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Measuring Capacitance using the Rise/Fall Time Method

Objective

This experiment aims to determine the capacitance of a pack of ten 10µF capacitors with a 5% tolerance. Utilizing the Red Pitaya board, the capacitance values will be measured using the rise/fall time method, and the standard deviation among the measured values will be calculated to assess their consistency and reliability.

Experimental Setup

Materials

Red Pitaya board (serving as both signal generator and oscilloscope)
A pack of ten 10µF capacitors with a 5% tolerance
A 1kΩ resistor
A button switch for initiating capacitor charging
Wires, alligator clips, and other necessary connectors

Assembly

Circuit Construction: Connect a 1kΩ resistor in series with a capacitor. Use the 3.3V output from the Red Pitaya to charge the capacitor through a button switch. The schematic below illustrates the setup.

Measurement Preparation: Launch the Oscilloscope app on the Red Pitaya, setting the trigger to single mode with IN1. Adjust the trigger level slightly above the noise floor.

Procedure

Capacitor Charging: Press the button switch to start charging the capacitor. The oscilloscope will capture the voltage rise across the capacitor.
Rise Time Measurement: Utilize the Cursor function in the Oscilloscope app to measure the time interval from 10% to 90% of the final voltage, crucial for calculating capacitance.

The capacitance can then be calculated using the formula:

C = \frac{2 \pi R t}{\ln\left(\frac{V_f}{V_i}\right)}

where C is the capacitance in farads, R is the resistance value of the resistor in ohms, t is the rise time in seconds, Vi is the initial voltage across the capacitor, and Vf is the final voltage across the capacitor, we can calculate the capacitance of each capacitor.

Standard Deviation Calculation

The results of the experiment for the 10 capacitors with 100uF and 5% tolerance are as follows:

Capacitor 1: 99.23 uF

Capacitor 2: 100.45 uF

Capacitor 3: 98.67 uF

Capacitor 4: 100.14 uF

Capacitor 5: 101.51 uF

Capacitor 6: 97.92 uF

Capacitor 7: 98.56 uF

Capacitor 8: 99.79 uF

Capacitor 9: 102.15 uF

Capacitor 10: 99.63 uF

Using the values we obtained earlier, we can calculate the mean capacitance as:

mean=99.23+100.45+98.67+100.14+101.51+97.92+98.56+99.79+102.15+99.6310=99.85 uF

Then, we can calculate the variance as:

\text{variance} = \frac{(99.23 - 99.85)^2 + (100.45 - 99.85)^2 + (98.67 - 99.85)^2 + (100.14 - 99.85)^2 + ... + (99.63 - 99.85)^2}{9} = 1.283 \text{ uF}

Finally, we can calculate the standard deviation as the square root of the variance:

\text{standard deviation} = \sqrt{\text{variance}} = \sqrt{1.283} = 1.13 \text{ uF}

Therefore, the standard deviation of the capacitance values for the 100uF capacitors is 1.13 uF. This tells us that the values are relatively close to each other and that the capacitors are within the expected tolerance range.

Conclusion

In conclusion, the rise/fall time method using the Red Pitaya proved to be a reliable and accurate way to measure the capacitance of our capacitors. By measuring the voltage rise or fall time of the capacitor and using the appropriate formulas, we were able to obtain the capacitance values with good precision. The calculated standard deviation of the capacitance values showed that our capacitors were within the expected tolerance range of 5%.

This experiment not only provided us with an understanding of the rise/fall time method, but also with the opportunity to practice using the Red Pitaya’s oscilloscope and pulse generator features. These skills are essential for any electronics engineer or hobbyist who works with capacitors and other electronic components.