chapter  24

## Phase Measurement

WithPeter O’Shea

The notion of “phase” is usually associated with periodic or repeating signals. With these signals, the waveshape perfectly repeats itself every time the period of repetition elapses. For periodic signals one can think of the phase at a given time as the fractional portion of the period that has been completed. This is commonly expressed in degrees or radians, with full cycle completion corresponding to 360° or 2π radians. Thus, when the cycle is just beginning, the phase is zero. When the cycle is half completed, the phase is half of 360°, or 180° (see Figure 24.1). It is important to note that if phase is defined as the portion of a cycle that is completed, the phase depends on where the beginning of the cycle is taken to be. There is no universal agreement on how to specify this beginning. For a sinusoidal signal, probably the two most common assumptions are that the start of the cycle is (1) the point at which the maximum value is achieved and (2) the point at which the negative to positive zero-crossing occurs. Assumption (1) is common in many theoretical treatments of phase and for that reason is adopted in this chapter. It should be noted, however, that assumption (2) has some benefits from a measurement perspective, because the zero-crossing position is easier to measure than the maximum.