so my lecturer released a past paper with the answers and I have no idea how he got the answer to this question. Please could someone explain it to me? Thanks.

The question is: A lossless quarter-wavelength transmission line is terminated by a load of 100+j50 Ω at one end. The input impedance seen at the other end is 100-j50 Ω. What is the characteristic impedance of the quarter-wavelength transmission line?

The answer is meant to be 112Ω

  • \$\begingroup\$ In order to perform Conjugate matching of Zin to Zout the Zo must be the RMS result of \$Z_o=(x^2+y^2)^{0.5}\$ for Zin=x+jy \$\endgroup\$ Jan 8, 2022 at 23:16
  • \$\begingroup\$ amanogawa.com/transmission.html \$\endgroup\$
    – Antonio51
    Jan 9, 2022 at 9:23

1 Answer 1



It's called a quarter wave impedance transformer and is covered thoroughly and extensively (and maybe quite beautifully) by this wiki site. That site contains this formula: -


If you rearrange that formula and solve for \$Z_0\$ you'll get the answer 111.803 Ω

  • \$\begingroup\$ Thank you so much, I was looking at the other formula for the characteristic impedance, hence why it didn't make sense. Much appreciated! \$\endgroup\$ Jan 8, 2022 at 21:35

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.