{{fa>pencil?32}} {{url>https://www.falstad.com/circuit/circuitjs.html?ctz=CQAgjCAMB0l5YCcyWrQDhAJmuyBmMANiwBZ1FSBWLIsUkKyRkU-RgUwFowwAoAIbhEWcAHYiIfFmZgJIROCogeysPHhRopMBVJYm5dOglFSDGDr1NdVNmMRVMTDXwBK4c+CLM835rKsgQFaVHwATlIy4pLSzAaS8a6RcdhUsdH4+IngrgDmUcxZGUU0UFB8AO6FaZJIogkV1fXCoi2NkFU1cpLmmD0VMmKs5DGMWP3yDACqAPoA8l30DMSyIv6DkMPLGzs7M7MAknwAzjWNpHC15RAAZgIANiccEUHx6axm10nw7p8MjRomA65UuLBCMDCAA9sH4sEhsIhhlgUaxsAw3HwYfgrijhoR4ji0bpwFjEfjILEtlJIIoVsCyVgxMjEMDKDSIACMWTSF8sPg6WIuaJ6VIeV5+Zy6Nh8AwuSBMdj0JIyHTIA0yvKAMp8AD2uW8oNpwOgyhgEHiBvwepA-Ryl1Z4OgEAgokw1qAA noborder}} You work in the company "HHN Mechatronics & Robotics" and are supposed to generate a bipolar signal ($-10 ~\rm V ... + 10 ~\rm V$) from a unipolar signal of a digital-to-analog converter ($0 ... 5 ~\rm V$) in a project. A colleague recommended the circuit shown on the right. - First, analyze what change is made by pressing the switch $S$. How does the output signal change? - Try to determine mathematically the relationship of $U_\rm O$ and $U_\rm I$ as $U_{\rm O}(U_{\rm I})$ by superposition. - The circuit still has the problem that for a positive positive half-wave the output is still negative. Which additional circuit must be provided so that this problem can be solved?