circuit_design:exercise_sheet_1 [MEXLE Wiki]

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<fs xx-large>Exercise Sheet 1</fs>
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<panel type="info" title="Exercise 1.1.1 Microphone amplifier I">
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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.<WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ </WRAP>
  - What power (P) does the loudspeaker consume? <WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ </WRAP> 
  - 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?  <WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ </WRAP>
  - 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.) <WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\  </WRAP>
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<panel type="info" title="Exercise 1.1.2 Microphone amplifier II">
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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? <WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\  </WRAP>
  - What effect does this have on the fuse? <WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\  </WRAP>
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<panel type="info" title="Exercise 1.1.3 Wheatstone bridge circuit">
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<imgcaption pic1_1_3_Wheat|Wheatstone bridge circuit with a temperature sensor>
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{{drawio>wheatstonesche_brueckenschaltung_tsensor.svg}}
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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.)].
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A short report is to be created; Tina TI is to be used as the analysis tool.
  - Create a problem description.<WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\  </WRAP> <WRAP pagebreak></WRAP> 
  - Rebuild the circuit in TINA TI and add this <wrap noprint>in your description</wrap><wrap onlyprint>here</wrap>. Take the following hint into account. <panel type="info" title="Hint">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).</panel><WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\  </WRAP>
  - 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.   <WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\  </WRAP>
  - 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. <WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\  </WRAP>
  - 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? <WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ </WRAP>
  - Discuss the results. <WRAP onlyprint> \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\    </WRAP>

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