# Confusion regarding considering a transmission line as lumped or distributed

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.

• That looks way too dense. You seriously think someone is going to read all that!? If you have a question, ask it, don't add a lecture. Jul 23, 2013 at 14:20
• Which books did you get this from? Effective length is very different for different purposes; e.g. signal interference lengths are different from bulk attenuation lengths, or just power transmission lines. Jul 23, 2013 at 14:41
• @user26129: i have high speed design, Black magic for effective length of a electrical parameter like risetime,. i am not sure about "signal interference lengths and bulk attenuation lengths".. Jul 24, 2013 at 3:21