General Control Loop block diagram:
Given schematic below, how to know which is which? Knowing
which is which is critical, as it allows the use of theory to achieve the best
result.
Equations that allowed us to identify corresponding blocks:
From simple voltage divider rule


vn = Ri/(Ri + Rf) * vout

eq 1

let α = Ri/(Ri+Rf)


vn = α * vout

eq 2

We see that vout is just opamp gain (Aamp) multiply by its input
voltage


vout = (vp  vn) * Aamp


vout = (vin  α * vout) * Aamp


vout * ( 1 + α * Aamp) = vin * Aamp


vout / vin = Aamp / ( 1+ α * Aamp)

eq 3

From close loop equation of control theory:


vout/vin = TF = Aforward/(1 + Aforward*β)

eq 4

Comparing eq 3 with eq 4 , we see that


Aforward = Aamp


Aforward*β = α
* Aamp


β = α = Ri/(Ri+Rf)


When loop gain (Aforward*β) is large enough, we see that


1 + Aforward*β ~= Aforward*β


TF = Aforward/ Aforward*β


TF = 1/β = (Ri + Rf)/Ri = 1 + (Rf/Ri)

Nice blog… Thanks for sharing very useful information about electrical circuits.
ReplyDeleteElectronic circuit design