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Consider the following dipole:

enter image description here

I want to calculate the s-matrix of this circuit: i think it is \$ b = S a \iff S = \frac{b}{a} = \frac{z_L - 1}{z_L +1}\$ with \$ z_L = \frac{Z_L}{Z_o} \$ But according to @AndyAka's answer the coefficient of reflection doesnt have a conjugate on the characteristic impedance as if they assumed its a real quantity, not a complex one.

EDIT

Here is my approach, so i think the diagram is just an abstracted version of this circuit -correct me if im wrong - :

enter image description here

enter image description here enter image description here

Finally : \$S = \frac{b}{a} = \frac{V_r}{V_i} = \frac{Z_0}{Z_0 ^*} \cdot \frac{Z_L - Z_0^*}{Z_L + Z_0}\$

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  • \$\begingroup\$ That looks like the reflection coefficient to me. Is that what you are trying to achieve? \$\endgroup\$ Commented Oct 22, 2024 at 9:08
  • \$\begingroup\$ yes @Andyaka the reflection coefficient as seen from dipole \$\endgroup\$ Commented Oct 23, 2024 at 11:31
  • \$\begingroup\$ Are you saying you want to derive the reflection coefficient mathematically i.e. you are looking for a proof? Maybe this will help if you are: electronics.stackexchange.com/questions/725837/… \$\endgroup\$ Commented Oct 23, 2024 at 11:32
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    \$\begingroup\$ Yes, I have assumed a standard resistive impedance (as you would see for any cable above 100 kHz). \$\endgroup\$ Commented Oct 23, 2024 at 19:26
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    \$\begingroup\$ Infinite thanks sir, i had upvoted ur answer in the former link @Andyaka \$\endgroup\$ Commented Oct 23, 2024 at 20:23

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