Dies ist eine alte Version des Dokuments!
~~REVEAL ~~
----> $I.\quad$ 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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| $\quad$ | $\frac{U_1}{R_1}= \frac{U_2}{R_2} = \frac{U_A}{R_1 + R_2}$ |
| Voltage divider, $I=const.$ | |
| $\quad\quad\quad$ | $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$ |
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| (10) | $U_2= U_A\cdot\frac{R_2}{R_1+R_2}$ |
| 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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| $\quad$ | $A_V=\frac{U_O}{\color{blue}{U_A\cdot\frac{R_2}{R_1+R_2}}+U_D}$ |
| $\quad$ | |
| $\quad\quad\quad$ | $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$ |
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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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