# How to express phase?

1. Jan 30, 2016

### brainbaby

If a phase is a sort of ''time relationship'' between two signals and tell by which extent the both signals lead or lag each other....then it should be expressed in milliseconds (or any unit lower than it)..but then why its expressed in degrees.

What kind of ease would it provide if phase is expressed in degrees but not in any significant unit of time?

2. Jan 30, 2016

### cnh1995

You can do it using time but then you'll need to specify the time period of the wave. If you say, I is lagging V by 90°, that means I reaches its peak 90° after V does. It's same for a 50Hz signal and a 100Hz signal. But if you speak in terms of time, you'll have to specify the time corresponding to 90°, which is 5ms for 50Hz and 2.5ms for 100Hz. Also, calculations in ac circuits can be done using only phasor algebra. Phasor diagrams are the heart of ac circuit analysis.

3. Jan 30, 2016

### brainbaby

So what i conclude is that expressing phase in terms of milliseconds and degrees each have its own pros and cons.
If the phase is expressed in terms of time then we have to tell like this that 50Hz wave lags with 2.5ms (5ms - 2.5ms = 2.5ms) by 100Hz wave at peak.
So here the advantage is that we are getting accurate information about the phase..
but the disadvantage is that we have to specify more variable (like time and location (peak))in order to determine phase....which makes the info lengthy..

If the phase is expressed in terms of degrees then we have to tell like this that a 50Hz wave lags a 100Hz wave by 90 degrees(peak)....
Here the advantage is that we are specifying less variable( like only location(peak) i.e 90 degrees) in order to determine phase...which makes are info concise and portable..
But the disadvantage is that we are not getting accurate information about the phase...we are only getting an approximation....

Have I concluded right......?

4. Jan 30, 2016

### cnh1995

I meant the comparison between two 50Hz signals or two 100Hz signals. When 50Hz I lags 50Hz V by 90°, the time lag is 5ms. When the both the signals are of 100Hz, the same 90° phase difference corresponds to 2.5ms. So, the time equivalent of phase angle changes with frequency. And ac circuit analysis can be done only through phasor diagrams and phasor algebra. The analysis involves trigonometry, which needs angles. Phasor diagram gives a generalized explanation of a particular V-I relationship. For example, inductor current lags inductor voltage by 90°. This is true for a sinusoidal signal of 50Hz ,100Hz or any other frequency. Actual time lag changes with frequency. But 'time' is not important for understanding general behavior of the circuit. Phase and phasors give this information.

5. Jan 30, 2016

### brainbaby

I want to to correct you that the time lag of 5ms which you have mentioned as a time lag is not actually the time lag(delay).....actually its the time require for the wave of freq 50Hz to reach the peak(90 degree)..

6. Jan 30, 2016

### cnh1995

Hence, when current is 0, voltage is at its peak. After 5ms, the current will reach its peak. In electrical terms, this means "current lags the voltage by 90°" or "current reaches its peak 5ms after the voltage does". Hence, in terms of time, you can say "there is a delay of 5ms between voltage peak and current peak".
For 50Hz frequency, 20ms corresponds to phase angle of 2π, for 100Hz frequency, 10ms corresponds to 2π.
phase angle Φ=2πt/T
where t is the time elapsed and T is the time period of the wave.

7. Jan 30, 2016

### meBigGuy

As expressed above:

Phase is a measurement of time and can be expressed in degrees or in time, and both are just as accurate. They have different uses in different situations.

If the period of a waveform is T sec, then 1 degree is T/360 sec. They both express exactly the same signal relationship.

For example FIR filters are what is called "linear phase" filters, which means they have a fixed time delay regardless of input frequency. So it is convienient to express the delay in time, rather than degrees. An IIR filter will have phase that is dependent on frequency, so they are typically characterized by phase/frequency plots in degrees since you may be interested in the frequency where the phase is 90 or 180 degrees.

8. Feb 1, 2016

### brainbaby

Finally after couple of days i got the right conclusion (fingers crossed )and its just two simple lines....
* if we express delay in terms of time then delay is different for different frequency signals
and
* if we express delay in terms of degrees then delay is same for different frequency signals
Hence expressing delay in terms of degrees save us from a mess of expressing delay in different time figures with the change in frequencies.

Hope so I am right now....

9. Feb 1, 2016

### cnh1995

Right. That's what I was trying to say in #2.

10. Feb 1, 2016

### brainbaby

thanks dude...

11. Feb 1, 2016

### vintageplayer

This is not really the reason. For most circuits, frequency remains constant throughout anyway.

The real reason is that for circuit analysis, you want to convert sinusoidal functions to phasors. A phasor is essentially a complex number (it has a magnitude and angle), and makes the maths of calculating AC voltages and currents in a circuit much easier. When converting a sinusoidal function to a phasor, the magnitude of the phasor is equal to the amplitude of the sinusoidal function, and the angle of the phasor is equal to the phase shift in degrees. For example, I could express 2sin(100t + 50°) in phasor notation as 2∠50°.

It's important to express the phase shift in degrees if you want to use phasors.

12. Feb 1, 2016

### Merlin3189

I would not agree with any of that at all.

If a signal is delayed in time, then the delay is the same for all frequencies, but the angular phase difference varies with frequency. This is what happens in many filters, so that as well as attenuating different frequencies by different amounts, the phase (angle) is shifted differently at different frequencies.
This is also how howl-around occurs (or used to occur before DSP) in PA systems. The fixed time delay as the sound travels from speaker back to mike corresponds to different (angular) phase shifts at different frequencies. Only at certain frequencies is the returning signal in phase with the original and that (combined with the frequency response of the amp system) determines the dominant frequency at which howl-around occurs.

If a signal is changed by a fixed angular amount (I say changed because there is no way of telling whether a phase angle is an advance or delay in phase: they are the same thing) that corresponds to a different time delay at different frequencies (for time I say delay, because you cannot have time advance in a causal system.) But this is a bit of a mathematical fiction, because it is very difficult to create an analogue circuit which does change signals by a fixed angular amount* at all frequencies. (A DSP can of course analyse a signal, give each frequency a different time delay corresponding to the required angle, then recombine them, along with all the noise, quantisation and rounding errors.) So "if we express delay in terms of degrees then delay is same for different frequency signals" is very rarely a situation met with in real electronics and audio.
*180o is a special case, which can be achieved with an inverter. 90o would be very useful, but is not easy.

13. Feb 1, 2016

### meBigGuy

I'd say it differently and try to keep it simple.

You can express time directly in units of time, or indirectly in units of degrees at a given frequency. Both express time. If you try to take it any further than that you will just confuse yourself. Sometimes you are interested in phase at a frequency, sometimes in absolute time.