What is the electrical length of a quarter-wave transformer used for impedance matching?

What is the electrical length of a quarter-wave transformer used for impedance matching?

• A. λ/4
• B. λ/2
• C. λ
• D. 3λ/4

Answer: (A)

The key idea is that a quarter-wave transformer is built from a piece of transmission line whose length is one quarter of the wavelength at the operating frequency. This λ/4 length causes the input impedance seen at the source to be Z_in = Z0^2 / Z_L for a lossless line, which is the essential impedance transformation that enables matching. By selecting the line’s characteristic impedance Z0 appropriately (for example, Z0 = sqrt(Z_S Z_L)), the input impedance can be made equal to the source impedance, achieving optimal power transfer. The λ/4 length also corresponds to a 90-degree phase shift between the ends, consistent with the transformation behavior. So the electrical length is λ/4.

The key idea is that a quarter-wave transformer is built from a piece of transmission line whose length is one quarter of the wavelength at the operating frequency. This λ/4 length causes the input impedance seen at the source to be Z_in = Z0^2 / Z_L for a lossless line, which is the essential impedance transformation that enables matching. By selecting the line’s characteristic impedance Z0 appropriately (for example, Z0 = sqrt(Z_S Z_L)), the input impedance can be made equal to the source impedance, achieving optimal power transfer. The λ/4 length also corresponds to a 90-degree phase shift between the ends, consistent with the transformation behavior. So the electrical length is λ/4.