Parameters of Quarter-Wave Impedance Transformer
- Length: The transformer is a transmission line segment whose length is precisely equal to a quarter of the signal’s wavelength (λ/4). This guarantees certain phase changes in the line.
- Impedance matching: Reflections arise when the transmission line’s characteristic impedance (Zo) and load impedance (ZL) disagree, leading to signal distortion and loss. In its capacity as an impedance transformer, the quarter-wave transformer reflects the signal back with a 180° phase shift. In order to achieve impedance matching and reduce reflections, this essentially “cancels out” the original reflected wave at the input.
- Duality: The output impedance of the transformer is equal to its termination impedance times two. This indicates that the transformer offers a lower impedance at its input if the load has a higher impedance than the line.
Remember our formula for the input impedance of a transmission line of length L that is connected to a load with an impedance of ZA and has characteristic impedance Z0:
Formula
Zin (-1) = Zo
ZA+ jZo tan(BL) Zo+jZA tan(BL)
When the line is one-fourth of the wavelength in length, an intriguing phenomenon occurs. The above equation is significant because it shows how the impedance of the load (ZA) can be changed using a transmission line with a quarter-wavelength. Through an example, the usefulness of this procedure is demonstrated.
Example
Match a load using a quarter-wave transformer to have an impedance of ZA = 100 Ohms to 50 Ohms.
The solution is to find Z0, our quarter-wavelength transmission line’s characteristic impedance, so that the load of 100 ohms is matched to 50 ohms. Using the equation above, the issue becomes straightforward:
Zin (L 50 = ==z3 100) 금 ZA =・→20=√ (50) (100) 70.712
Quarter Wave Transformer
To match impedances, a quarter-wave transformer is a basic tool in electrical engineering and RF circuit design. Basically, it’s a section of transmission line that helps guarantee effective power transfer from a source to a load. It has a set length. In radio frequency (RF) and microwave engineering, a quarter-wave transformer is an essential tool for matching the impedance of a transmission line to that of a load. This reduces signal reflections and guarantees effective power transfer .