Transmissielijnen/Voortplantingscoëfficiënt: verschil tussen versies

:<math>\,\gamma^2 = \alpha^2-\beta^2+2j\alpha \beta = (r+j\omega c)(g+j\omega l) = (rg-\omega^2lc) + j\omega (rc+lg)</math>.

:<math>\,\alpha^2-\beta^2 = rg-\omega^2lc = -p</math> (voor de meeste gevallen p > 0)

:<math>\,2\alpha \beta = \omega (rc + lg) = q</math> (q > 0)

:<math>\, \alpha \sqrt 2 = \sqrt{\sqrt{p^2+q^2} - p}</math>

:<math>\, \beta \sqrt 2 = \sqrt{(\sqrt{p^2+q^2} + p)}</math>.

:<math>\, \alpha \sqrt 2 = \sqrt{p\sqrt{1+q^2/p^2} - p} \approx \sqrt{p(1+q^2/2p^2) - p}=\frac{q}{\sqrt{2p}}</math>

:<math>\, \alpha \approx \frac{q}{2\sqrt{p}} \approx \omega \frac{rc + lg}{2\sqrt{\omega^2lc}} = \fractfrac 12 (r\sqrt{\frac{c}{l}} + g\sqrt{\frac{l}{c}})</math>

:<math>\, \beta \approx \sqrt{p+q^2/4p}\approx \omega\sqrt{lc} - \frac{rg}{4\omega\sqrt{lc}}</math>.

:<math>\,\alpha^2 \approx \alpha^2-\beta^2 = rg-\omega^2lc \approx rg.</math>

:<math>\,2\alpha \beta = \omega (rc+lg)</math>

:<math>\,