# Feedback Error Equation

I am currently digging into some amplifier feedback analysis tools papers and literature. I found some "term" right at beginning of this topic that I don't quite understand. That is "Error equation of system/circuit". Simple feedback system incorporating this term looks like this: At the beginning I thought of it as being a closed loop error or something in that direction, but this figure represents it as something else. So, system error (or E) is just a summed signal resulting from $V_{IN}$ signal and $\beta$ (or feedback path signal)?

Also, in paper I am currently learning from (published by Texas Instruments) gives these three equations for feedback system (incorporating E):

$$V_{OUT} = EA$$ $$E = V_{IN} - \beta V_{OUT}$$ $$E = \frac {V_{IN}} {1+A\beta}$$

These equations tells me that System Error actually is a summing output. But why is it named "Error"? I first thought of it is being some miscalculation of fault term. And I probably wasn't the first that thought of it this way.

• Error in this case represents the difference between the setpoint (Vin) and the output (Vout) multiplied by the feedback gain. As you dive deeper, you should encounter how designing the feedback gain can change properties of your entire system which is hopefully advantageous. – user159625 Aug 13 '18 at 22:49
• This results in $\dfrac{V_{out}}{V_{in}}=\dfrac{A}{1+A\beta}$ – Tony Stewart Sunnyskyguy EE75 Aug 14 '18 at 0:08
• So what happens when the forward gain A>>$\beta$? e.g. in Op Amps and the Vin+=0V=gnd ? Then Vin is a “virtual gnd” because the E is almost 0. – Tony Stewart Sunnyskyguy EE75 Aug 14 '18 at 0:18
• This tells you a proportional (P) system always has some error according to the gain $1=A\beta$ – Tony Stewart Sunnyskyguy EE75 Aug 14 '18 at 0:32
• @TonyEErocketscientist But why is it named as "Error"? To me it doesn't seem like a fault or sth like that - this is what error usually represents. – Keno Aug 14 '18 at 4:45