# Distributed LC vs Distributed RC

The usual rule with LC circuits is to use the lumped model if the circuit is considerably smaller than the wavelength, or if the propagation time is considerably smaller than the rise time.

With RC circuits however, using the distributed model is important no matter the wavelength and there are relations between the lumped and distributed models. For example, the time to reach 63% of the final voltage is half for the distributed model (the Elmore delay).

I'm concerned about the difference in terms of ringing period and peak ringing amplitude between the distributed and lumped LC, not considering any wave behaviour (the circuit is much smaller than the wavelength). I couldn't find any relation between the two approaches. It would be useful to simulate it as lumped and use a simple conversion to get the real behaviour, like for distributed RC.

So my questions are:

1.What are the relations between distributed and lumped LC?

2.If the circuit is much smaller than the wavelength, is it true that all the voltages measured on the line have the same phase? Is the LTspice (or PSpice) simulation accurate?

later edit: in the picture above the voltages are in phase because it is not long enough or it doesn't have enough inductance or capacitance. I've managed to get the same delay as for the transmission line component by using 10 LC elements and enough inductance.

• I think you meant propagation time less than rise time to avoid wave reflections. – Tony Stewart Sunnyskyguy EE75 Mar 9 '19 at 23:51
• yes, corrected. I've read that reflections and ringing are in fact the same thing, and if the electrical length of the circuit is much smaller than the wavelength then there shouldn't be any ringing. The simulation however shows a different result, for the conceptual 0.02 uH inductor at least. – user10010101 Mar 10 '19 at 0:04
• the circuits shown are not equivalent. – Tony Stewart Sunnyskyguy EE75 Mar 10 '19 at 0:10
• In the RC cascade each stage is impeded by the following stage, thus raising the breakpoint, so not the same. Also the LC ladder, the load impedance is affected by the source so you get much greater bandwidth with a 16th order LPF with high ripple. Near the breakpoint. A cable length of a known impedance has a distributed RLC network which is not what you are using. – Tony Stewart Sunnyskyguy EE75 Mar 10 '19 at 1:33