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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

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Hint

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: -

$$\dfrac{Z_{IN}}{Z_0}=\dfrac{Z_0}{Z_L}$$

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

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  • \$\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\$
    – asifkhan123
    Jan 8 at 21:35

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