# What is a 'phase' exactly....

#### Himanshoo

Joined Apr 3, 2015
260
Hello guys....

What exactly is a phase and phase shift? I want a complete intuitive explanation because I am tired of reading explanations which explains phase/ phase shifts in terms of degrees and radians because it makes me hard to visualise phase physically.

I have read numerous content over it like.....

1.The time relationship between two or more signals in a circuit is called phase.

2.Phase is delay.

3.Phase shift is a ‘delay’

4.The phase is the timing of oscillations at some point.

5.The phase shift means the two signals will arrive at the receiving antenna, at two different times.

6.Phase is a frequency dependent time delay......and so on and so forth..

Can someone provide a singular theory about phase? so that I could conclude my findings above.

Thanks!

#### Hypatia's Protege

Joined Mar 1, 2015
3,208
The time difference between two or more signals in a system represents phase differential
---Edited and emphasized ---

Respectfully - You seem to be over-thinking the matter -- the above quoted/edited text encapsulates the concept nicely (if less than eloquently)...

Best regards
HP

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#### AnalogKid

Joined Aug 1, 2013
8,298
Phase is a word used to describe a particular aspect of the relationship between two signals. It does not describe something new or different, just in a way that captures an important aspect. Here is how it works.

A sine wave, square wave, or any periodic waveform has a frequency, and the inverse of its frequency is its period. For example, a 1 kHz sine wave has a period of 1 millisecond, 1 ms. Starting at the positive zero-crossing, one quarter of the way through one cycle is 0.25 ms, and the wave is at its positive peak. So you can describe where you are within the cycle by counting over the fractions of milliseconds. But if you also are talking about a 5 kHz sine wave, the positive peak is not at 0.25 ms, it is at 0.05 ms. So a discussion about where you are in both sinewaves becomes very difficult because you always have to talk about two different numbers. To improve this mess, divide a single cycle of any wave into 360 parts, called degrees. Now, 1/4 of the way through a cycle is 90 degrees, no matter how fast or slow a cycle is. Milliseconds describe absolute location; degrees describe relative location. 90 degrees always is 1/4 of the way through a cycle, no matter how long a cycle is. Once you understand the difference, this makes some kinds of discussions more clear and easier to follow.

If you have two sine saves, both 1 kHz, then for each one the period is1 millisecond, 1 ms. Imagine an oscilloscope display with two traces. If the two signals are "in phase", this is another way of saying that there is no time difference between the positive zero crossings of the two waves; the two wave images can be superimposed perfectly, looking like one wave. Now, what happens if the two waves are not perfectly synchronized? One wave looks like it is shifted to the right or left of the other wave. The zero crossings and peaks to not align perfectly. One way to describe this is that (for example), the positive peak or wave B occurs 125 microseconds after the positive peak of wave A. That's a nice number, but unless you know the exact frequency of the waves it doesn't tell you how big the delay is compared to the overall period of one cycle. BUT, it you express the time difference in terms of a fraction of one cycle, then the discussion becomes more clear. If we measure that fraction in 360ths of a cycle called degrees, then the example above can be stated as wave B is 45 degrees behind wave A. The name of this kind of time relationship between two similar waves is called Phase. A difference is called a phase shift or phase delay. Technically, these two terms mean exactly the same thing. They are used in different situations to describe what is happening in different contexts. For example, if you are comparing the propagation time of a radio wave signal and the same signal coming through coax cable, you can say that over a one mile distance the signal from the cable arrives xxx nanoseconds later than the radio signal, or you can say that the cable has a phase delay of yyy degrees. When designing an active filter, the inband and out of band frequencies are affected differently, and this usually is called a phase shift.

ak

#### Dodgydave

Joined Jun 22, 2012
8,797
Phase shift, or phase delay, is when two identical signals are transmitted or received that are not in synchronisation with each other, one signal arrives before the other, so the time difference between them is referred to as a # phase shift# which is from 1 to 180' degrees alignment,rather than in seconds or microseconds.

Look at pictures of a single sinewave, and look at three phase signals, each sinewave is 120 degrees apart,

As for TV signals, if you receive a signal direct from the transmitter it will give you a perfect picture, if you receive the same signal from a reflective object like a metal building or hill, there will be a delay when the second signal arrives, thus a phase shift which will cause ghosting.

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#### Hypatia's Protege

Joined Mar 1, 2015
3,208
@Himanshoo

As a visual aid, please consider these plots of the sine and cosine functions -- note that they represent two sine waves having a phase relationship of π/2 (i.e. 90°)

Best regards
HP

#### wayneh

Joined Sep 9, 2010
16,235
"Phase" is the comparison of when the wave peaks arrive for multiple signals. If they arrive together, they are in phase. If not, there are various ways to describe the gap. Because the waves are cyclic, it's most convenient to relate the gap to degrees or radians of a circle. Both describe how far along the cycle you go for the first wave until the second signal's wave peak comes along.

#### Papabravo

Joined Feb 24, 2006
12,878
Hello guys....

What exactly is a phase and phase shift? I want a complete intuitive explanation because I am tired of reading explanations which explains phase/ phase shifts in terms of degrees and radians because it makes me hard to visualise phase physically.

...
Thanks!
I think this is an unreasonable request and does you an enormous disservice. I am truly sorry for your difficulties in acquiring information which is presented in precise and unambiguous terms which you cannot adequately process. I urge you to redouble your efforts to process the appropriate information so you can make maximal use of the knowledge you have gained.

#### GetDeviceInfo

Joined Jun 7, 2009
1,679
A bus takes 1hour to complete its route, so if it stops in front of your house, it will stop every hour, on the hour. This is the 'phase' of that bus. To increase service, a second bus is added to the route, in such a way that it stops every hour, but on the 1/2 hour. The 'phase' of this bus is equivalent to the first bus, shifted by 1/2 the period. Imagine if one falls behind schedule by ten minutes. You are envisioning a further phase shift.

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#### Papabravo

Joined Feb 24, 2006
12,878
To supply some intuition. If I tell you I have a coordinate system that uses two numbers, x and y, to locate any point in a 2 dimensional plane. That is a fairly precise and intuitive description of something we all learned in high school. Now if I tell you that I can transform any pair of numbers, (x,y), into another pair called M and φ, and that these two numbers can also locate any point in a two dimensional plane; what would you say? Next, if I tell you that φ is called 'phase'; what would you say? Lastly, if I say there is a one to one correspondence between all the sinewaves that ever were and all the points in a plane; what would you say?

In short φ is just a coordinate we use to describe certain types of periodic waveforms called sinewaves.

Example:
(M,φ) = (1,0) defines the sinewave with unit amplitude (M=1), with Msin(0)=0 @ t=0
Example:
(M,φ) = (1,π/4) defines the sinewave with unit amplitude (M=1) with Msin(π/4)=0.707 @ t=0

Locating this single point on the sine function tells us where all the other points from -∞ to +∞ must be.

What is that transformation? Glad you asked.

$$M=\sqrt{x^2+y^2}$$
$$\phi=tan^{-1}(\frac{y}{x})$$

How about the inverse transformation? Sure -- no problem.

$$x=M cos(\phi)$$
$$y=M sin(\phi)$$

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#### Himanshoo

Joined Apr 3, 2015
260
But if you also are talking about a 5 kHz sine wave, the positive peak is not at 0.25 ms, it is at 0.05 ms. So a discussion about where you are in both sine waves becomes very difficult because you always have to talk about two different numbers. To improve this mess,
Your explanation is making sense to me..thanks for it and appreciation…..
Reading your explanation i forgot to mention one thing….i.e. amplitude…..

We can easily say that wave of frequency 5khz is ahead of wave of frequency of 1 kHz by 0.2 ms (.05 minus .25)..so it seems fairly easy for me to conclude it this way. But this is only possible because the amplitude are considered to be the same. Had the amplitude be different then its wasn't possible anyhow to tell exactly by which amount one wave is leading or lagging other(phase shift).
So until an unless the amplitude is same there isn't any problem determining the phase shift..so where is the mess which you are talking about…

#### AnalogKid

Joined Aug 1, 2013
8,298
Reading your explanation i forgot to mention one thing….i.e. amplitude…..

We can easily say that wave of frequency 5khz is ahead of wave of frequency of 1 kHz by 0.2 ms (.05 minus .25)..so it seems fairly easy for me to conclude it this way. But this is only possible because the amplitude are considered to be the same. Had the amplitude be different then its wasn't possible anyhow to tell exactly by which amount one wave is leading or lagging other(phase shift).
Not true. Phase is a frequency and timing concept, and is independent of the amplitudes of the signals being compared. Measuring phase can be messy. This is why most discussions about phase shift are based about the signal relationships at their zero crossings. For waveforms with clearly defined peaks, such as sine, triangle, and sawtooth waves, phase can be determined by comparing the timing at the waveform peaks. But a square wave has no peaks, so phase shift can be measured only at the zero crossings. There is no requirement that a periodic waveform have a clearly defined peak or valley, but all periodic waveforms have zero-crossings, so this is the most universally consistent place for phase measurements.

ak

#### shteii01

Joined Feb 19, 2010
4,647
Your explanation is making sense to me..thanks for it and appreciation…..
Reading your explanation i forgot to mention one thing….i.e. amplitude…..

We can easily say that wave of frequency 5khz is ahead of wave of frequency of 1 kHz by 0.2 ms (.05 minus .25)..so it seems fairly easy for me to conclude it this way. But this is only possible because the amplitude are considered to be the same. Had the amplitude be different then its wasn't possible anyhow to tell exactly by which amount one wave is leading or lagging other(phase shift).
So until an unless the amplitude is same there isn't any problem determining the phase shift..so where is the mess which you are talking about…
Not true.
Period, frequency are show on the x axis.
Amplitude is shown on the y axis.
Therefore, if I am comparing times of two signals, I have not interaction with the amplitudes of the two signals at all because I am looking at the x axis for the information describing the signals, I am NOT looking at the y axis.

So if I am looking at one signal at time 0.02 ms and another signal at time 0.05 ms, then I don't care what their amplitudes are because I am not looking at the y axis, I am looking at the x axis.