getting into chapter 8
feedback topology invented by harold black in 1928 at western electric
portion of output gained and summed with input in some way
reduces non-linear distortion
reduce effects of noise (preamp)
allows control of input and output impedances

Xs is the input
Xi is the input after feedback modifications
Xo is the output
Xf is the feedback signal after modification from the output
A is primary gain
B is feedback gain

Xi = Xs-Xf -> Xs=Xi+Xf
Xf=BXo
Xo=AXi
Xo/Xs = A/(1+AB)

AB = loop gain
1+AB = amount of feedback
if AB>>1, Xo/Xs = 1/B

gain of a FB amp is det by FB element
opamps have built in feedback via the capacitor and internal resistance

the X variables can be current or voltage

find beta for opamp: voltage divider: R1/(R2+R1)
open loop gain: A=10000
find R2/R1 to get closed loop gain: Vo/Vs, Af = 10
Af = A/(1+AB) = A/(1+AR1/(R1+R2)) = A/(1+A/(1+R2/R1)) ~~> 1/(1+R2/R1) = 1/10 -> R2/R1 = 9

find amount of FB in dB -> 20log(1+AB) = 20log(1+10000R1/(R1+R2)) = 20log(1+1000) = 60dB

if Vs = 1V, find Vo,Vf,Vi
Vo = 10Vs = 10V
Vf = AB/(1+AB) = 1000/1001 = 0.999V
Vi = Vs/(1+AB) = 0.001V

drop gain to 80%, end up with Af = 9.98V/V