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In the homework I have been working on, I encountered with such a statement:

If the rise time over transmit time in a circuit element is greater than 6, the circuit element can be treated as a lumped circuit element.

However, I couldn't understand where 6 comes from. If somebody can explain this, I will be really happy.

Thanks.

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    \$\begingroup\$ It's just a rule of thumb, similarly to how after 5 time constants you can assume the signal settled. It is a decent proportion where the lumped approximation becomes "good enough" \$\endgroup\$ – jbord39 Feb 7 '17 at 17:31
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There's a rule of thumb that says you need to begin to regard a cable as a transmission-line if the time it takes a signal to travel down the cable is greater than one tenth the wavelength of the signal.

It's all about reflections and how a cable (or pcb track) will reflect power back to the input end in sufficient levels to cause "problems" if not terminated correctly.

It's very similar to "rise time versus transit time" but works with a lower "safety factor".

So, a signal that has a long rise time relative to the cable length (length dictates transit time) won't be as "corrupted" by reflections in comparison to a rise time that is very short.

There is nothing special about the number 6 or the number 10 - they are just convenient rules of thumb numbers and, treating a circuit or a cable or a pcb track as a lumped element means you don't regard it as important enough to apply line terminations.

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