Could some electronics guru please clarify a few subtle questions regarding lumped parameter model of transmission lines ? The simple loss-less lumped parameter model consists of an ideal capacitor-inductor pair per unit length. OTOH, the lossy model includes a series resistance with the ideal inductor and an dielectric conductance in parallel with the ideal capacitor. Similarly, the non-ideal capacitor model includes a series resistance and a series inductance with the ideal capacitor. The non-ideal inductor model includes parasitic capacitance and resistance values. So, the question is: if one were to replace the ideal capacitor/indcutor pair in the lossless transmission line model with a non-ideal capacitor/inductor pair, then would this new model effectively re-create the lossy transmission line model ? I have done some SPICE modelling on this idea, and the results look encouraging. What do you gurus feel ? Any hints/suggestions would be greatly appreciated. Thanks in advance.
Ideal vs. lossy transmission line model question
Started by ●February 27, 2015
Reply by ●February 28, 20152015-02-28
On Fri, 27 Feb 2015 20:54:30 -0700, <dakupoto@gmail.com> wrote:> Could some electronics guru please clarify > a few subtle questions regarding lumped > parameter model of transmission lines ? > > The simple loss-less lumped parameter model > consists of an ideal capacitor-inductor pair > per unit length. > > OTOH, the lossy model includes a series > resistance with the ideal inductor and an > dielectric conductance in parallel with > the ideal capacitor. > > Similarly, the non-ideal capacitor model > includes a series resistance and a series > inductance with the ideal capacitor. The > non-ideal inductor model includes parasitic > capacitance and resistance values. > > So, the question is: if one were to replace > the ideal capacitor/indcutor pair in the > lossless transmission line model with a > non-ideal capacitor/inductor pair, then > would this new model effectively re-create > the lossy transmission line model ? I have > done some SPICE modelling on this idea, > and the results look encouraging. What do > you gurus feel ? > > Any hints/suggestions would be greatly > appreciated. Thanks in advance.Didn't understand a lot of what you said, except 'ideal' rarely represents what I want. Don't forget the resistance of the shield. It can have more effect than you might think. I like using a very small 'lumped' model segment used ovre and over to form the whole length. You just have to watch that the smallest segment is at least 10 times your highest frequency of interest to maintain a hope of phase accuracy. Although the resulting model has an upper frequency limit, you can use the model to represent DC feed, include skin effects in BOTH the shield and the conductor, etc etc. So you end up with a fairly good model that represents the dispersion of your cable. if you add an external 377 ohm Zo line, you can even start to explore radiation from your shield as you actually use the model in an overall circuit. I've gotten such to get close to the NEC predictions for single ended radiators.
Reply by ●February 28, 20152015-02-28
On Fri, 27 Feb 2015 19:54:30 -0800, dakupoto wrote:> Could some electronics guru please clarify a few subtle questions > regarding lumped parameter model of transmission lines ? > > The simple loss-less lumped parameter model consists of an ideal > capacitor-inductor pair per unit length. > > OTOH, the lossy model includes a series resistance with the ideal > inductor and an dielectric conductance in parallel with the ideal > capacitor. > > Similarly, the non-ideal capacitor model includes a series resistance > and a series inductance with the ideal capacitor. The non-ideal inductor > model includes parasitic capacitance and resistance values. > > So, the question is: if one were to replace the ideal capacitor/indcutor > pair in the lossless transmission line model with a non-ideal > capacitor/inductor pair, then would this new model effectively re-create > the lossy transmission line model ? I have done some SPICE modelling on > this idea, > and the results look encouraging. What do you gurus feel ? > > Any hints/suggestions would be greatly appreciated. Thanks in advance.You might like to read this s.e.d. thread from last century: https://groups.google.com/d/msg/sci.electronics.design/uvkEtEJgDwM/etiIa79Rq5YJ To answer your question: It wouldn't be a great wideband model, but might meet your accuracy goals at low frequencies. The ESL of the capacitor would cause the shunt impedance to rise at frequencies above the SRF of the capacitor. Real cables don't do that. Regards, Allan
Reply by ●February 28, 20152015-02-28
On Fri, 27 Feb 2015 19:54:30 -0800 (PST), dakupoto@gmail.com wrote:>Could some electronics guru please clarify >a few subtle questions regarding lumped >parameter model of transmission lines ? > >The simple loss-less lumped parameter model >consists of an ideal capacitor-inductor pair >per unit length.Yes. It is an OK model at frequencies well below the LC cutoff. Its step response is very ringy, which is unrealistic.> >OTOH, the lossy model includes a series >resistance with the ideal inductor and an >dielectric conductance in parallel with >the ideal capacitor. > >Similarly, the non-ideal capacitor model >includes a series resistance and a series >inductance with the ideal capacitor. The >non-ideal inductor model includes parasitic >capacitance and resistance values. > >So, the question is: if one were to replace >the ideal capacitor/indcutor pair in the >lossless transmission line model with a >non-ideal capacitor/inductor pair, then >would this new model effectively re-create >the lossy transmission line model ? I have >done some SPICE modelling on this idea, >and the results look encouraging. What do >you gurus feel ? >Heaviside derived the "telegraphers equation" around 1880. People who didn't believe in inductance kept building telegraph systems, including expensive undersea cables, that didn't work at the expected speeds. https://en.wikipedia.org/wiki/Telegrapher%27s_equations He also invented the loading coil. In most cases, the serious lossy element is the series resistance part of the inductor. Shunt conductance and capacitor losses are usually minor. The bummer with the series loss is that it involves skin effect, and the resistance increases with frequency. So a step response in, say a coaxial cable, has a horrible long slow drool, clearly visible on an oscilloscope. PCB traces have a similar drool. https://dl.dropboxusercontent.com/u/53724080/TDR/Chimera_TDR/TDT_risetime.JPG I think we had a thread a while back on modeling a transmission line that includes skin effect. You might search for that. Bottom line, adding the series Rs to an L-C string makes it more like a real-life lossy line, but doesn't replicate the skin effect. I used to use ECA, a nice DOS, text-netlist simulator. It didn't have a delay line part. I wrote a Basic program to generate the netlist for LC delay lines. The bummer is that the number of LC sections goes up as the square of the delay/risetime ratio. (I also paid for Electronics Workbench, and their delay line model was broken. Got my money back.) -- John Larkin Highland Technology, Inc picosecond timing laser drivers and controllers jlarkin att highlandtechnology dott com http://www.highlandtechnology.com
Reply by ●February 28, 20152015-02-28
On 2/28/2015 11:13 AM, John Larkin wrote:> On Fri, 27 Feb 2015 19:54:30 -0800 (PST), dakupoto@gmail.com wrote: > >> Could some electronics guru please clarify >> a few subtle questions regarding lumped >> parameter model of transmission lines ? >> >> The simple loss-less lumped parameter model >> consists of an ideal capacitor-inductor pair >> per unit length. > > Yes. It is an OK model at frequencies well below the LC cutoff. Its > step response is very ringy, which is unrealistic. > > >> >> OTOH, the lossy model includes a series >> resistance with the ideal inductor and an >> dielectric conductance in parallel with >> the ideal capacitor. >> >> Similarly, the non-ideal capacitor model >> includes a series resistance and a series >> inductance with the ideal capacitor. The >> non-ideal inductor model includes parasitic >> capacitance and resistance values. >> >> So, the question is: if one were to replace >> the ideal capacitor/indcutor pair in the >> lossless transmission line model with a >> non-ideal capacitor/inductor pair, then >> would this new model effectively re-create >> the lossy transmission line model ? I have >> done some SPICE modelling on this idea, >> and the results look encouraging. What do >> you gurus feel ? >> > > Heaviside derived the "telegraphers equation" around 1880. People who > didn't believe in inductance kept building telegraph systems, > including expensive undersea cables, that didn't work at the expected > speeds. > > https://en.wikipedia.org/wiki/Telegrapher%27s_equations > > He also invented the loading coil. > > In most cases, the serious lossy element is the series resistance part > of the inductor. Shunt conductance and capacitor losses are usually > minor. > > The bummer with the series loss is that it involves skin effect, and > the resistance increases with frequency. So a step response in, say a > coaxial cable, has a horrible long slow drool, clearly visible on an > oscilloscope. > > PCB traces have a similar drool. > > https://dl.dropboxusercontent.com/u/53724080/TDR/Chimera_TDR/TDT_risetime.JPG > > > I think we had a thread a while back on modeling a transmission line > that includes skin effect. You might search for that. > > Bottom line, adding the series Rs to an L-C string makes it more like > a real-life lossy line, but doesn't replicate the skin effect. > > I used to use ECA, a nice DOS, text-netlist simulator. It didn't have > a delay line part. I wrote a Basic program to generate the netlist for > LC delay lines. The bummer is that the number of LC sections goes up > as the square of the delay/risetime ratio. > > (I also paid for Electronics Workbench, and their delay line model was > broken. Got my money back.)IIRC, LTSpice has a lossy line model.
Reply by ●February 28, 20152015-02-28
On Sat, 28 Feb 2015 09:13:28 -0800, John Larkin wrote: [snip]> In most cases, the serious lossy element is the series resistance part > of the inductor. Shunt conductance and capacitor losses are usually > minor.At a high enough frequency with a practical (i.e. non-air) dielectric, the shunt conductance will dominate the loss. This matters e.g. when running 10Gb/s NRZ across an FR4 PCB. I guess that doesn't meet your "In most cases" qualification :) Regards, Allan
Reply by ●February 28, 20152015-02-28
On Fri, 27 Feb 2015 19:54:30 -0800, dakupoto wrote:> Could some electronics guru please clarify a few subtle questions > regarding lumped parameter model of transmission lines ? > > The simple loss-less lumped parameter model consists of an ideal > capacitor-inductor pair per unit length. > > OTOH, the lossy model includes a series resistance with the ideal > inductor and an dielectric conductance in parallel with the ideal > capacitor. > > Similarly, the non-ideal capacitor model includes a series resistance > and a series inductance with the ideal capacitor. The non-ideal inductor > model includes parasitic capacitance and resistance values. > > So, the question is: if one were to replace the ideal capacitor/indcutor > pair in the lossless transmission line model with a non-ideal > capacitor/inductor pair, then would this new model effectively re-create > the lossy transmission line model ? I have done some SPICE modelling on > this idea, > and the results look encouraging. What do you gurus feel ? > > Any hints/suggestions would be greatly appreciated. Thanks in advance.If you're just interested in Spice simulation (rather than actually building a lumped model out of physical components), perhaps this series of articles by old s.e.d. poster Roy McCammon might help: http://www.edn.com/electronics-blogs/anablog/4311804/Improved-Spice-model-of-a-transmission-line I haven't tried it, but it would seem to avoid some of the pitfalls of the usual lumped model. Regards, Allan
Reply by ●February 28, 20152015-02-28
On 01 Mar 2015 00:16:55 GMT, Allan Herriman <allanherriman@hotmail.com> wrote:>On Sat, 28 Feb 2015 09:13:28 -0800, John Larkin wrote: > >[snip] >> In most cases, the serious lossy element is the series resistance part >> of the inductor. Shunt conductance and capacitor losses are usually >> minor. > >At a high enough frequency with a practical (i.e. non-air) dielectric, >the shunt conductance will dominate the loss. > >This matters e.g. when running 10Gb/s NRZ across an FR4 PCB. >I guess that doesn't meet your "In most cases" qualification :) > >Regards, >AllanI specifically mentioned telegraph lines and coax, both dominated by copper loss. There's a reason why the phone company thinks that a twisted pair is 600 ohms. Microwave laminates have lower losses, but they also generally have lower Er, so allow wider traces hence less copper loss. And the good laminates are sold with rolled or otherwise fine-finish shiny copper, not the black oxide crud usually used to stick copper to FR4. Copper matters for fast signals on PCBs, too. In something like a twisted pair or coax, copper skin loss is dominant. That's plainly visible on an oscilloscope. -- John Larkin Highland Technology, Inc picosecond timing laser drivers and controllers jlarkin att highlandtechnology dott com http://www.highlandtechnology.com
Reply by ●March 1, 20152015-03-01
On Sat, 28 Feb 2015 17:32:49 -0700, Allan Herriman <allanherriman@hotmail.com> wrote:>> ....snip.... > If you're just interested in Spice simulation (rather than actually > building a lumped model out of physical components), perhaps this > series of articles by old s.e.d. poster Roy McCammon might help: > > http://www.edn.com/electronics-blogs/anablog/4311804/Improved-Spice-model-of-a-transmission-line > > I haven't tried it, but it would seem to avoid some of the pitfalls > of the usual lumped model. > > Regards, > AllanAllan, Thanks for posting that URL. The article is circa 2011, so will post comment here instead: Roy mentions non-noise sources of variations. But, NEVER mentions a true bane of all cable manufacturers. Triboelectric effect. If the cable moves wind, thermal flexing, whatever; the triboelectric effect will generate more noise than one would think possible. The Manufacturers can reduce effect depending on how 'tight' they can wrap that insulation around the conductors and the material selection they use with teflon being VERY energetic. Not sure, but expect to get worse with aging. Security Industry purposely use this effect to make 'sensor' cables. I once took a foot long piece such cable on the bench, put a scope probe on the center and shield, tapped the cable in the middle with the handle of a screw driver to watch more than 8Vpp appear on the scope trace! Now THAT's energetic!
Reply by ●March 1, 20152015-03-01
On Sat, 28 Feb 2015 10:13:28 -0700, John Larkin <jlarkin@highlandtechnology.com> wrote:>> ...snip... >Yes. It is an OK model at frequencies well below the LC cutoff. Its > step response is very ringy, which is unrealistic.Use a LOT of tiny lumped models in series and get decent bandwidth. uh, only ringy *if* the input signals exceed your upper frequency range. It's pretty easy to include skin effect with a lumped model WITHOUT slowing down the analyses for either .ac or .tran In other words, do not use laplace equations, which will take such to a crawl.
