This calculator determines the characteristic impedance of a quarter-wave transformer, used to match two transmission lines with different impedances. It helps minimize reflections and ensure maximum power transfer between RF stages.
Useful for RF engineers, filter designers, and students who want to design simple and efficient matching networks.
Formula
Z₀ = √(ZL × Zin)
Explanation of the formula
- ZL is the load (output) impedance.
- Zin is the input (source) impedance.
- The quarter-wave transformer operates at a wavelength λ/4 to achieve perfect matching to the design frequency.
- The calculated characteristic impedance Z₀ corresponds to the value that the intermediate line section must have to balance the two impedances.
50 ohm to 100 ohm quarter wave transformer
Input : ZL = 100 Ω, Zin = 50 Ω
Output : Z₀ = 70.7 Ω
Benefits and uses
- Allows efficient impedance matching without an active component.
- Reduces losses due to reflections in RF lines.
- Useful for microwave antennas, amplifiers and filters.
- Simple to calculate and implement in practical designs.