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Why -3db frequency shows 45degree phase shift?

  1. Apr 10, 2007 #1
    help me guys....
    i reall need the answer ASAP....:cry:
    Thanx in advance..
     
  2. jcsd
  3. Apr 10, 2007 #2
    In a simple RC filter yes.
     
  4. Apr 10, 2007 #3

    berkeman

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    Staff: Mentor

    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:

    [tex]\frac{V_o}{V_i} = -6dB [/tex]

    or

    [tex]\frac{P_o}{P_i} = -3dB [/tex]

    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.
     
    Last edited: Apr 11, 2007
  5. Apr 10, 2007 #4
    thanx...really apperitiate if u guys can explain to me in deapth..:smile:
     
  6. Apr 11, 2007 #5

    berkeman

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    Staff: Mentor

    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.
     
  7. Apr 11, 2007 #6
    the question is:

    why we choose -3db as a corner frequency?
    why -3db show 45 degree phase shift?
     
  8. Apr 11, 2007 #7
    i just need your help to enhance my answer.
     
  9. Apr 11, 2007 #8

    berkeman

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    Staff: Mentor

    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.
     
  10. Apr 11, 2007 #9

    berkeman

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    Staff: Mentor

  11. Apr 14, 2007 #10
    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.
     
    Last edited: Apr 14, 2007
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