Objective

To understand the concept of impedance matching using a transformer and measure the output voltage and power transfer efficiency in a circuit.

Theory

An impedance matching transformer is used to transfer maximum power between a source and a load by matching their impedances. When the impedances are matched, the voltage across the load is maximized, and power transfer efficiency is improved.

The turns ratio of the transformer (\( n \)) is related to the impedance transformation as follows:

Z_{out} = Z_{in} * (n^2)

Where:

• \( Z_{out} \) = Load impedance
• \( Z_{in} \) = Source impedance
• \( n \) = Turns ratio (secondary turns / primary turns)

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Components Required

• Transformer (with specified turns ratio)
• Resistors for load and source (e.g., 50Ω and 100Ω)
• Function generator (to provide an input signal)
• Oscilloscope (to measure voltages)
• Multimeter (to measure current and resistance)
• Connecting wires
• Breadboard (optional)

Circuit Diagram

Below is the circuit diagram for the impedance matching transformer setup:

In this diagram:

• The input signal is connected to the primary winding of the transformer.
• The load resistor is connected to the secondary winding.

Procedure

1. Set up the circuit on a breadboard according to the circuit diagram.
2. Connect the function generator to the primary winding of the transformer.
3. Connect the load resistor to the secondary winding.
4. Use the oscilloscope to measure the voltage across the primary and secondary windings.
5. Record the input voltage (\( V_{in} \)) and output voltage (\( V_{out} \)) across the load.
6. Calculate the load impedance and compare it with the source impedance.
7. Measure the current through the load resistor and calculate power transfer efficiency using:

Efficiency = (V_{out}^2 / R_{load}) / (V_{in}^2 / R_{source})

Results

Document your findings in a table format:

Conclusion

The experiment demonstrates the importance of impedance matching in electrical circuits. By using a transformer to match the impedances, the output voltage and power transfer efficiency can be significantly improved. This principle is widely applied in audio equipment, RF circuits, and many other electronic applications.