Coaxial Transformer in RF Experiment

Objective

This experiment demonstrates how to design and implement a coaxial transformer for impedance matching in RF (radio frequency) applications. The focus is on understanding how to transform impedance values between different sections of an RF circuit using coaxial cable.

Materials Needed

Theory

A coaxial transformer is a type of impedance transformer used in RF applications to match the impedance of a source to the load for maximum power transfer. By selecting the appropriate length of coaxial cable, it is possible to transform impedances between sections of an RF circuit. The relationship is based on the electrical length of the cable and the characteristic impedance of the coaxial line.

The impedance transformation can be expressed as:

Zout = Zin × (Z0² / Zload)

Where:

The length of the coaxial transformer is often chosen as a quarter-wavelength (λ/4) to achieve the desired impedance transformation at a specific frequency.

Steps

  1. Calculate the Quarter-Wavelength

    Use the formula to calculate the electrical length of the coaxial transformer for the frequency of interest:

    λ = c / f

    Where λ is the wavelength, c is the speed of light (~3 × 108 m/s), and f is the frequency in hertz. For a quarter-wavelength, use λ/4.

    Example: If the frequency is 100 MHz, then the wavelength is 3 meters, and a quarter-wavelength is 0.75 meters (75 cm).

  2. Cut the Coaxial Cable

    Cut a length of coaxial cable corresponding to the calculated quarter-wavelength at the desired operating frequency. Be sure to account for the velocity factor of the coaxial cable, which is typically between 0.66 and 0.85, depending on the type of cable.

  3. Connect the Coaxial Cable

    Strip both ends of the coaxial cable and connect one end to the RF signal generator and the other end to the load (e.g., 50Ω or 100Ω resistor). Use appropriate connectors such as BNC or SMA to ensure secure and low-loss connections.

  4. Measure the Impedance

    With the signal generator set to the desired operating frequency, measure the input impedance of the coaxial transformer using an RF power meter or oscilloscope. Compare this impedance to the expected value, which should show impedance transformation based on the coaxial transformer characteristics.

  5. Adjust the Design

    If the impedance transformation is not as expected, check the length of the coaxial cable and ensure proper connections. Fine-tuning the length of the cable may be necessary to achieve optimal impedance matching at the target frequency.

Example Calculation

Consider a coaxial transformer designed to match a 50Ω source to a 100Ω load at 100 MHz. First, calculate the quarter-wavelength:

λ = 3 × 108 m/s / 100 × 106 Hz = 3 meters

The quarter-wavelength (λ/4) is:

λ/4 = 3 meters / 4 = 0.75 meters

Considering the velocity factor (e.g., 0.66 for RG58 coaxial cable), the adjusted length of the coaxial cable would be:

Adjusted Length = 0.75 meters × 0.66 = 0.495 meters

Cut a length of 49.5 cm coaxial cable for the transformer. Once connected, the impedance should show an appropriate transformation between the 50Ω input and 100Ω load.

Conclusion

The coaxial transformer is a simple and effective method for impedance matching in RF circuits, ensuring maximum power transfer between components operating at different impedance levels. By carefully calculating the quarter-wavelength and using appropriate coaxial cable, you can create a transformer for a wide range of RF frequencies and applications. This experiment illustrates the importance of impedance matching in RF design and demonstrates a practical approach to achieving it.