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lab_electrical_engineering:6_opamps_2 [2026/06/17 10:58] – mexleadminlab_electrical_engineering:6_opamps_2 [2026/06/17 13:08] (current) – mexleadmin
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-=====Rectangular-to-Triangle Signal Conversion - Integrator=====+<wrap onlyprint>{{drawio>lab_electrical_engineering:namingtitle.svg}}</wrap> 
 +\\  
 +====== Experiment 6: Operational Amplifier II - Pulse Width Modulation ====== 
 +  * Circuits on the breadboard 
 +  * Integrator 
 +  * Non-inverting Schmitt trigger 
 +  * Triangle–square-wave generator 
 +  * Pulse-width modulation and control of a DC motor
  
-====Background Information====+<wrap #challenge-description> 
 +{{page>.:6_opamps_2:Challenge_description&nofooter}} 
 +</wrap>
  
-The operation of an OPV in the linear operating range can be enforced by means of circuitry by feeding back the output signal, i.e., returning it to the inverting input (- input). In the circuit shown, the negative feedback is provided by a capacitor.\\ +<wrap #nuggets> 
-\\ +  {{page>Rectangular-to-Triangle_Signal_Conversion_(Integrator)&nofooter}} 
-\\ +  {{page>Triangle-to-Rectangular_Conversion_(Schmitt_Trigger)&nofooter}} 
-<wrap left> {{drawio>mexlefirst_intern:integrator_circuit.svg}} </wrap>\\ +  {{page>Combination_of_Integrator_and_Schmitt_Trigger_(Oscillator)&nofooter}} 
-\\ +  {{page>Duty_Cycle_Adjustment&nofooter}} 
-Analysis of the circuit:\\ +  {{page>LED_Brightness_Control_using_PWM&nofooter}} 
-Negative feedback+</wrap>
  
-$\Rightarrow u_\mathrm{d} = 0 \Rightarrow i_R = \frac{u_\mathrm{e}}{R}$ +===== Preparation =====
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-$i_R=i_C$ (because OPV input current $i_\mathrm{n} = 0$) +
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-$u_\mathrm{a}=-u_C=-\frac{1}{C}\int i_\mathrm{C}\,dt=-\frac{1}{RC}\int u_\mathrm{e}\,dt$\\ +
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-The integrated input voltage appears at the output. The product of resistance and capacitance has the character of a time constant: +
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-$T_\mathrm{i}=RC$\\ +
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-<wrap left> {{drawio>mexlefirst_intern:integrator_u-t-diagramme.svg}}\\ +
-</wrap>\\ +
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-The figure shows the output voltage of an integrator with a square wave voltage at the input. The output voltage at the start $u_\mathrm{a}(t=0)$ depends on the charge state of the capacitor when switched on.\\ +
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-====Experimental Tasks==== +
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-To analyze the behavior of the integrator, the following circuit is used:\\  +
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-<wrap left> +
-{{drawio>mexlefirst_intern:integrator_experiment.svg}} +
-</wrap> +
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-__Supply voltages (from power supply unit):__\\  +
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-$UCC=+3~V, UEE~=-3~V$\\  +
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-__Values of the components used:__\\  +
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-$R1.3=10~kΩ, C1=10~nF$\\  +
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-  - Calculate the time constant $T_\mathrm{i}$ of the integrator from the given values. +
-  - Assumption: the capacitor is initially uncharged. A voltage $u_\mathrm{e}=+3~V$ is applied to the input. How long does it take for the output voltage to reach $u_\mathrm{Tr}=-3~V$? Document your calculation. +
-  - Roughly sketch the voltage curves that you expect at the TR output when you apply a bipolar square wave signal to the $u_\mathrm{e}$ input.\\ \\ **Output TR**\\ \\ <wrap left>{{drawio>mexlefirst_intern:oscilloscope_screen.svg}}</wrap>\\ \\ \\ Channel 1:$\frac {Volt}{Div}=$\\ \\ \\ Time basis: $\frac {T}{Div}=$\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\  +
-  - Build the circuit on the MEXLE-board. **Please use the level shifting circuit at the input of the circuit.** Make sure that the jumper at the bottom of the op-amp is set to the left so that the op-amp is supplied with +/- 3V. Connect channel 1 on the oscilloscope to $U_\mathrm{e}$ and channel 2 to TR. Connect the function generator to the $U_\mathrm{e}$ input. Set to square wave (bipolar) with a frequency of 3kHz and a voltage of 3 V (amplitude). Switch on the power supply. Take a photo of the oscilloscope screen image. \\ \\ \\ **C1 = 10 nF, f = 3 kHz**\\ \\ <wrap left>{{drawio>mexlefirst_intern:oscilloscope_screen.svg}}</wrap>\\ \\ \\ Channel 1: $\frac {Volt}{Div}=$\\ \\ Channel 2: $\frac {Volt}{Div}=$\\ \\ \\ Time basis: $\frac {T}{Div}=$\\ \\ \\ \\ \\ \\ \\ \\ \\  +
-  - Compare your measurement with the calculation from part 2 and the forecast from part 3. Explain your result. +
  
-====Test Questions - Integrator==== +For this experiment, you should be able to apply and explain the following concepts: 
-  +  - "golden rules" for the negatively feedback, idealized operational amplifier 
 +  - deviating properties of the real operational amplifier (e.g., output swing range, slew rate) 
 +  - output-voltage waveform $U_A$ of the inverting integrator (inverting integrator) for different input voltages $U_E$, e.g. 
 +    - DC voltage 
 +    - square-wave voltage 
 +    - arbitrary voltage waveform 
 +  - integration time constant of the inverting integrator 
 +  - Schmitt trigger 
 +    - difference in feedback compared to the inverting integrator 
 +    - idealized relationship between $U_E$ and $U_A$ 
 +    - idealized line diagram: $U_E$ and $U_A$ as a function of time 
 +    - switching thresholds 
 +    - threshold voltage 
 +    - hysteresis 
 +    - real behavior: output "in saturation" 
 +  - structure of the triangle–square-wave generator