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

 

http://en.wikipedia.org/wiki/Control_theory#Closed-loop_transfer_function

X----e->G------>Y
   ^----H<---'

Y = eG
e = X - HY
gives Y = (X-HY)G = XG - YGH
Y(1 + GH) = XG
Y = XG/(1+GH)

transfer function Y/X = G/(1+GH)

 

why are we using the 1?

 

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

 

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.