# Phase and Polarity …in 60 seconds

Education — By on September 30, 2010 08:00

Phase and polarity are very common and different terms which are all too often used interchangeably. There are very important differences between the two. Here a common misuse of terminology is cleared up.

Phase
In practical terms, ‘phase’ describes the offset measured in degrees that a wave is delayed from its starting position. It is not noticeable when a single wave is played in isolation.

Figure 1 shows two sine waves, one of which (red) has been delayed by a varying number of degrees.

In the first example the red wave has been put 90 degrees out of phase with the blue wave. If the signals are summed together they produce a wave approximately 45 degrees out of phase from the original but with a slightly larger amplitude.

In the second example the waves are 180 degrees out of phase with each other. When the red wave is at maximum amplitude, the blue wave is at minimum amplitude. In theory summing these waves together would result in a wave with zero amplitude.

In the third example, the red wave has been delayed by 360 degrees, in other words it has been delayed by a whole cycle. The two waves are perfectly in phase, just as they would be had there been no delay applied at all. Summing these waves results in a perfectly phase coherent wave of double amplitude.

The fourth example shows the red wave with a delay of 540 degrees. As discussed in the previous post on sine waves, 540 degrees is equivalent to 180 degrees, so the same result occurs as in the second example.

Because the red wave is being delayed by an angular value, which relates directly to a position in the cycle, the frequency of the waves is irrelevant. As long as both waves are at the same frequency, these waves could be of any frequency and the results would remain the same.

Delaying by time
If there are two sine waves of the same frequency and one is delayed by a time value (for example 1ms) instead of by an angular value relative to a cycle, the frequency of the waves determines the amount that they will be in or out of phase.

Figure 2 shows some examples of this behavior. A 1kHz sine wave has a period of 1ms and so if it is delayed by 1ms it remains perfectly in phase with the original wave. If a 500Hz sine wave with a period of 2ms is delayed by 1ms it ends up 180 degrees out of phase with the original.

Multi-frequency and non periodic waveforms
The concept of phase does not transfer simply to a signal made up of more than one frequency. It is easy to see how two simple sinusoids can be out of phase but consider that there are two identical signals, each made up of a 1kHz sine wave and a 650Hz sine wave. As the overall signal is delayed by a certain time value, both frequencies that make up the signal will have different phase relationships to the frequencies in the original, non-delayed signal.

Non-periodic waveforms have more complex phase relationships. If the signal was broken down into its simple sine wave components then each of these could be examined for its periodicity, however this still does not determine the overall period of the signal.

So how is it that a button on an audio console allows a signal of any number of frequencies or any non-periodic length to be put 180 degrees out of phase?

The answer is, it doesn’t. It inverts the polarity of a signal.

Polarity
Inverting the polarity of a signal means to flip its amplitude so that the positive components become negative and the negative components become positive.

If a sine wave has its polarity inverted its plot can look as if it has been put 180 degrees out of phase which is possibly where confusion can occur, however a plot of a non-periodic waveform will clearly reveal this inversion. this can be seen in Figure 3.

Technically the phase reverse, or 180 degree phase button on a console should be labelled ‘polarity inversion’ but convention over time has led some to use this ambiguous term ‘phase’.

Tags:

### 1 Comment

1. Chris Nixon says:

“Here a common misuse of terminology is cleared up.”

Not quite…

The third and fourth examples and diagrams aren’t correct.

Example three says:

“In the third example, the red wave has been delayed by 360 degrees, in other words it has been delayed by a whole cycle. The two waves are perfectly in phase, just as they would be had there been no delay applied at all. Summing these waves results in a perfectly phase coherent wave of double amplitude.”

The two waves are only perfectly in phase during cycles 2 and 3. The waveforms on the left show 3 blue cycles and 2 red cycles. Why is the 3rd red cycle not shown? The first cycle in the resulting signal would be made up of only the first blue cycle. The second cycle in the resulting signal would be made up of the second blue cycle and the first red cycle, this cycle would be of double the amplitude of the first cycle. Cycle 3 would be made up of the third blue cycle and the second red cycle, again, double amplitude. Cycle 4 which for some reason isn’t shown would be made up of only the third red cycle, this wave would be of “normal” amplitude. Why on earth does the resulting signal show 3 cycles of equal amplitude?

This is absolutely NOT the same as if there had been no delay applied. The resulting signal is now one cycle longer and has amplitude variation.

There’s also a rise above the centre line at the end of the red and blue waves which hasn’t managed to appear in the resulting signal.

Example four says:

“The fourth example shows the red wave with a delay of 540 degrees. As discussed in the previous post on sine waves, 540 degrees is equivalent to 180 degrees, so the same result occurs as in the second example.”

540 degrees is NOT equivalent to 180 degrees. You could call it “one complete cycle plus 180 degrees” if you wanted. As explained above, this matters at the beginning and end of the resulting signal.

Just look at the fourth diagram! Why are those first two blue cycles not present in the resulting signal? There isn’t anything there to null them! Where is the last red cycle?

It wouldn’t matter so much, but the intention of the article is apparently to clear up confusion, so it needs to be spot on.

Chris