![]() Maybe it is more convenient to use Z 0=Z t Smith chart for obtaining impedance transformation graphically without formulas (Smith chart center at Z t, not at 50 Ohm)įor deeper understanding of Smith chart I recommend to calculate impedance change for different line lengths using formulas, then calculate corresponding reflection coefficient Г (vector) for each case and draw it on a Smith chart. Why overlay the Smith chart scaled for ZT on top of the Z0 Smith Maybe for emphasizing that it is not an arithmetic mean (Zout+Zin)/2.įormula for Zt is derived without using Smith chart. ![]() Why "ZT-line is the geometric mean of Zout and Zin." ? A reading around the 50 ohm or 75 ohm rating of the cable indicates that the cable is working properly across its length. Rotation go through upper or lower half circle depending on particular values of Z out and quarterwave transformer line impedance Z t. Cutting physical line length will result in counter-clockwise direction. On a Smith chart phase delay corresponds to clockwise rotation around some center depending on Zline(phase decreases clockwise). Traverse is across the upper half of a circle is because of adding physical line with length θ=90° delays reflection from Г(Z out) by 2*θ=180° (90° before reflection and 90° after reflection). ![]() Why traverse across the upper half circle ?
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