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Getting Started with the MEXLE-Board

Background Information

MEXLE is a Multimodal Experimental and Learning platform, designed to support self-directed and hands-on learning in electrical engineering.
The MEXLE-board is designed as a “lab-in-a-box” system that comes with a corresponding app. Electrical circuits can be built and tested on the board, while the app provides the experimental tasks together with the required background information.
At the moment, the system requires an external signal generator and an external oscilloscope. In a future version, the board itself will generate the required signals, with all signal settings controlled via the app. The oscilloscope function will also be integrated into the app, making an external oscilloscope no longer necessary.

MEXLE-board - Overview




MEXLE electronic components





Handling of the MEXLE components





RC network
RC circuits are commonly used to implement timers and delay circuits. In such applications, a capacitor is charged and discharged through a resistor. Since the capacitor voltage does not change instantaneously but rises and falls over time, the component values can be used to determine how long it takes to reach a specific voltage level.This principle is used, for example, in power-on delay circuits and timer-based flashing circuits. In the following experiment, the charging and discharging behavior of a capacitor will be investigated.

Capacitors must be charged via an electrical source.

A capacitor charges the faster the smaller the series resistor $R$ is. During charging, the voltage $u_{\rm C}$ results from a differential equation as:
$$ u_{\rm C}({\rm t})=U\cdot ({\rm 1}-e^{-\frac{t}{\tau}}), {\rm with~~} \tau = R\cdot C $$
The constant $\tau$ is called the time constant. After this time, the capacitor is charged to approx. ${\rm 63}~{\rm\%}$. The fundamental equation for the relation between current and voltage at a capacitor is:
$$ i_{\rm C}({\rm t})=C\cdot \frac{{\rm d}u_{\rm C}}{{\rm dt}} $$
From the two equations, the current through the capacitor is: $$ i_{\rm C}({\rm t})=\frac{U}{R}\cdot e^{-\frac{t}{\tau}} $$
The graphical representation of voltage and current during the charging of a capacitor over time is shown in figure 1.

Fig. 1: This is my little caption

Because of the exponential function, charging is theoretically only complete after an infinitely long time. The capacitor voltage equals ${\rm 63}~{\rm\%~} U$ after ${\rm 1}\cdot \tau$, ${\rm 86}~{\rm\%~} U$ after ${\rm 2}\cdot \tau$, ${\rm 95}~{\rm\%~} U$ after ${\rm 3}\cdot \tau$, ${\rm 98}~{\rm\%~} U$ after ${\rm 4}\cdot \tau$, and ${\rm 99}~{\rm\%~} U$ after ${\rm 5}\cdot \tau$. It is assumed that the capacitor is fully charged after a time span $T = {\rm 5}\cdot \tau$ and the voltage across the capacitor has reached $U$.

If the charged capacitor $C$ is discharged through a resistor $R$, the solution of the differential equation for the voltage is:

$$ u_{\rm C}({\rm t})=U\cdot e^{-\frac{t}{\tau}} $$
For the current accordingly:

$$ i_{\rm C}({\rm t})=- \frac{U}{R}\cdot e^{-\frac{t}{\tau}} $$

Experimental Tasks

To plot the charging and discharging curves of a capacitor, the following circuit is used:

- Configure the function generator of the handheld oscilloscope to provide a unipolar square-wave signal for the RC circuit shown. Use the following settings: * Amplitude: 3 V * Frequency: 1 000 Hz * Duty Cycle: 50%
- Place the power supply module in the upper-right corner of the board and the ground module on the bottom of the MEXLE-Board. After that, assemble the circuit shown on the board. Connect the alligator clips of the signal generator to the RC circuit to provide the input voltage $u_\mathrm{F}(t)$, and supply the MEXLE board with power via the Micro-USB connector. Then connect Channel 1 of the handheld oscilloscope to the input voltage $u_\mathrm{F}(t)$and Channel 2 to the capacitor voltage $u_\mathrm{C}(t)$. Move the CH1 and CH2 reference markers to the oscilloscope reference line. By pressing MOVE, you can switch between adjusting CH1 und CH2. Sketch the waveforms displayed on the oscilloscope.

- Calculate the time constant $\tau$ of the circuit. - Determine the time constant τ experimentally by measuring how long it takes for the capacitor voltage to rise from 0 to 63% of the maximum voltage during charging. To do so, press MENU and go to Cursor Measurement. For this task, you need to use both the X1–X2 and Y1–Y2 cursors. Return to the oscilloscope screen and press SELECT repeatedly until “X1 Y1” or “X2 Y2” is displayed at the top of the screen. Use all four arrow keys to position the selected cursor line. Press MOVE to switch between X1 Y1 and X2 Y2, and place each cursor as required. Compare your results with the time constants calculated theoretically. (Please leave the circuit assembled after completing the tasks, as it will be used again in the next experiment.)