active and passive filters

Discussion in 'Homework Help' started by PG1995, Jun 1, 2012.

  1. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Hi

    Please have a look on this document. My question is about the text in maroon on page #3 where it says, "The cutoff frequency fc is the frequency above or below which the power of the circuit, which is most often a filter, is ½ the input power...".

    At the critical frequency output voltage is 70.7% of the input voltage in a RC filter. What does it mean where the text says, "The cutoff frequency fc is the frequency above or below which the power of the circuit, which is most often a filter, is ½ the input power." Does it mean that at the critical frequency output power is half of input power in a RC circuit? I assume this is the case. Then, it says, "Since P = V^2/R, half the power is proportional to sqrt(1/2) the voltage." How is power proportional to sqrt(1/2) the input voltage?

    Please help me. Thank you.

    Regards
    PG
     
  2. WBahn

    Moderator

    Mar 31, 2012
    17,758
    4,800
    Let's say you have a voltage Vo. How much power is that signal dumping into a resistive load R? Call that Po.

    In terms of Vo, what would the voltage need to be in order to dump Po/2 into that same resistive load, R?

    The definition of their cutoff frequency is a bit too simplistic, especially since the title of the thread includes active filters.

    A much better description of the cutoff frequency of a filter is the frequency at which the power delivered to a resistive load becomes half of what it nominally is in the passband. This way, the definition is unamgiguous even if the filter has a loss or gain throughout the passband.
     
  3. justtrying

    Active Member

    Mar 9, 2011
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