Quarter-Wave
Understanding Quarter-Wave Sections
The quarter-wave transformer is arguably the most important single concept in transmission line design. Its impedance-inverting property enables matching, filtering, power division, and antenna feed design at microwave frequencies where lumped components are impractical.
Quarter-Wave Properties
- Impedance inversion: Z_in = Z0^2 / Z_load. A 70.7-ohm quarter-wave transforms 100 ohms to 50 ohms.
- Short to open: A quarter-wave line terminated in a short circuit presents an open circuit.
- Open to short: A quarter-wave line terminated in an open circuit presents a short circuit.
Applications
- Matching: Quarter-wave transformers between different impedances.
- Decoupling: Quarter-wave shorted stub for DC feed without RF leakage.
- Filters: Quarter-wave coupled resonators in bandpass filters.
- Antennas: Quarter-wave monopole. Quarter-wave matching section.
L = lambda/4 = c / (4f) (free space)
L = c / (4f sqrt(er_eff)) (in dielectric)
At 1 GHz: L = 75 mm (free space)
At 10 GHz: L = 7.5 mm
At 28 GHz: L = 2.68 mm
Impedance inversion: Z_in = Z0^2 / Z_load
Quarter-wave transformer: Z0 = sqrt(Z1 x Z2)
Frequently Asked Questions
What is a quarter-wave section?
A quarter-wave section is a transmission line of length lambda/4 (90 degrees). It inverts impedance: Z_in = Z0^2/Z_load. This property is used for impedance matching, stubs, filters, and antenna design.
How is quarter-wave length calculated?
L = c/(4f) in free space. In a transmission line: L = c/(4f x sqrt(er_eff)). At 10 GHz in free space: 7.5 mm. On a PCB with er_eff = 3: 4.33 mm. The physical length depends on the effective dielectric constant.
What is a quarter-wave transformer?
A quarter-wave transformer is a lambda/4 line with characteristic impedance Z0 = sqrt(Z_in x Z_load) that matches between two different impedance levels. It provides a perfect match at the design frequency and degrades at other frequencies.