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I have this easy schematic

enter image description here

Next to this is stated that:

$$Vb = \frac{Z_{in1}e_{b}}{R_{B}+Z_{in1}}$$

non Latex-version of the formula: Vb = (eb*Zin1)/(Rb+Zin1)

  • I would like to know from where this formula comes and what it actually calculates. Is it based on Ohm's law? If yes, how do you eventually modify ohm's law in order to obtain this?

  • It is also stated that Vb can be a complex number. Under which conditions would this be true?

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  • \$\begingroup\$ Where is \$V_b\$ in your schematic? \$\endgroup\$ – The Photon Apr 16 '16 at 16:29
  • \$\begingroup\$ @ThePhoton edited my post. \$\endgroup\$ – J.Doe Apr 16 '16 at 16:33
  • \$\begingroup\$ \$Z_{in1}\$ is the impedance looking into the transmission line at the first pair of terminals, as indicated by the arrow. This impedance may be (and usually is) complex. Then apply the voltage divider to \$e_b\$, \$Z_{in1}\$ and \$R_b\$ to obtain the equation for \$V_b\$. \$\endgroup\$ – Chu Apr 16 '16 at 16:42
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Your formula is just the voltage divider formula. \$E_b\$ is the input voltage, which is divided between the source resistance \$R_b\$ and the effective input impedance \$Z_{in1}\$.

\$V_b\$ will always be a complex number (since real numbers are a subset of the complex number). The imaginary part will be non-zero whenever \$Z_{in1}\$'s imaginary part is nonzero. This will almost always be true. There are a few special cases where it won't, like if \$Z_{c1}=Z_{c2}\$ and \$R_l=Z_{c2}\$, or if you use a special combination of transmission line lengths and load impedances that happens to add up to give a reflection with 0 or 180 degree phase.

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