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Below you will find circuits with an ideal operational amplifier, which are similar to the non-inverting amplifier and whose voltage gain $A_V$ must be determined.
__Assumptions__
* $R_1 = R_3 = R_4 = R$
* $R_2 = 2 \cdot R$
* $U_\rm I$ comes from a low-resistance source
* $U_\rm O$ is due to a high-resistance consumer
__Exercises__
- Enter the voltage gain $A_\rm V$ for each circuit. A detailed calculation as before is not necessary.
- For Figure 7, indicate how the voltage gain can be determined.
- Generalize with the following justifications:
- How has a short circuit of the two OPV inputs must be taken into account?
- How do resistances have to be considered in the following cases:
- with one terminal (so "one connector") directly and exclusively on an OPV input,
- with both terminals each directly connected to an OPV input.
- In which circuits do resistors $R_3$ and $R_4$ represent an unloaded voltage divider?
To approach the problems, you should try to use the knowledge from the inverting amplifier. It can be useful to simulate the circuits via [[http://www.falstad.com/circuit/|Falstad-Circuit]] or Tina TI. In the first two circuits, tips can be seen under the illustration as support. \\
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**__Important__**: As always in your studies, you should try to generalize the knowledge gained from the task.
**Tipps**
* How big is the current flow into the inverting and non-inverting input of an ideal operational amplifier? So what voltage drop would there be across a resistor whose one connection only leads to one input of the operational amplifier ($R_3$)?
* The operational amplifier always tries to output as much current at the output that the required minimum voltage $U_\rm D$ results between the inverting and non-inverting input. How high can $U_\rm D$ be assumed? Can this voltage also be built up via a resistor ($R_4$)?
* Can different resistors (e.g. because they are between the same nodes) be combined?
Abb. 1 \\ {{drawio>pic3_5_2_Aufgabe1.svg}} \\ \\ \\ \\ \\ \\ \\ \\
++++ Hints|
* How high is the current flow into the inverting and non-inverting input of an ideal operational amplifier? What voltage drop would there be across a resistor whose one connection only leads to one input of the operational amplifier? ($R_3$)?
* The operational amplifier always tries to output enough current at the output so that the required minimum voltage is between the inverting and non-inverting input $U_\rm D$ results. How big can $U_\rm D$ be accepted? Can this voltage also via a resistor ($R_4$) being constructed?
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Abb. 2 \\ {{drawio>pic3_5_2_Aufgabe2.svg}}
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++++ Hints|
* How much current must flow through $R_4 = R$ so that the expected voltage $U_4$ results?
* How much current must flow through $R_2 = 2 \cdot R$ fließen?
* How much current must flow through $R_1 = R$? How high is the voltage at $R_1$?
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Abb. 3 \\ {{drawio>pic3_5_2_Aufgabe3.svg}}
Abb. 4 \\ {{drawio>pic3_5_2_Aufgabe4.svg}}
Abb. 5 \\ {{drawio>pic3_5_2_Aufgabe5.svg}}
Abb. 6 \\ {{drawio>pic3_5_2_Aufgabe6.svg}}
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Abb. 7 \\ {{drawio>pic3_5_2_Aufgabe7.svg}}
Abb. 8 \\ {{drawio>pic3_5_2_Aufgabe8.svg}}
Abb. 9 \\ {{drawio>pic3_5_2_Aufgabe9.svg}}