Objective
The objective of this experiment is to demonstrate the use of a variable capacitor in tunable circuits, exploring how changes in capacitance affect the performance and frequency response of the circuit.
Materials Needed
- Variable capacitor (e.g., 10pF to 100pF)
- Inductor (e.g., 10µH)
- Resistors (e.g., 1kΩ, 10kΩ)
- Power supply (DC source)
- Oscilloscope
- Function generator
- Breadboard or PCB for assembly
- Multimeter
- Jumper wires
- Safety equipment (gloves, goggles, etc.)
Theory
Variable capacitors are widely used in tuning applications, allowing the user to adjust capacitance and thereby modify the frequency response of a circuit. The resonant frequency of an LC circuit is given by:
f₀ = 1 / (2 * π * √(L * C))
Where **f₀** is the resonant frequency, **L** is the inductance, and **C** is the capacitance. By varying the capacitance, the resonant frequency can be tuned across a desired range.
Steps
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Set Up the Circuit
Assemble the LC tuning circuit on a breadboard. Connect the variable capacitor in parallel with the inductor to form a resonant circuit. Ensure that all components are securely connected.
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Connect the Power Supply
Connect the power supply to the circuit. Set the voltage to a safe level (e.g., 5V to 12V) for the components used.
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Generate a Signal
Use the function generator to provide a sine wave signal to the circuit. Set the frequency range to cover the expected resonant frequency based on the component values.
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Measure Output Voltage
Connect the oscilloscope probes across the output (across the inductor or the variable capacitor) to measure the output voltage. Observe the waveform displayed on the oscilloscope.
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Tune the Capacitor
Adjust the variable capacitor and observe the changes in the output voltage amplitude and frequency response. Record the output voltage and resonant frequency for different capacitance settings.
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Analyze Results
Compare the output voltage levels and resonant frequencies as the capacitance is varied. Analyze how the tuning affects the circuit's performance.
Data and Calculations
Record the measured output voltages and resonant frequencies in the table below:
| Capacitance (pF) | Output Voltage (V) | Measured Frequency (kHz) |
|---|---|---|
| 10 | 2.0 | 12.6 |
| 50 | 3.5 | 7.1 |
| 100 | 4.8 | 5.0 |
Conclusion
This experiment illustrates the importance of variable capacitors in tuning circuits. The ability to adjust capacitance allows for precise control over the resonant frequency and overall circuit behavior, which is critical in applications such as radio frequency tuning and filter design.