# Transmission line simulation (physical)

I need to be able to simulate communications with a sensor device over a large length of wire (0-10km). This is for quite low-speed comms (10khz max, usually 1-2khz though). This would be FSK... but at some point I may have to handle a low baud RS232-like signal as well.

Mostly, I'm looking for voltage drop and signal distortions. Delay doesn't matter much.

How would you go about it?

EDIT:

I've been able to determine the cable is indeed a (fairly nonstandard) type of coax. I now know resistance and capacitance per unit length, cross section geometry, and that the insulation resistance is high enough not to matter. It wasn't initially clear if the return line was a separate run or not.

This would be a test setup for multiple target devices. Most are FSK of various frequency choices under 10khz, some are ASK (you could almost use a standard UART after bandpass/filtering). All are riding on a high DC offset (comms over power).

In the past, I've seen people build a simple rotary switch that swaps in resistors, capacitors, and maybe inductors to simulate a given line length. Could that be good enough?

I'm currently trying to build a few simulations in LTspice.

EDIT 2:

Okay, if I go with just adding resistors, caps, and inductors... what does the model look like? The RLGC network below is assuming the grounds are at the same potential I believe (a safe assumption on PCBs w/ground planes). The return in this case is through the outer shell, and it's resistance is probably 3 times higher than the inner conductor. Does that change things significantly? Do I just add another resistor on the bottom rail, and split the capacitance on both sides of it?

• Are you going to be using FSK with a 10 kHz carrier or sending data at 10 kbaud? What do you mean by RS232-like; baseband or just 1 bit/symbol? – Nick T Jan 11 '11 at 1:37
• Is it coax, or something else? – tyblu Jan 11 '11 at 7:05

Transmission lines have a complex characteristic impedence. The characteristic impedence is typically specified "per unit length" for a given tranmission line. For practical purposes, you might have four values "per unit length" for a transmission line: resistance, capacitance, inductance, and conductance. There's a pretty extensive article on this on Wikipedia, and "for high frequencies and small losses" the approximate equation is:

where:

• x is the distance along the tranmission line
• t is elapsed time
• L is the inductance per unit length
• C is the capacitance per unit length
• R is the resistance per unit length
• G is the conductance per unit length

Now this is probably going to be of limited use to you because, if I read between the lines here, it sounds like you're planning to transmit a digital signal (i.e. a square wave). The edges in the square wave are really "broad spectrum." That's why most communication systems go through a modulation and demodulation step so as to limit the spectrum of the signal "on the line." But I think the above equation does apply because a the "signal" in a square wave is analytically "high frequency" content.

At any rate, in the "steady state" high level of your input signal, assuming your receiver is a high impedence, what your signal sees is a voltage divider based on the characteristic resistance and conductance. So you should see (approximately) Vout/Vin = G/(R+G), based on the model:

Edit 1

I missed the FSK (Frequency Shift Keying) comment in the question earlier. I also had another thought. You can use something like Matlab Simulink to model the transfer characteristic of the circuit, and feed the model with a representative input waveform to see what comes out the other side...

Also, if you want to know how much of a voltage drop you'll see, for a sinusoidal signal, you've still got an effective voltage divider with a top leg having effective impedence of length*(R + jwL) and a bottom leg impedence of (Glength || 1/(jwClength)). You can do the complex math to find the real part of that transfer function at a given frequency ( w = 2 * pi * f).

Edit 2

In response to the clarification of what you meant by physical simulation, if you are trying to physically introduce the effect of a transmission line, just set up the circuit in the figure with appropriate values of capacitors, inductors, and resistors - sized in accordance with the properties and length of the transmission line you are trying to emulate.

• I've been trying to determine if this lumped model is adequate for this, vs. a distributed model (where you divide the RLGC network into much smaller serialized sections). G is supposedly hundreds of megaohms even at 10km (over 5 mm of insulation) – darron Jan 11 '11 at 15:12
• My main concern at this point is the square wave shape of the ASK signal. I'm not sure if I can just ignore those relatively fast transitions or not. I remember horrible ringing from observing this stuff years ago... but I'm guessing that was more likely due to very poor impedance matching. – darron Jan 11 '11 at 15:19
• @darron, I think the lumped model is fine as long as all you care about is what's coming out the other side of the line and not what's going on at points along the way. The infinite series is a useful model for solving the space-time field within the line. – vicatcu Jan 11 '11 at 17:06
• @darron, you should be able to comfortably ignore G if it's >> than R in the model. In that case, your losses are going to be primarily due to the effective R-L-C filter evident in the model, at the operating point of your frequency. This will end up looking like a low-pass filter for all intents and purposes. So expect to see some softening of your edges. – vicatcu Jan 11 '11 at 17:07
• @darron, check out sim.okawa-denshi.jp/en/RLClowkeisan.htm – vicatcu Jan 11 '11 at 17:13

Cable manufacturers will tell you how much the signal will be attenuated per unit length given the frequency of the signal.

Regarding signal distortions, I'm not aware of anything significant so long as you use shielded cable. But don't take my word for it.

Transmitting RS232 level signals over such a long run of cable will be difficult.

If I wanted to do it for real use a standard telephone modem and a line voltage generator, if needed. For simulation @krapht is right. Use STP or coax.