I am just elaborating my question.
I have came across different formula's to say whether a Transmission line is lumped or distributed.
in one of the books i read
" Effective length of a electrical feature like rise time is = \$tr(rise\space time\space in\space ps)\over D(time\space delay\space in\space {ps\over in})\$.
If the trace length is > \${Effective\space length\over 6}\$ ==> then Trace is distributed in nature.
from basics what i remember,
"when any trace length is comparable to wavelength (\${\lambda\over 4}\$ or sometimes \${\lambda \over 5}\$ or \${\lambda\over (\sqrt{2\pi})}\$" ===> Considered as distributed line.
if i take rise time = 1ns and freespace velocity = \$3*10^8{m\over s}\$.==> delay as \$85{ps\over inch}\$ \${10^{12}\over 3*10^8*39.37}\$
first reference will give
effective length= \${1000ps\over 85 {ps\over in}} = 11.765 in.\$
\${effective\space length\over 6} = 1.96 in\$
So, any transmission line which exceeds length of 2 in will be considered as distributed.
As per 2nd refernce which i mentioned.
for rise time tr = 1ns
Maximum freq \$(fknee) = {0.5\over tr} = {0.5\over 1ns} = 500Mhz\$
So, wavelength of this feature \$= {3*10^8 \over 500Mhz} = 0.1meters ==>~ 3.94inches\$(approx)
So, now
\${\lambda\over 6} = 0.6562in.\$
\${\lambda\over 5} = 0.787 in.\$
one of the value is almost double to the other method ( because of factor 0.5 used in calculating knee frequency)
in some references i have seen knee freq was mentioned as \${1\over \pi*tr}\$ where \$\pi=3.14\$
in some references i have seen if the round time delay of the signal is comparable to the rise time then it is considered as distributed line.
if i am wrong please correct me.
Why these many variations.
I clearly don't know are there any different conditions under which each formula will be valid.
Best Answer
The lumped model of a wire (or any other element) is an approximation. It's not entirely accurate, but it can be useful in many circumstances.
The distributed transmission line model given by the telegrapher's equations is another approximation. It's useful in some circumstances where the lumped model becomes very inaccurate. But it will itself break down and be inaccurate in some cases.
If you are worried that the lumped approximation might not be accurate enough in your situation, you should solve your problem both ways (or maybe a small piece of your problem that will reveal the scale of the discrepancy between the models). If the difference is big enough to affect the final conclusions you are trying to draw from the model, then you should use the transmission line model. If the differences are too small to affect your conclusions, then you may be able to save some time and effort by using the lumped-element model.