Maximum Power Transfer

Discussion in 'General Electronics Chat' started by mlkcampion, Jun 26, 2007.

  1. mlkcampion

    Thread Starter Active Member

    Nov 16, 2006
    59
    0
    Hey
    I was reading through my copy of Schuams Outlines (Electric Circuits)
    and i came across the theory of Maximum Power transfer, i have already
    looked at the threads on this topic however my question regards the
    equation used to describe the power absorb by the load.

    I have scanned the small section from Schuams Outline. (see attachment)
    I can't work out how you go from the first equation to the final one
    which i have underlined in orange, i understand that the part inside
    the square braces is the effeciency but still can't get to this result.

    [​IMG]

    Can someone explain?

    Cheers
     
  2. recca02

    Senior Member

    Apr 2, 2007
    1,211
    0
    one way to get to the expression RL=R
    wud be
    differentiating the PL expression(the simple one derived from power =sq(i).r) and equating to zero and u may even check with second derivative whether it implies a maxima or minima by finding if the value of second derivative is positive or negative.



    edit: right now i can only explain how to reach that expression (manipulation has been my specialty).
    multiply numerator and denominator by 4R.
    now manipulate as (RL+R)^2 -(RL+R)^2= 4RL.R
    rest shud be easy split the fraction in two parts and cancel (RL+R)^2 take out common factor V^2/4R.
    got it?
     
  3. mlkcampion

    Thread Starter Active Member

    Nov 16, 2006
    59
    0
    Cheers recca
    I see what your doing alright, though for some reason i end up with
    4R^2 under the line!!

    Mike
     
  4. recca02

    Senior Member

    Apr 2, 2007
    1,211
    0
    do not try to simplify the denominator,
    just cancel what'er term can be cancelled. do not mess with the brackets :p
     
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