wave that has different positive and negative peak amplitudes.

**Fig. 13-9** . Positive and negative peak amplitudes. In this case, they are equal.

**Fig. 13-10** . A wave in which the positive and negative peak amplitudes differ.

**Peak-to-peak Amplitude**

The *peak-to-peak (pk-pk) amplitude* of a wave is the net difference between the positive peak amplitude and the negative peak amplitude (Fig. 13-11). Another way of saying this is that the pk-pk amplitude is equal to the positive peak amplitude plus the absolute value of the negative peak amplitude.** **

**Fig. 13-11** . Peak-to-peak amplitude.

Peak to peak is a way of expressing how much the wave level “swings” during the cycle.

In many waves, the pk-pk amplitude is twice the peak amplitude. This is the case when the positive and negative peak amplitudes are the same.

**Root-mean-square Amplitude**

Often it is necessary to express the *effective amplitude* of an ac wave. This is the voltage, current, or power that a dc source would produce to have the same general effect in a real circuit or system. When you say a wall outlet has 117 V, you mean 117 effective volts. The most common figure for effective ac levels is called the *root-mean-square* , or *rms, value* .

The expression *root mean square* means that the waveform is mathematically “operated on” by taking the square root of the mean of the square of all its instantaneous values. The rms amplitude is not the same thing as the average amplitude. For a perfect sine wave, the rms value is equal to 0.707 times the peak value, or 0.354 times the pk-pk value. Conversely, the peak value is 1.414 times the rms value, and the pk-pk value is 2.828 times the rms value. The rms figures often are quoted for perfect sine-wave sources of voltage, such as the utility voltage or the effective voltage of a radio signal.

For a perfect square wave, the rms value is the same as the peak value, and the pk-pk value is twice the rms value and twice the peak value. For sawtooth and irregular waves, the relationship between the rms value and the peak value depends on the exact shape of the wave. The rms value is never more than the peak value for any waveshape.

**Superimposed Dc**

Sometimes a wave can have components of both ac and dc. The simplest example of an ac/dc combination is illustrated by the connection of a dc source, such as a battery, in series with an ac source, such as the utility main.

Any ac wave can have a dc component along with it. If the dc component exceeds the peak value of the ac wave, then fluctuating or pulsating dc will result. This would happen, for example, if a 200-V dc source were connected in series with the utility output. Pulsating dc would appear, with an average value of 200 V but with instantaneous values much higher and lower. The waveshape in this case is illustrated by Fig. 13-12.

**Fig. 13-12** . Composite ac/dc wave resulting from 117-V rms ac in series with + 200-V dc.

**Amplitude Practice Problems**

**Problem 1**

An ac sine wave measures 60 V pk-pk. There is no dc component. What is the peak voltage?** **

**Solution 1**

In this case, the peak voltage is exactly half the peak-to-peak value, or 30 V pk. Half the peaks are + 30 V; half are −30 V.

**Problem 2**

Suppose that a dc component of +10 V is superimposed on the sine wave described in Problem 13-5. What is the peak voltage?

**Solution 2**

This can’t be answered simply, because the absolute values of the positive peak and negative peak voltages differ. In the case of Problem 13-5, the positive peak is +30 V and the negative peak is −30 V, so their absolute values are the same. However, when a dc component of +10 V is superimposed on the wave, both the positive peak and the negative peak voltages change by + 10 V. The positive peak voltage thus becomes +40 V, and the negative peak voltage becomes −20 V.

Practice problems of these concepts can be found at: Alternating Current Practice Test