Frequency and phase relationship

[likephysics]

Frequency is the time derivative of phase? But how?
Can someone explain?

 

[f95toli]

No, it is not.
At least not if you use the normal meaning of "phase", in which case it is a parameter (usually a constant) which tells you the relative postion in time of two or more periodic waveforms

e.g. if you have

$\sin (2\pi ft+\theta)$)

then $\theta$ would be the phase. Note that it is only meaningfull to talk about phase when you are comparing waveforms; the "starting point" for a periodic function is arbitrary so there is no such thing as absolute phase.

 

[waht]

Group delay is a derivative of phase with respect to angular frequency:

$$\tau_g = -\frac{d\phi}{d\omega}$$

 

[likephysics]

I was reading about I and Q demodulation when I came across this time derivative of phase.
Here's a link to a book that mentions the same, but does not provide an explanation-
http://books.google.com/books?id=Qt...ency is the time derivative of phase&f=false"

 

[f95toli]

OK, now I understand where you got that from.
This is why I was referring to the "normal meaning of phase" above.

People (meaning EEs) who work with modulations schemes (in this case FM) have a tendency to refer to the argument of the sine function as "phase" ; i.e "the phase" in this case would be $\omega t+\theta$ and if you take the time derivative of this you obviously get $\omega$ (which also happens to be the angular frequency, not the frequency).

So -unless I am missing something- this is just another case of confusion due to differences between EE and physics terminology.
The "definition" of phase I wrote above is certainly what you would find in a physics book.