Subelement A: — Topic :
Question 6A432
Element 6 (Radiotelegraph)The correct formula for determining the surge impedance of a quarter wavelength matching line is:
Explanation
A quarter-wavelength matching line, also known as a quarter-wave transformer, is a specialized transmission line section used to match two different impedances. Its surge impedance (characteristic impedance, $Z_0$) is critical for this transformation.
The correct formula dictates that the characteristic impedance of the quarter-wavelength matching line must be the geometric mean of the two impedances it connects. If $Z_{ant}$ is the antenna impedance and $Z_{line}$ is the impedance of the main feedline (or the other impedance being matched), then the surge impedance of the matching section, $Z_0$, is given by:
$Z_0 = \sqrt{Z_{ant} \times Z_{line}}$
This relationship ensures maximum power transfer between the source and the load by transforming one impedance to match the other.
Option C, when correctly interpreted as $Z_0 = \sqrt{\text{impedance of antenna} \times \text{impedance of line}}$, aligns with this fundamental principle of quarter-wave impedance transformers. Options A and B present formulas that do not correspond to the established theory for determining the surge impedance of a quarter-wavelength matching line.
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