Improved Spice model of a transmission line
Diligent reader Roy McCammon wrote me to point out an article he did over at EETimes. He felt that not many “real” engineers would see it over there, so he wanted me to republish it in EDN. Sorry, Roy, that can’t happen. If you wanted EDN readers to see it, you should have sent it to EDN, not my sister management/lifestyle publication. I did have to admit Roy worked up a dandy article, so I figured the least I could do would be to blog about over here at EDN so you can check it out. Roy sent me a dozen emails over the last few months, some with LTspice models, so I will try to dig those out and attach them here, our web tool permitting. So anyhow, here are the three parts to Roy’s original article:
Spice Simulation of transmission lines by the telegrapher’s method
- Part 1, Putting the telegrapher’s equations into a circuit (pdf)
- Part 2, Putting frequency dependence into the simulation (pdf)
- Part 3, Putting the telegrapher’s equations into a usable sub-circuit (pdf)
I will next post some comments by my analog pals whom I sent the article around to. Henry Ott, Barry Harvey, Barrie Gilbert, Don Sauer, and Edison Fong all had good comments. That will be the very next blog. Roy was nice enough to elaborate on the significance of the article:
- Regarding the article: it is about a very good SPICE simulation of a telephone transmission line with all of its frequency dependencies. It successfully simulates reflections, voltage doubling, dispersion, bridge taps, gauge changes, frequency dependent impedance, load coils, TDR responses and just about any linear behavior. I also used it to simulate test leads, coaxial cables and multimode transmission lines, but the editor wanted it shorter so all that got left out. Please have a look at the attached spread sheet to see how well the SPICE simulation matches an actual telephone cable. One thing that the real cable has that is not seen in the simulation is “structural noise”. It looks like noise, but it is not. It is just the small random deviations of impedance that you see in a cable of multiple twisted pairs. It is a good simulation, but that is not why I wrote it. The article was a vehicle for the publication of figure 2.
- The figure depicts an equivalent circuit for a transmission line. The circuit exactly simulates the solution of the telegrapher’s equations. It simulates all the linear behaviors of a transmission line, which are normally very linear, at least until the dielectric breaks down. That figure is my gift to everybody who cares about transmission lines. Now probably I’m not the first to draw this circuit, but I have searched widely and have not found it anywhere. Everybody else wants to solve differential equations, match boundary conditions with forward and backward waves and then calculate parameters of a two port using ABCD matrixes. My circuit does all that. All you have to do is add a model for your source and load. And if my circuit turns up elsewhere as someone’s prior discovery, then I will praise it. Of course, since I invented it (or reinvented it) my opinion is biased; but I believe it is the most intuitive representation of a transmission line that has ever been published. Please take a look; I think your readers will find it useful.
Roy also sent me some figures that show the great correlation his transmission line model gives to TDR (time domain reflectrometry) measurements from the real cable. These came from a spreadsheet that EDN’s webtool will not let me upload for you due to “security guidelines”. Seamless. Write Roy at his email at the bottom of this post if you want the spreadsheet.
Full trace with structural noise
Reflected pulse with dispersion
Roy mentioned LTspice models he would work up, and he didn’t disappoint. A subsequent email delivered a zip file which the EDN web tool will not let me post and after and hour of tryhing to make them all into a giant pdf I gave up so write Roy at the address at the end of this post and he will send them. Roy had this explanation:
- I promised to send LT SPICE schematics and symbols. Instead, I’m sending hierarchical schematics. The reason is that hierarchical schematics expect everything to be in the same directory. That makes it much easier to distribute. The attached WinZip has three examples of models for unbalanced transmission lines like coax. Each of the circuits depicted are completely linear which gives us two ways to simulate each circuit (except UBTL2 which only works with transient analysis). You can do a straight transient simulation, or you can do an AC simulation and then use the FFT to calculate the time domain. If you get the same curve it gives you confidence. Each schematic comes with the correct parameters for both types of simulation (except UBTL2). There is a slight issue that the FFT has a huge gain factor. It’s not unusual to see kilovolts. But everything is proportional so if transmission line reduces voltage by half in a transient simulation it will do so when using AC and FFT. Although these schematics model unbalanced transmission lines like coax, the parameter data is for telephone twisted pair with plastic insulation. So, just consider these as something to play with.
Roy then sent the balanced line models in a zip file while the EDN web tool will not let me post despite it being a zip ofd ASCCI. Roy noted:
- I have some balanced examples attached as a Winzip file. They are based on telephone 24 gauge, plastic insulated cable data. These circuits are likewise completely linear and can be computed in the frequency domain or the time domain.
- I have some bonus material that was cut from the EE Times article (pdf). It covers:
This figure seems to be for the balanced line model simulation, there is a BTL_2_Bridge_Tap.net file that must go with it, but yeah, the EDN web tool thinks a plain-text file is a security hazard and will not let me upload it, even wrapped in a zip, or any zip for that matter. You know the drill, contact Roy at the address at the bottom of the post for these goodies.
Roy went on to send yet more material.
- Transforming the circuit from figure 2 to an actual SPICE friendly schematic.
- Solving for the transfer function.
- The dc case.
And yes, Roy has megabytes more, according to him,
- There are six examples. All have a main schematic, 2 to 4 sub schematics, 2 to 4 symbol definitions and one netlist.
If you want to see these, Roy has set up an email address:
roymccammon[ at ] ieee [dot ] org
include “transmission line” or SPICE in the subject line.
And a tip to you would be authors-if you want to publish a book, you should contact a book publisher. What EDN and EETimes publish are articles, 2000-3000 words, tops. Any longer it you get the TLDR (too long didn’t read) effect.