Modelling an RS-485 Bus

I am trying to model an RS-485 bus in LTSpice that consists of two power conductors and two data conductors within a single cable. The power conductors are twisted together and shielded, and the data conductors are also twisted together and shielded. The shield is not connected to ground -- it is left floating in the current setup. I inherited this project so I am going with what I have.

This cable will extend for a few thousand feet and I am looking at the impact the length has on the bus voltage, and its susceptibility to supply droop when one of several circuits, placed along the cable, switches on. In order to model this in LTSpice I have been trying to determine what factors apply, such as series inductance and resistance, parallel capacitance, mutual inductance between the conductors, and so on. However, I'm not sure all of these apply.

The basic model for a differential data transmission line consists of two conductors, each with a series resistor and inductor, and a capacitance between them. Additionally there is a high value resistance between them, but I am considering that negligible in my case.

However, there are four conductors plus a shield in this cable (two power, two data, and one drain/shield) which I am assuming are located fairly symmetrically in a square within the cable around the drain conductor:

In order to get an accurate simulation I have been trying to model this complete setup by adding two more conductors with series resistance and inductance, parallel capacitance to each of the other conductors, etc. Additionally, I have been trying to calculate the coupling coefficient between the cable inductances so that I can simulate it in LTSpice. However, I am not at all confident that I am doing this correctly and how much I really need to take into account. If I extended the elements from the two cables to all four, I came up with something like this:

Ignore the Rp, I am not worried about that right now.

Am I going about this correctly? Am I leaving anything out, or including something I shouldn't? I realize there will probably be capacitance between each conductor in each pair and its shield as well, but I'm not sure whether or not to include that. Also, I am assuming the mutual inductance between each of the conductors and each of the other ones are identical (which in reality they won't be, but I'm just trying to get a basic idea). This is why I have the K1 L1 L2 L3 L4 0.48 statement. I'm not even sure about my math to get 0.48, but that's another question in itself.

• there is distributed mutual inductance with your mutual capacitance. This affects common mode vs differential impedance and CM & DM crosstalk . Shield must be connected at one end only to frame unless dual shielded – Tony Stewart Sunnyskyguy EE75 Jan 10 '17 at 20:36
• Just an idle thought - if you assigned a  value to the time you're spending on modeling this, and then divided that by the cost of a foot of your cable - how many feet would you have - and could you do some measurements ... ? ;-) – brhans Jan 10 '17 at 20:37
• good point, no two shields are identical but use only wire rated for RS485 – Tony Stewart Sunnyskyguy EE75 Jan 10 '17 at 20:39
• @TonyStewart.EEsince'75 There are two shields in the cable -- one around the bus power wires and one around the data wires – DerStrom8 Jan 10 '17 at 20:39
• ok not exactly as shown in green dwg. – Tony Stewart Sunnyskyguy EE75 Jan 10 '17 at 20:40