Transposition of Formula

Discussion in 'Math' started by Steve1992, Feb 17, 2007.

  1. Steve1992

    Thread Starter Senior Member

    Apr 7, 2006
    In context to an non-inverting op-amp (from text book)

    Vin = Vo x Ri/Ri + Rf


    Vo = (1 + Rf/Ri) x Vin

    I believe Ri is the common factor from the first equation, but I dont know how to get to the second equation.
    If any one can give me the sequence of steps?:confused:
  2. hgmjr

    Retired Moderator

    Jan 28, 2005
    First, the equation you have shown should have parenthesis around the two terms in the denominator like below.
    Vin = Vo x Ri/(Ri + Rf)

    Start by multiplying both sides of the equal sign by (Ri + Rf).

    Next, multiply both sides of the equal sign by Ri.

    Then, you should have the expression

    Vo = Vin*(Ri+Rf)/Ri

    Next, expand the fraction to Vin*(Ri/Ri + RF/Ri)

    Since Ri/Ri = 1 then you can substitute to get:

    Vo = Vin*(1+(Rf/Ri))