Contrary to Popular Belief, Phase and Polarity Are Not the Same Thing
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FIG. 4:Complex tones, such as musical sounds, contain many partials. Here, the first four partials of a simple musical tone are shown. You can see that each partial's cycle is a different length. |
This isn’t true with complex signals, because they contain many partials at different frequencies. As a result, each partial’s cycle has a different length, which means they can’t all be shifted by half of a cycle at the same time. For example, Fig. 4 shows the components of a complex tone with a fundamental frequency of 100 Hz and other partials at 200 Hz, 300 Hz, and 400 Hz. The partials have been graphed separately to illustrate the different cycle lengths.
Suppose you make a copy of this signal and shift the copy’s phase by 180 degrees at the fundamental. The copied signal would be moved in time by one-half of the fundamental’s cycle. If you then combine the original and the copy, the fundamentals cancel each other out. Just as in Fig. 1, the voltages would always add up to 0V.
However, the next partial, 200 Hz, has a cycle that is only half as long as the fundamental’s cycle. When the fundamental is shifted by 180 degrees, the second partial is shifted by one full cycle, or 360 degrees. Therefore, the second partial retains the same polarity in both signals (offset by one cycle), and its amplitude doubles instead of getting canceled out. The phase shift of the third partial is 540 degrees, or one cycle (360 degrees) plus 180 degrees more, so it’s canceled out. At 400 Hz, there’s 720 degrees of phase shift. Because 720 degrees is twice 360 degrees, or two complete cycles, the 400 Hz partial also doubles in amplitude. In this simple example, the odd-numbered partials are canceled out, and the even-numbered partials double in amplitude. The result is comb filtering.
The bottom line is this: applying a phase shift of 180 degrees to a complex signal is not the same thing as reversing its polarity, as it is with sine waves. Nevertheless, identical signals with opposite polarities are often referred to as being “out of phase.” For example, on many mixing consoles, each input has a switch labeled “Phase,” and the user manual might say that the switch “puts the signal 180 degrees out of phase.” This switch doesn’t really shift the signal in time; it simply inverts the signal’s polarity.
Why the “Phase” label? Well, in the early days of electronics, the term phase was used to refer to the polarity of audio signals, and the word polarity was reserved for describing power signals. Technically, this terminology isn’t correct for complex signals, but the industry still uses this convention.
Reprinted with permission from
Magazine, November, 2000© 2000, Intertec Publishing, A Primedia Company All Rights Reserved.