# steady state closed loop gain

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

1. ### amilton542 Thread Starter Active Member

Nov 13, 2010
496
64
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

Nov 29, 2010
199
16
3. ### amilton542 Thread Starter Active Member

Nov 13, 2010
496
64
why are we using the 1?

4. ### tyblu Member

Nov 29, 2010
199
16
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
5,151
1,266
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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