Why -3db frequency shows 45degree phase shift?

[ida_fahani]

help me guys...
i reall need the answer ASAP...
Thanx in advance..

 

[lpfr]

In a simple RC filter yes.

 

[berkeman]

Write the transfer equation for a simple RC lowpass filter as lpfr suggests, using complex impedances. Then solve for the frequency where the magnitude of the transfer function is:

$$\frac{V_o}{V_i} = -6dB$$

or

$$\frac{P_o}{P_i} = -3dB$$

and then plug that frequency back into the transfer function equation to find the phase shift at the -3dB point. Show us your work.


EDIT -- fixed a power versus voltage error that I had in the transfer function equations.

 

[ida_fahani]

thanx...really apperitiate if u guys can explain to me in deapth..

 

[berkeman]

thanx...really apperitiate if u guys can explain to me in deapth..

We'd be happy to. Show us your work in writing the equations that I mentioned, and then we can start discussing them if you don't get something. Again, we do not do your work here on the PF -- you need to show your work here, in order to get our help.

 

[ida_fahani]

the question is:

why we choose -3db as a corner frequency?
why -3db show 45 degree phase shift?

 

[ida_fahani]

i just need your help to enhance my answer.

 

[berkeman]

the question is:

why we choose -3db as a corner frequency?
why -3db show 45 degree phase shift?

AFAIK, -3dB power (or -6dB voltage) is just a handy convention for the "corner" frequency. Although the -45 degree phase shift may be the reason that it is the handy convention.

For you to give a good answer to these questions, you need to do the math that I described. You will see why the -45 degree phase shift corresponds to a -3dB in power for the transfer function, or equivalently a -6dB in the voltage transfer function.

BTW, I see now that I was careless and showed -3dB in the voltage tranfer function. I've gone back and corrected that. in my previous post in this thread.

 

[berkeman]

And here's a wikipedia.org article that may be of help:

http://en.wikipedia.org/wiki/Low-pass_filter

 

[pooface]

There is a 45 degree shift because R=C at fc. So the circuit is neither capacitive nor resistive. arctan -Xc/R where Xc=R so arctan -Xc/R == arctan -1 ==-45deg.
that was a little shortcutish way.

real angle derivation is from the transfer function berke is talking about. vo/vi. you will find the angle to be -90 - arctan -Xc/R for lowpass RC.

hope that was helpful.