PDF version here: https://sealevel.info/linear_feedback_system_diagram1.pdf

see also: https://sealevel.info/feedbacks.html

in = input

out = output

G = open-loop gain (assume 1.0 for simplicity)

ƒ = feedback (shown as +10%)

i2 = in + (ƒ × out)

out = i2 × G

= G × (in + (ƒ × out))

assume G = 1, then:

out = in + (ƒ × out)

out – (ƒ × out) = in

out × (1 – ƒ) = in

out = in / (1 – ƒ)

if ƒ = +10% then out = in / 0.9 = 1.11111… × in

if ƒ = +50% then out = in / 0.5 = 2 × in

if ƒ = –50% then out = in / 1.5 = 0.66666… × in