Feedback: the loop gain is the truth meter

Từ vựng

English	Ý nghĩa
loop gain	độ khuếch đại vòng
gain-bandwidth product/ɡeɪn ˈbændwɪdθ ˈprɒdʌkt/	gain-bandwidth product: tích hệ số khuếch đại - băng thông

English

The golden rules are a loop-gain statement: with loop gain $A_{OL}\beta_{fb}$ large the inverting gain is exactly $-R_f/R_{in}$; in real life it is off by $1/(1 + A_{OL}\beta_{fb})$.
The gain-bandwidth product is a hyperbola: closed-loop gain 100× with GBW 1 MHz gives 10 kHz of bandwidth; 10× gives 100 kHz — the product is conserved until the corner, where the rules die.

Example

Closed-loop gain 100 ($\beta_{fb} = 0.01$). With $A_{OL} = 10^5$: $A_{CL} = 100/(1 + 1/1000) = 99.90$ — 0.1% error. Where the open-loop gain has fallen to $10^3$ (it rolls off — unit 7): $A_{CL} = 90.9$ — 9.1%. Check: at 10 kHz the 1 MHz op-amp's open-loop gain is exactly 100 = the closed-loop gain, loop gain 1 — precisely the −3 dB corner.