In one of the article of "All About Circuits" about capacitance and inductance of twisted pair cable i found a set of formulae for computing capacitance and inductance of twisted pair cable based on diameter , spacing and dielectric constant as seen in the snapshot..
Can anybody give me the basis OR any published literature OR any standard OR any reference book which describes derivation of these formulae ??
Thanks !!!!

 

Try the Belden Cable Company website https://www.belden.com/resources
If you can't find it there an inquiry to them would also be suggested. They are one of the industries leading providers of twisted pair communications cables.

 

How sure are you that those relationships are derived. They might be empirical relationships based on constructing and measuring different products.

 

You might also want to inquire about the units for those calculations Are they

1. Independent of length?
2. Henries per foot, meter, kilofoot?
3. Farads per foot, meter, kilofoot?

Giving the uninitiated a formula without the units is just asking for trouble.

 

This series might give you what you want
https://www.bing.com/videos/search?...4F1FE2F9DC00EF7230F04F1&view=detail&FORM=VIRE


BUT, its not what the wire manufacturers do,

As you see, the theory is simple, you have a number of conductors that react to each other, whilst surrounded by various dielectrics. Essentially its "just" some capacitors which have inductance. Maxwells field theories and all that,

But by the time you include the twists of the cable, the different dielectrics around the cables, as the cables touch , as voids are formed, all affects the impedance.

The answer is they use 3d field solvers, solving Maxwell's equations , and come up with an equivalent circuit.

 

In one of the article of "All About Circuits" about capacitance and inductance of twisted pair cable i found a set of formulae for computing capacitance and inductance of twisted pair cable based on diameter , spacing and dielectric constant as seen in the snapshot..
Can anybody give me the basis OR any published literature OR any standard OR any reference book which describes derivation of these formulae ??
Thanks !!!!View attachment 212445

Those formulas are derived from the fundamental definition of capacitance and inductance. The derivation is often rather tedius. So what is the motivation for seeking the derivations?

 

How sure are you that those relationships are derived. They might be empirical relationships based on constructing and measuring different products.

Thank you @Papabravo.
Actually as you pointed out correctly I am not sure if these relationships are derived or whether they have an empirical relationship based on MOC of conductor and insulation.
I am seeking, if there is any published resource which can confirm if the formulae that i found on this site are 100% correct and can be used as it is for any further computations.

 

Those formulas are derived from the fundamental definition of capacitance and inductance. The derivation is often rather tedius. So what is the motivation for seeking the derivations?

Thank you @MisterBill2

I am currently more interested to verify the correctness of those formulae via some published Standard or any published resource.
Considering that, i want to further use those formulae to study the effect of ambient temperatures on mutual capacitance and mutual inductance values or the twisted pair cable, since the given formula uses "diameter of cable" and "dielectric of insulation" as parameters , which could be affected by ambient temperature
I wanted to ensure that i am using the correct base formulae before proceeding further.

 

Now I am wondering about what sort of application requires an analysis of the effect of temperature on cable capacitance and inductance. High speed data transmission through inexpensive cabling comes to mind as the most likely, but we already have cables suitable for that. We have quite enough standards already, with CAT6 being the latest rather obnoxious one.

There is a second thing that would need to be considered if the temperature changes are not small, which is the variation of dielectric properties of the non-conductor materials with temperature changes. Those changes may be non-linear at some points.

 

Thank you @MisterBill2

I am currently more interested to verify the correctness of those formulae via some published Standard or any published resource.
Considering that, i want to further use those formulae to study the effect of ambient temperatures on mutual capacitance and mutual inductance values or the twisted pair cable, since the given formula uses "diameter of cable" and "dielectric of insulation" as parameters , which could be affected by ambient temperature
I wanted to ensure that i am using the correct base formulae before proceeding further.

Can you rely upon the equations you ask,
yes is the answer.


Just a touch of reality.

All cables vary just by bending them,
the start and end of the cables also have different characteristic, not least as they are not as uniform as the middle of the cable, and are connected to different impedances, ( the driver and the receiver )

,
In the real world, to account for this, you do not design circuits to have wires that must be a very tight characteristics,
If your using "standards" such as 422, 485, ethernet, microphones, rf circuits, then the drivers / receivers and the cables are all sorted for you,


IMHO, The basic of engineering, is to have a working knowledge of all the fundamentals, but not in depth, and know where to find the info if you might need it.

Just as an example, when I started, metastability and ESD did not exist !
well they did, in theory, and we knew the theory, but most of what I was doing was DTL and valve logic circuits running at KHz, and they just did not exhibit the problems. But we new about them ,

 

Andrew is certainly correct about cables, although there are cables made for those really high frequencies that are far more stable. But they cost so much that only those applications that really need them get them. And it makes a lot of sense to design circuits that will work satisfactorily with cables and connectors at both ends of the specification, and beyond. Not only for the best production yields, but also because the price of almost everything goes up as the specifications get tighter. And cable variations in non-spec grades of cables may vary a bit more, even on the same spool of cable.