feedback amps
Xo/Xs = A/(1+AB)
B = R1/(R1+R2)
Af = 20 log(1+AB)
in the example, Af = 8000/(1+8000/10.01) = 9.9975V
% diff: (10-Af)/10 = 0.02%


gain stabilization
Af = A/(1+AB)
dAf/dA = 1/((1+AB)^2)
dAf/Af = (dA/A)/((1+AB)^2)

recall general freq response for amp is a bandpass
Am = midband gain

Af = Am/(1+BAm+s/wh)

you end up trading higher midband gain for bandwidth when using feedback networks
if you need to bump gain and network, you need to pay for more beta(B)

noise reduction
Vo = A1(Vs+Vn)
put A1 in a feedback network with a low noise preamp
2 primary props of a preamp: low noise, A2 (the preamp) must be operating small signal
equations end up being:
Va2 = Vs - BVo 

V1 = V2+Vn
Vo = A1A2Vs/(1+BA1A2) + A1Vn/(1+BA1A2)
SNR = A2Vs/Vn

all noise assumed to be lumped into Vn source no matter the source of the noise, good working assumption
preamp is designed to op under small signal conditions
examples: MC14753 cmos opamp, input voltage noise: 200nV/sqrt(hz)
LT1115 BJT ultra low noise opamp input voltage noise: 1.2nV/sqrt(hz)

A2=100V/V
B=1
improve by 40dB

section 8.3, types of feedback topologies
type	name		input	output	error	amp name	feedback network units
a	series/shunt	voltage	voltage	voltage	voltage gain	dimensionless
b	shunt/shunt	current	voltage	current	x-resistance	ohms
c	series/series	voltage	current	voltage	x-conductance	siemens
d	shunt/series	current	current	current	current gain	dimensionless

when dealing with new stuff, it's a mixed mode analog/digital world
operating together