# Trace capacitance vs telegraphers equation

I haven't taken a course on transmission lines or RF so bear with me.

Using EM we can calculate the capacitance and inductance of traces. I'm somewhat confused on the value of this calculation, though, because the telegraphers equation basically says you can't consider the trace as a lumped element.

Under what circumstances can you use the trace capacitance as a replacement for a lumped element? What is the value of these calculations and where can you use them?

• Inductance per unit length is a log ratio of l/w times some constant that starts around 10nH/cm which for 10:1 probes and long ground leads into the coax C of about 20pF/m causing resonant ringing on square waves around 20MHz so keep grounds short. Stray C between traces can be about 0.3 pF/cm for 8 mil gaps creates crosstalk at high f into high impedance.. Commented Jan 3, 2022 at 1:56

Using EM we can calculate the capacitance and inductance of traces. I'm somewhat confused on the value of this calculation though because the telegraphers equation basically says you can't consider the trace as a lumped element.

Using EM we can calculate the capacitance and inductance per unit length of a trace.

These are exactly the parameters needed to set up the telegrapher's equations.

Could someone explain under what circumstances you can use the trace capacitance as replacement for a lumped element?

Typically if the length of the line is less than 1/10 (or 1/20 if you want a very accurate model) of the wavelength at the frequency of interest, you can ignore transmission line effects and treat the line as lumped RLGC element.

What is the value of these calculations and where can you use them?

You can use an EM simulation to calculate the parameters of a short segment of a line (less than 1/10 or 1/20 wavelength) and cascade several such segments together to get a transmission line model built from lumped elements. In the limit as you take shorter segments and cascade more of them together, your model will give the same results as an analytical solution of the telegrapher's equations.

• Hmm I see, so you treat them as lumped under certain frequency, and higher you treat as Tline with the telegraphers equation. It's confusing partially because at even lower frequencies you just ignore them completely. Commented Jan 3, 2022 at 9:29
• Also it's very interesting how you can simulate this way, I know of fdtd approach but this is way simpler. Commented Jan 3, 2022 at 9:53
• The model I described is essentially a FEM model (reduced to 1-D). Commented Jan 3, 2022 at 17:34

Transmission line effects depend upon ratio of the length of the transmission line to the wavelength of the highest frequency of interest traveling along the transmission line. If the length of the transmission line is less than, say 1/10th of the wavelength of the maximum frequency of interest, then one often chooses to ignore transmission line effects. The ratio of 1/10 used to decide when to ignore transmission line effects is somewhat arbitrary. You could use 1/15 or 1/20. But in practice 1/10 is often used.

The maximum frequency of interest is typically higher than the frequency of a pulse train. Pulse trains typically consist of "square" pulses. The rise time of the pulses generally determines the maximum frequency of interest. The shorter the rise time, the higher the maximum frequency of interest. An alternative rule of thumb is that if the rise time is longer than (or maybe twice as long as) the time it takes for a signal to travel the length of a transmission line and back, then transmission line effects may be ignored.

With that in mind, at "low" frequencies (where "low frequencies" is defined in relationship to the length of the transmission line) the capacitance and inductance of the transmission line may be treated as lumped elements.

This is just a rule of thumb, and others may give different variations, but if you have a reasonably sized PCB, and your max clock rate is 10 MHz or less, you can treat the trace capacitances and inductances as lumped elements.