steady state closed loop gain

Discussion in 'Homework Help' started by amilton542, Dec 3, 2010.

  1. amilton542

    Thread Starter Active Member

    Nov 13, 2010
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    im having trouble trying to figure out where the 1 is coming from? all i can think of is the forward gain (G) is receiving the feedback factor as a voltage and sending out the error signal as a voltage so it will be dimensionless so the 1 will be a constant. But when you have your value for loop gain it says you add a 1 to it for example 1 + GH, then for closed loop gain it will be G/(1+GH). i just cant understand where the 1 is coming from and why were using it
     
  2. tyblu

    Member

    Nov 29, 2010
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  3. amilton542

    Thread Starter Active Member

    Nov 13, 2010
    494
    64
    why are we using the 1?
     
  4. tyblu

    Member

    Nov 29, 2010
    199
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    just algebra. Here's a breakdown of what happens between the line "gives Y = (X-HY)G = XG - YGH" and "Y(1 + GH) = XG".

    Y = (X-HY)G ... multiply through
    Y = XG - YGH ... move "YGH" to LHS
    Y + YGH = XG ... collect term "Y"
    Y(1+GH) = XG ... continue
     
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  5. Georacer

    Moderator

    Nov 25, 2009
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    Just follow tyblu's operations closely and you will notice that the 1 comes as a result of a factorization.
    Math often solves many questions.
     
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