Resonant Circuit Design Experiment

Objective

Understand the behavior of resonant circuits by designing and analyzing an LC circuit that resonates at a specific frequency. The experiment demonstrates the resonance phenomenon and its effects on circuit impedance and current.

Materials Needed

Theory

In a resonant LC circuit, the inductive reactance and capacitive reactance cancel each other at a particular frequency, called the resonant frequency (fr). At this frequency, the impedance of the circuit is purely resistive, and the current reaches its maximum value.

The resonant frequency of an LC circuit is given by:

fr = 1 / (2π√LC)

Steps

  1. Calculate Resonant Frequency

    Choose values for the inductor (L) and capacitor (C). Calculate the resonant frequency fr using the formula provided in the theory section.

  2. Build the LC Circuit

    Assemble the inductor and capacitor in series on the breadboard. You may add a small resistor in series to observe the voltage drop across the circuit elements.

  3. Connect Function Generator and Oscilloscope

    Connect the function generator to the LC circuit to apply a sinusoidal signal. Connect the oscilloscope across the circuit to measure the voltage and observe the signal.

  4. Measure and Observe

    Set the function generator to output a frequency near the calculated resonant frequency. Gradually adjust the frequency and observe the voltage amplitude across the circuit using the oscilloscope.

  5. Calculate and Compare

    Compare the observed resonant frequency to the calculated value. Measure the bandwidth and quality factor (Q) by observing the resonance curve.

Conclusion

By designing a simple resonant LC circuit, we can observe the phenomenon of resonance and how it affects the circuit’s impedance and current. This experiment highlights the importance of resonance in radio-frequency and communication systems.