# Transmission Lines (and my confusion)

I’m trying to learn about transmission lines to simulate the loading effects of coaxial cables in a low-frequency analog system. I don’t understand the rules. I expected the lossy and lossless lines would behave as wires (with or without resistance) passing the DC signals as expected. It looks like the current flows as expected, but the voltages are surprising to me. I’ve been unable to locate any tutorials on SPICE transmission lines related to DC characteristics. I’d appreciate any hints or links to tutorials.
I’ve attached my current experiments in case you are interested in viewing my circuit. Look at the voltages present on the four terminals of the transmission lines.

Thanks,
Carl

In you’re simulation problem is that your TL expects a characteristics load like in indeal 50 ohms and in lossy Z=sqrt(L/C). Here i have simulation to show the difference.

if Z ≠ 50 ohms → you will have reflections

TL.qsch (2.5 KB)

Best regards

I understand transmission line theory. I want to understand the transmission line characteristics with respect to DC. If I cut a length of coaxial cable, I can use it to power something at the end of the cable, in addition to transmitting data down the coaxial cable. When I made the DC connections as shown in my schematic, I expected both ends of the transmission line to have similar DC voltages. I don’t see that result in the simulation. For a lossless transmission line, I expected that I would get similar DC results to what would happen if I shorted out the top conductor and shorted out the bottom conductor. This is not the case, so there is something wrong with my understanding of the DC characteristics of the transmission line. Have you tried my circuit?

Looks like there is bug in LTRA model. When you add C and L parameters to the TL it gives wrong results, even in op simulation. You can remove C and L parameters and add G=1n. Then result is same as ideal TL.

Best regards

With my simulation, I got strange results for DC operation with both the lossy and the lossless transmission line models. If you short out the “conductors” on both models, the resultant voltage drops across the resistors makes sense. Without the shorts, look at both ends of each “line”. The right side of the top “line” seems to be shorted to the left side of the bottom “line” (nets B and C are the same voltage and nets F and G are the same voltage).
lossless transmission line testing (with and without shorts).qsch (18.1 KB)

I never simulate a transmission with their 2nd and 4th node not connected to GND (i.e. shield of transmission line). In simulator like Keysight ADS, transmission line is two terminal which always assume shield is grounded. It may be easier to show both transient and steady response with a step source.

In this example, when T2 characteristic impedance is 50ohms and with a 50ohms load, there is no reflection and the input signal is delayed by transmission line by Td (100ns). And as R3 and R2 formed a voltage divider, output voltage is divided by half.

For T1, at source and load are terminated with mismatch impedance, signal reflect back and forth, and finally settled at half of input voltage as voltage divided by R4 and R1.

Tline-1.qsch (5.5 KB)

To simulate the load where both terminals are connected to a transmission line, this can be the setup. I changed the transmission line symbol to a coaxial cable to demonstrate how the physical structure should appear.

Tline-2.qsch (6.2 KB)

I’m not really doing transmission line stuff. I’m trying to simulate an analog impedance measurement system using a 1kHz sinewave source and coaxial cables making 4 terminal connections. The connections to the unknown impedance uses shielded cables and current cancellation effects by running the test current out the center conductors and returning it through the shields of the cables. This eliminates the effects of cable movement which usually shows up as changes in inductance when the cables are moved. I was hoping that the lossy transmission line would help me to understand stray effects in my system. My concern is that I’m getting results that my simple circuits (attached, above) are giving me strange results for DC connections to the transmission lines. Shouldn’t both ends of the t-line have essentially the same DC value? Why do the DC voltages on the upper right end and the lower left end match? Can somebody run my circuits to verify my “strange” results?
Thanks,
Carl

Are you trying to floating your entire transmission line?
Your ideal transmission line setup still give correct DC result, or I am missing something?

This example circuit is just to show my confusion. Let’s discuss my schematic instead of yours because yours has different letters. On my attached circuit, notice that the voltage at A is 6.6V, B is 3.3V, C is 3.3V and D is 0V.
My brain says that A is correct at 6.6V and B should be 6.6V, C should be 3.3V and D should be 3.3 V. Maybe I don’t understand the DC performance of the simulation of the t-line, but a piece of coaxial cable would give my expected results.
Is there a reason that A and B shouldn’t have the same DC voltage? How can D be 0V and C have the same voltage as B?

Please load my circuit and then try to explain why there is a 3.3V drop from A to B.

Thanks,
Carl

I see your point now. This is one of the reason why at the beginning I am unsure if a transmission model can be simulated with no ground node at its 2nd and 4th node.

What you can see is that, the simulation is forcing V(D) to ~0V to give correct differentiate voltage but not absolute voltage. Currently, if you disable R2 and add a resistor connecting V(C) and V(D), you will get V(A)=V(B).

But if you have anything in right side having a ground path, V(D) will goes to 0V again.
OR, short V(C) and V(D) and you will have right side voltage not be affected by R2.

Possibly this topic need expert in transmission line simulation (line is floating) to answer.

The transmission lines you are considering do not carry a DC component of voltage in all Spice programs. I know that transmission cables are used to carry DC power in antenna amplifiers. To properly model this case, I made a transmission line model consisting of tens or hundreds of RLC sections. I did this in LTspice. Qspice also allows you to do this easily.

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As pointed out by @bordodynov this behavior of the transmission line model is indeed a feature in all versions of SPICE. I recently mentioned this in Transmission line simulation - #3 by frank.wiedmann. The easiest way of understanding the behavior of the model is imagining an ideal 1:1 transformer (working all the way down to DC) being connected in series with the transmission line.

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I’ll do some more research and report back when I understand what the model is doing.
Thanks,
Carl

I now understand that I was misusing the T-line model. I got the following response from Mike Engelhardt:

There’s a common misconception about the SPICE transmission line element.
Neither the Lossless nor the Lossy transmission line models a length of coax. It only models one mode of the cable, i.e., the internal node. That means that usually you want to ground both ends of the transmission line.
Like this:

Since a cable has as many modes and wires, to model a piece of coax, you need two transmission line elements like below. Note the typically different modes propagate at different speeds(through air instead of the cable dielectric) and have different characteristics. Note that the characteristic impedance of the shield to the world is usually not uniform, so modeling other than the internal mode is usually as meaningless as those schematics you have.

Thanks to all who contributed to this educational experience.
Later,
Carl

This is N=256 lumped transmission line symbol based on @bordodynov 's input.

[Files refer to latest post]

I have created a lumped model (10 or 20 stages) of a coaxial cable that meets my needs. I used the “open parent” option to create the hierarchical parent and then made the blocky representation. I can use this approach to satisfy my present cable-related simulation task.
I love the look of your X1 component and I want to steal it for my models. I see that you are using entries like Ro=<50> that show up without the <> characters in the schematic. You are also doing things with the string attributes that seem useful but I haven’t found the proper documentation to help me understand what would make my variable length coaxial cable pieces more useful (and beautiful). Can you suggest a tutorial on the best way to make useful components?
Thanks,
Carl

I have several user guidelines in my Github, this is the one with explanation and example of hierarchy and symbol.
Goto Part 2B, there is a procedure to create embedded subckt symbol from hierarchy, which may give you more information.
But from your reply, I think you already figure out many important things in symbol creation.

Qspice/Guideline/Qspice - General Reference Guide by KSKelvin.pdf at main · KSKelvin-Github/Qspice

I found an issue in previous lumped model, the resistance has to divided by 2. Here is a correct version by comparing lossy line with finite R. As there was an issue in lossy transmission when R is included and Mike just fixed that, I didn’t fully verify if R is included. This is an updated version. Please discard previously downloaded file.

TLine-Lumped-N=016.qsym|attachment (3.3 KB)
TLine-Lumped-N=256.qsym|attachment (29.0 KB)
Parent.TLine-Lumped.qsch (40.0 KB)

Strange result in Qspice. Not the same as in LTspice.