The impedance measurement method provides a straightforward approach for determining the inductance of an inductor. By forming a series circuit with a known resistor and applying a sinusoidal voltage, the inductance can be deduced from the voltage measurements across the components. This experiment leverages the capabilities of the Red Pitaya board to accurately measure the inductance of an unknown inductor.

**Objective**

The aim is to calculate the inductance of an unknown inductor by analyzing its impedance in a series circuit with a resistor. Utilizing the Red Pitaya’s function generator and oscilloscope functions, the experiment seeks to apply the impedance formula for inductance calculation.

**Experimental Setup**

**Materials**

- Red Pitaya board
- A known resistor (100Ω)
- An unknown inductor
- Sinusoidal voltage signal (1 kHz) from Red Pitaya’s function generator
- Breadboard and jumper wires

**Assembly**

**Circuit Construction:**Assemble the circuit on a breadboard by connecting the known resistor in series with the unknown inductor. Connect the series circuit between the Red Pitaya’s positive function generator output (OUT1) and ground (GND).**Measurement Configuration:**Attach oscilloscope probes across the inductor (IN1) and across the entire RL circuit (IN2) to measure the respective voltages.

**Procedure**

**Signal Generation:**Configure the Red Pitaya to output a 1 kHz, 1V peak-to-peak sinusoidal signal.**Waveform Observation:**Adjust the oscilloscope settings to properly display the waveforms. Start with a 1 kHz frequency and gradually increase until a 50% voltage drop across the inductor is observed. Record this frequency.

At the half-power frequency (50% voltage drop), the inductive reactance (X_L) is equal to the resistance (R). Therefore:

$X_L = R$Given that the inductive reactance is calculated using the following formula:

$X_L = 2\pi f L$We can rearrange this formula to find the value of the inductor (L):

$L = \frac{X_L}{2\pi f}$Now we know that X_L = R, we can substitute R for X_L:

$L = \frac{R}{2\pi f}$Substitute the values you provided (R = 100 ohms, f = 12300 Hz) into the equation:

$L = \frac{100}{2\pi \times 12300}$Calculate the inductance:

$L \approx 0.001326 , \text{H} = 1.326 , \text{mH}$Thus, the estimated value of the unknown inductor is approximately 1.326 mH. Keep in mind that this is an approximation and may not be the exact value, but it should provide a reasonable estimate for your experiment. The specified inductor value was 1mH but note that is made with 15% tolerance, which means our measurement was really an approximation of the value.

**Conclusion**

Utilizing the impedance measurement method with the Red Pitaya facilitated an accurate estimation of the unknown inductor's inductance. This method underscores the effectiveness of the Red Pitaya in conducting electrical measurements and its utility in educational and experimental settings. Despite the approximation, the calculated inductance value closely aligns with the expected range, considering the inductor's tolerance. This experiment highlights the practical application of impedance principles in inductance measurement and the versatility of modern electronic measurement tools.