# Cable Impedance Calculator

Created by Álvaro Díez
Reviewed by Steven Wooding
Last updated: Feb 02, 2023

"What is this cable impedance calculator?" you might be asking. Don't worry. We will get into it, and into what impedance is, and the impedance formula. Just a brief summary to remind you of what you know or to bring you up to speed on the differences between impedance vs. resistance if you're starting up. So read ahead for all the information you need about twisted pair or coaxial cable impedance and, most importantly, the numbers you need!

## How to use Omni's Cable Impedance Calculator

Let's cut to the chase; if you came here for the numbers, we will tell you how to get them. IF you look to your left, you will see a calculator. Like all calculators from Omni, you put the numbers in, and it will automatically spit out the results, no need to press any button like a caveperson.

All banter aside, there is a bit more going on under this cable impedance calculator. Of course, we have fed the engine with the appropriate impedance equations to give the correct results, but we have also "taught" the calculator what variables you need for each cable type.

I might add that if you're looking to calculate the electrical impedance of a circuit, they have a separate impedance matching calculator and a PCB impedance calculator for various PCB-mounted conductors.

Due to its geometry, the coaxial cable impedance requires you to know the inner wire's diameter and the outer shielding. However, the twisted pair cable requires the conductors' diameter and the spacing between them; there is no shielding. But you don't need to remember that; the calculator will show only the relevant variables for your calculations.

So getting the numbers is as easy as 1 (select the type of cable), 2 (write down the values), 3 (enjoy the results appearing automatically). We literally cannot make it easier for you.

But we could make it more complete, right? Yes, and we have. Because when you are trying to find your cable impedance, you generally are also after values like the cut-off frequency (for coaxial cables), the capacitance, the inductance, and the signal's delay. We have also baked those into the calculator so that you don't need to look elsewhere.

However, the one thing the calculator cannot do for you is to explain how we get those numbers, what impedance is or how the coaxial cable impedance differs from the twisted pair cable. It's a calculator, not an "explanator".

## Impedance definition: What is impedance?

And that's precisely why we have a text accompanying the calculator, explaining how it works, the science behind it, and why you want to use it. You probably don't need a why; you probably came here because you need that value for something you are doing. But some of you, especially those starting out in electronics, might need a refresher on what impedance is.

So, let's start with the definition of electrical impedance and the difference between impedance and resistance. The electrical impedance is the effective resistance that a material has to the flow of alternate current (AC). Put simply, in AC, impedance is equivalent to the resistance in DC (direct current). We don't talk about resistance in AC because impedance also includes the reactance of the material as the current changes direction.

That's all fine and dandy, but knowing what something is doesn't mean you can calculate its value. This is why after we have delved into the impedance definition, we necessarily need to move onto the impedance formula, the mathematical instructions on how to calculate impedance.

## Impedance formula: How to calculate impedance?

Before I give you the impedance equation, I need to be frank: there is no unique impedance equation. Despite the many differences between impedance and resistance, they share one feature: they are both properties of the material. They depend on the geometry and configuration of the material, meaning there are impedance formulas for certain conductors, but there is no one unique final impedance formula, unfortunately.

It is true that if you had access to the circuit, you could try to measure the I/V curves, and from there, you could get the impedance value. At that point, you are not calculating from an equation as much as you are measuring indirectly.

The situation we want to help you with is the one you would typically find when designing the cable runs for transmitting an AC or RF signal (check the RF unit converter if that is your case). In such a situation, you will want to know the twisted pair or coaxial cable impedance, capacitance, delay, etc., before you build or buy anything, only using the manufacturer's specifications for the cables.

So let's see how to calculate the impedance in this particular situation. The first thing to know is whether we are dealing with a coaxial cable or a twisted pair cable. It should be easy enough to sort that one out given your circuit's design, the manufacturer's documentation, etc. Once you have that, you need the geometric measurements of the cables and their conductors.

In particular, you need to know the effective substrate dielectric (of the material around the conductor) called $\varepsilon_r$, the diameter of the inner conductor (the only conductor in the case of a twisted pair) $d$ and then the inner diameter of the outer shielding (for a coaxial cable) called $D$ or the spacing between wires (for a twisted pair) denoted by $s$.

Once you have all those values, you simply apply the corresponding impedance formula:

• Coaxial cable:
$\qquad \footnotesize \text{Impedance} = \frac{60 \times \ln(D/d)}{\sqrt{\varepsilon_r}}$
• Twisted pair:
$\qquad \footnotesize \text{Impedance} = \frac{120 \times \ln(2s/d)}{\sqrt{\varepsilon_r}}$

As you can see, it is not overly complicated to calculate by hand, but it will definitely take longer than using our calculator. So move to your left, use Omni's Cable impedance calculator and enjoy immediate results with no effort!

Álvaro Díez
Cable Type
Coaxial Inner conductor diameter (D1)
mil
Inner diameter of surface shield (D2)
mil
Substrate dielectric
Results
Impedance
Ω
Capacitance
pF/inch
Delay
ns/inch
Inductance
nH/inch
Cutoff frequency
GHz
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