Exercise Sheet 1 \\ \\ \\ \\ Please upload the filled PDF in ILIAS. Details, tips and tools for filling and inserting images can be found at: \\ [[:tools_fuer_lehr_lern-veranstaltungen|Tools für Lehr/Lern-Veranstaltungen]] \\ \\ \\ \\ ^ Name ^ First Name ^ Matrikelnumber ^ | $\quad\quad\quad\quad\quad\quad\quad\quad$ \\ (nbsp) \\ (nbsp)| $\quad\quad\quad\quad\quad\quad\quad\quad$| $\quad\quad\quad\quad\quad\quad\quad\quad$ | | (nbsp) \\ (nbsp) \\ (nbsp)| | | \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ {{fa>pencil?32}} An amplifier circuit shall amplify a microphone signal so that a loudspeaker ($R_{\rm LS}= 8.0 ~\Omega$) can be driven. The [[https://en.wikipedia.org/wiki/Alternating_current#Root_mean_square_voltage|rms value]] of the desired voltage across the loudspeaker shall be $U_{\rm RMS, LS} = 10 ~\rm V$. It is assumed that a sinusoidal signal is to be output. The power is supplied by two voltage sources, with $V_{\rm S+} = 15 ~\rm V$ and $V_{\rm S-} = - 15 ~\rm V$. For understanding (especially for tasks 2. and 3.), look at the simulation under the subchapter [[1_amplifier_basics#equivalent_circuit_diagram|equivalent circuit]] in chapter "1. amplifier basics". This example shows a realistic amplifier, and the idealized current flow can be guessed from this. Draw a labeled sketch of the circuit with the amplifier as a black box. \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ - What power (P) does the loudspeaker consume? \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ - From this, how can we determine the RMS current $I_{\rm RMS, S}$ of the power supply at which the above-desired voltage $U_{\rm RMS, LS}$ is output at the loudspeaker? \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ - Determine from the previous task the maximum current $I_{\rm max, S}$ for which the two power supplies must be designed at least. \\ (Note that for simple amplifiers, the output current $I_\rm O$ is always less than or equal to the current $I_\rm S$ of the power supply.) \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ {{fa>pencil?32}} A voltage amplifier circuit is given, which shall amplify a microphone signal in such a way that a loudspeaker ($R_{\rm LS}= 8.0 ~\Omega$) can be driven. Neither amplification nor the desired voltage at the loudspeaker is known. This amplifier circuit is internally protected against over-currents above $I_{\rm max, amplifier}= 5.0 ~\rm A$ by a fast fuse. It is known that no over-currents occur in the allowed voltage operation of $8.0 ~\Omega$ loudspeakers. - By what factor does the current change if a $4.0 ~\Omega$ loudspeaker is used instead of an $8.0 ~\Omega$ loudspeaker? \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ - What effect does this have on the fuse? \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ {{fa>pencil?32}} {{drawio>wheatstonesche_brueckenschaltung_tsensor.svg}} Imagine that you work in the company "HHN Mechatronics & Robotics". You are developing an IoT system that will be used in a harsh environment and will contain a rechargeable battery. The temperature of the battery must be monitored during operation and charging. If the temperature is too high, charging must be aborted or a warning issued. For the temperature measurement at the housing of the used lithium-ion cell {{elektronische_schaltungstechnik:ncr18650b.pdf|NCR18650}} a measuring circuit is to be built up. A suggestion for the circuit is as follows: - Wheatstone bridge circuit with $R_1 = R_2 = R_3 = R_4 = 1.0 ~\rm k \Omega $. - Let the resistor $R_4$ be a PT1000 with a temperature coefficient $\alpha = 3850 ~\rm \frac{ppm}{K}$. - For the other resistors, two components are chosen, that have an unknown temperature coefficient. According to the datasheet, the temperature coefficient is within $\alpha = \pm 100 ~\rm \frac{ppm}{K}$. - The voltage source of the system generates a voltage of $5~V$ with sufficient accuracy. - The determined voltage $\Delta U$ is amplified by a factor of 20 through another amplifier circuit, output as $U_{\rm O}$, and further used by an analog-to-digital converter in a microcontroller [(Note3>In real systems, an analog-to-digital converter would most likely not be used because of its relatively large power consumption for IoT applications. For Atmel chips, this is a few $10 ~\rm µA$, which adds up to a rapid battery drain over time.)]. ~~PAGEBREAK~~~~CLEARFIX~~ A short report is to be created; Tina TI is to be used as the analysis tool. - Create a problem description. \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ - Rebuild the circuit in TINA TI and add this in your descriptionhere. Take the following hint into account. Use a simple resistor for the PT1000 in the simulation. With Tina TI, $27~°C$ (room temperature) is selected as the reference temperature for the temperature curve. For the PT1000, the reference temperature is often $0~°C$ (in practical applications, this should be checked in the datasheet). With Tina TI, the reference temperature can be changed by entering the value 27 under ''Temperature [C]'' in the properties (double-click on Resistor). \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ - From the datasheet linked above, determine in what range from $T_{\rm min}$ to $T_{\rm max}$ may be charged and what temperature $T_{\rm lim}$ may not be exceeded in any of the states. \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ - First, for temperature invariant $R_1 = R_2 = R_3 = 1.0 ~\rm k \Omega$ and a temperature variable resistor $R_4$, determine the voltage change $\Delta U$ over the temperature of $-30...70 ~°C$ in TINA TI. To do this, create a plot with $\Delta U$ as a function of temperature. \\ Read $\Delta U^0 (T_{\rm min})$, $\Delta U^0 (T_{\rm max})$, $\Delta U^0 (T_{\rm lim})$, from the diagram and check the plausibility of the values by calculation. \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ - Determine $\Delta U$ when the temperature dependence of $R_1$, $R_2$ and $R_3$ is taken into account. To do this, create a suitable diagram with $\Delta U$ as a function of temperature in TINA TI. \\ At what voltages $U_O (T_{\rm min})$, $U_O (T_{\rm max})$ must the microcontroller intervene and disable charging? \\ At what value $U_A (T_{\rm lim})$ must a warning be issued? \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ - Discuss the results. \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\