### Expressions of Amplitude

Amplitude is also 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). In addition to this, there are several different ways in which amplitude can be expressed.

#### Instantaneous Amplitude

The instantaneous amplitude of an ac wave is the amplitude at some precise moment, or instant, 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.

#### Peak Amplitude  (A) A cycle is divided into 360 equal parts, called degrees. (B) A wave with unequal positive and negative peak amplitudes.

The peak (pk) amplitude of an ac wave is the maximum extent, either positive or negative, that the instantaneous amplitude attains. In many situations, the positive and negative peak amplitudes of an ac wave are the same. But sometimes they differ. Figure A is an example of a wave in which the positive peak amplitude is the same as the negative peak amplitude. Figure B is an illustration of a wave that has different positive and negative peak amplitudes.

#### 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 (above figure). The peak-to-peak amplitude is equal to the positive peak amplitude plus the negative peak amplitude. When the positive and negative peak amplitudes of an ac wave are equal, the peak-to-peak amplitude is exactly twice the peak amplitude.

#### 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 have to produce in order to have the same general effect as a given ac wave. When you say a wall outlet provides 117 V, you mean 117 effective volts. This is not the same as the peak or peak-to-peak voltage.

The most common expression for effective ac intensity is called the root-mean-square (rms) amplitude. The terminology reflects the fact that the ac wave is mathematically operated on by taking the square root of the mean (average) of the square of all its instantaneous amplitudes.

In the case of a perfect ac sine wave, the rms value is equal to 0.707 times the peak value, or 0.354 times the peak-to-peak value. Conversely, the peak value is 1.414 times the rms value, and the peak-to-peak value is 2.828 times the rms value. The rms amplitude is often specified when talking about utility ac, radio-frequency (RF) ac, and audio-frequency (AF) ac.

For a perfect square wave, the rms value is the same as the peak value, and half the peak-to-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. But the rms value is never greater than the peak value for any type of ac wave.

#### Superimposed DC Sometimes a wave has components of both ac and dc. The simplest example of an ac/dc combination is illustrated by the connection of a dc voltage source, such as a battery, in series with an ac voltage source, like the utility mains. An example is shown in the schematic diagram of Above figure. Imagine connecting a 12-V automotive battery in series with the wall outlet. (Do not try this experiment in real life!) When this is done, the ac wave is displaced either positively or negatively by 12 V, depending on the polarity of the battery. This results in a sine wave at the output, but one peak is 24 V (twice the battery voltage) more than the other.

Any ac wave can have dc components 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 output of a common utility ac outlet, which has peak voltages of approximately 165 V. Pulsating dc would appear, with an average value of 200 V but with instantaneous values much higher and lower. The wave shape in this case is shown in following Figure. Waveform resulting from a 117-V ac sine-wave source connected in series with a +200-V dc source.