# Calculating parameters of an RG58 cable

#### Dritech

Joined Sep 21, 2011
888
Hi all,

I used some basic calculations to determine the dielectric constant, velocity factor and characteristic impedance of the RG58 CU cable shown in the attached datasheet.
For determining the dielectric constant, the equation below was used, where C was taken as 100pF/m (listed in the datasheet), D as 3mm and d as 0.7818mm. With these values, I am getting a dielectric constant of 2.42 pF/m. Theoretically, for polyethylene this should be 2.3.

Also, the equation below was used to determine the velocity factor, which gives a result of 64%. Datasheet states 66%.

Using the dielectric constant found earlier, the characteristic impedance was also calculated and got 52ohms as a result. This should be 50ohms.

Since these are not practical results where some tolerances are expected, is there something which I am missing? Shouldn't these match with the info listed in the datasheet?

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#### MrChips

Joined Oct 2, 2009
26,062
In summary:

dielectric constant = 2.3 vs 2.42
velocity factor = 66% vs 64%
impedance = 50Ω vs 52Ω

How precise do you want to be?
What are the errors in the values you chose?

#### sagor

Joined Mar 10, 2019
694
The specifications in the datasheet have +/- errors specified. In the case of the 3mm diameter, it is +/- 0.1mm. That is just over 3% for that one measurement alone...
Thus 3% of your calculated 52 ohms is about 1.56 ohms, so it could be very close to 50 ohms.
All coax has a +/- error in impedance and tolerances.

#### Dritech

Joined Sep 21, 2011
888
Agree regarding the tolerances, but I believe the values listed in the datasheet was the optimal values (+/-0). This is why I was expecting the values to be spot on. Now sure about the tolerances I was expecting, but for instance I read that dielectric constant for polypropylene should we in the range of 2.2 to 2.36. So theoretically speaking, 2.42 is not an acceptable range. It would not have bothered me if the value was within this range, hence why I was cross-checking if I made any mistakes in the calculations.

#### Papabravo

Joined Feb 24, 2006
18,400
It is a mistake to view things that you can measure or calculate as having a single defined value. You will be much better off treating those things as random variables with a defined mean and variance. Datasheets will not always directly specify both things but may do it indirectly by quoting a "typical" value along with a minimum and a maximum. The range, if quoted will typically be 6σ (standard deviations) and cover 99.5% of all the samples you will ever see.

#### DickCappels

Joined Aug 21, 2008
8,704
I gave an engineer who was the R&D department in a Taiwan display lab in about 1986 the formula for calculating the cathode current for a CRT given the operating conditions. The next time I saw him he complained that the result was 20% off from what he calculated. I congratulated him, telling him obtained better results than most of us. Formulas are perfect, real life is another matter.

#### Papabravo

Joined Feb 24, 2006
18,400
I gave an engineer who was the R&D department in a Taiwan display lab in about 1986 the formula for calculating the cathode current for a CRT given the operating conditions. The next time I saw him he complained that the result was 20% off from what he calculated. I congratulated him, telling him obtained better results than most of us. Formulas are perfect, real life is another matter.
Sometimes we discover "New Physics" to boot.
Just consider the evolution of the switch-mode power supply from 1970 to the present.

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#### DickCappels

Joined Aug 21, 2008
8,704
I alternatively suffered and enjoyed that transition. That was probably the most enlightening 10 years of my career.

#### Papabravo

Joined Feb 24, 2006
18,400
I alternatively suffered and enjoyed that transition. That was probably the most enlightening 10 years of my career.
I came to it rather more recently having spent most of my career in software, firmware, and embedded control. I made up my mind to rectify that subsequent to my retirement.

#### DickCappels

Joined Aug 21, 2008
8,704
Yes, and after retirement electronics became a lot more fun.

#### Janis59

Joined Aug 21, 2017
1,383
Dick - hope after 1.5 years I shall be capable to test Your said
But about thing - I had met the RG cables look like 50 Ohm but showing 75 or 67 Ohms, I have met the cables having in datasheet V(f)=0.6 but having 0.66 or 0.75 etc thus my warm advice - DONT trust datasheets ever, except if that is freshly bought from factory having good reputation. Other - use what You have but BEFOREHAND make the exact measurement of Z and v(f). Thats so rapid - connect and push the button!! So, explore the Nano-VNA v2 and learn to use it extensively.

#### DickCappels

Joined Aug 21, 2008
8,704
I recall that RG-59 is 75 Ohms and RG-58 is 52 ohms. There many types of coaxial cable with differing impedance, loss as a function of frequency,etc. Or am I missing your point?