~~REVEAL ~~



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$I.\quad$ Analysis of the Currents
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|by (2)+(3)|$\color{blue}{I_p} = \color{blue}{I_m} = 0$  |
|  | therefore, $I_p$ and $I_m$ are defined|
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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|by (6)|$\color{blue}{I_O} = I_1 $  |
|  |$I_O$ is defined, when $I_1$ is defined|
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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|by (7)+(3)|$I_1 - I_2 -\color{blue}{0} = 0 $  |
|  |$\quad$|
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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|$\quad$|$I_1 = I_2 = I_O$  |
|  |$\quad$|
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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|$\quad$|$\color{blue}{I_1} = \color{blue}{I_2} = \color{blue}{I_O} $  |
|  |with (8) and (9): $I_\boxed{}=\frac{U_\boxed{}}{R_\boxed{}}$ and (5)|
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$ |$\frac{U_1}{R_1}= \frac{U_2}{R_2} = \frac{U_O}{R_1 + R_2}$   |
|  |Voltage divider, $I=const.$ |
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| (10)|$U_2= U_O\cdot\frac{R_2}{R_1+R_2}$   |
|  |Voltage divider|
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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$II.\quad$ Analysis if the Voltage Amplification
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|by (0)  |$\color{blue}{A_V}=\frac{U_O}{U_I}$  |
|  |  $\quad$|
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{U_O}{\color{blue}{U_I}}$  |
|  |with (4): $U_I=U_2+U_D$|
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{U_O}{\color{blue}{U_2+U_D}}$  |
|  | $\quad$  |
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{U_O}{\color{blue}{U_2}+U_D}$  |
|  | with (10): $U_2= U_O\cdot\frac{R_2}{R_1+R_2}$  |
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{U_O}{\color{blue}{U_O\cdot\frac{R_2}{R_1+R_2}}+U_D}$  |
|  | $\quad$ |
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{U_O}{U_O\cdot\frac{R_2}{R_1+R_2}+U_D}$  |
|  | $\quad$ |
|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{U_O}{U_O\cdot\frac{R_2}{R_1+R_2}+\color{blue}{U_D}}$  |
|  | with (1)|
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{U_O}{U_O\cdot\frac{R_2}{R_1+R_2}+\color{blue}{\frac{U_O}{A_D}}}$  |
|  | $\quad$ |
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{U_O}{U_O\cdot\frac{R_2}{R_1+R_2}+\frac{U_O}{A_D}}$  |
|  | $\quad$ |
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{\color{blue}{U_O}}{\color{blue}{U_O}\cdot\frac{R_2}{R_1+R_2}+\frac{\color{blue}{U_O}}{A_D}}$  |
|  | Expand with $\frac{1}{U_O}$ |
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{1}{\frac{R_2}{R_1+R_2}+\frac{1}{A_D}}$  |
|  | $\quad$  |
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{1}{\frac{R_2}{R_1+R_2}+\color{blue}{\frac{1}{A_D}}}$  |
|  | with $\frac{1}{A_D} \xrightarrow{A_D \rightarrow \infty} 0$   |
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{1}{\frac{R_2}{R_1+R_2}}$  |
|  | reshaping the fraction |
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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| $\quad$  |$A_V=\frac{R_1+R_2}{R_2}$  |
|  | $\quad$   |
|$\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
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