Coax cable calculation

[Trevor Wilson]

Here's a question that stumped me back in the old slide rule days:

A coaxial cable, having an inner diameter of 0.0254mm (0.001") and using
an insulator with a dielectric constant of 2.56, is yo have a
characteristic impedance of 2,000 Ohms. What must be the outer conductor
diameter?

You guys can locate the appropriate method of calculation.

--
Trevor Wilson
www.rageaudio.com.au

 

On Tuesday, April 10, 2018 at 2:42:50 AM UTC-4, Trevor Wilson wrote:

Here's a question that stumped me back in the old slide rule days:

A coaxial cable, having an inner diameter of 0.0254mm (0.001") and using
an insulator with a dielectric constant of 2.56, is yo have a
characteristic impedance of 2,000 Ohms. What must be the outer conductor
diameter?

You guys can locate the appropriate method of calculation.

--
Trevor Wilson
www.rageaudio.com.au

It's pretty hard to get impedances above that of free space.
(377 ohms) An air gap would be better.

 

[Jeff Liebermann]

On Tue, 10 Apr 2018 16:42:43 +1000, Trevor Wilson
<trevor@SPAMBLOCKrageaudio.com.au> wrote:

Here's a question that stumped me back in the old slide rule days:

A coaxial cable, having an inner diameter of 0.0254mm (0.001") and using
an insulator with a dielectric constant of 2.56, is yo have a
characteristic impedance of 2,000 Ohms. What must be the outer conductor
diameter?

<https://www.rfcables.org/coax-calculator.html>
- Select inches.
- Plug in any number for outside dia (D) trial an error.
- Plug in 0.001 for inner diameter (d).
- Plug in 2.56 for permittivity (er) (same as dielectric constant
in this example).
- Punch "calculate"

I used 1,000,000 inches for outside diameter and still obtained only
776 ohms. 1,000,000,000 inches yielded 1035 ohms. I don't think it's
going to make it to 2,000 ohms unless the coax cable is absurdly huge.



--
Jeff Liebermann jeffl@cruzio.com
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558

 

[Allodoxaphobia]

On Tue, 10 Apr 2018 08:11:37 -0700, Jeff Liebermann wrote:

On Tue, 10 Apr 2018 16:42:43 +1000, Trevor Wilson
trevor@SPAMBLOCKrageaudio.com.au> wrote:

Here's a question that stumped me back in the old slide rule days:

A coaxial cable, having an inner diameter of 0.0254mm (0.001") and using
an insulator with a dielectric constant of 2.56, is yo have a
characteristic impedance of 2,000 Ohms. What must be the outer conductor
diameter?

https://www.rfcables.org/coax-calculator.html
- Select inches.
- Plug in any number for outside dia (D) trial an error.
- Plug in 0.001 for inner diameter (d).
- Plug in 2.56 for permittivity (er) (same as dielectric constant
in this example).
- Punch "calculate"

I used 1,000,000 inches for outside diameter and still obtained only
776 ohms. 1,000,000,000 inches yielded 1035 ohms. I don't think it's
going to make it to 2,000 ohms unless the coax cable is absurdly huge.

Almost sounds like an OLD ("slide rule") homework problem....

Jonesy

 

[Trevor Wilson]

On 11/04/2018 8:10 AM, Allodoxaphobia wrote:

On Tue, 10 Apr 2018 08:11:37 -0700, Jeff Liebermann wrote:
On Tue, 10 Apr 2018 16:42:43 +1000, Trevor Wilson
trevor@SPAMBLOCKrageaudio.com.au> wrote:

Here's a question that stumped me back in the old slide rule days:

A coaxial cable, having an inner diameter of 0.0254mm (0.001") and using
an insulator with a dielectric constant of 2.56, is yo have a
characteristic impedance of 2,000 Ohms. What must be the outer conductor
diameter?

https://www.rfcables.org/coax-calculator.html
- Select inches.
- Plug in any number for outside dia (D) trial an error.
- Plug in 0.001 for inner diameter (d).
- Plug in 2.56 for permittivity (er) (same as dielectric constant
in this example).
- Punch "calculate"

I used 1,000,000 inches for outside diameter and still obtained only
776 ohms. 1,000,000,000 inches yielded 1035 ohms. I don't think it's
going to make it to 2,000 ohms unless the coax cable is absurdly huge.

Almost sounds like an OLD ("slide rule") homework problem....

**Correct. It was.

I thought someone would have come up with an answer before now. It's not
an overly difficult calculation.


--
Trevor Wilson
www.rageaudio.com.au

 

[Dave Platt]

In article <fj4r7gF4b4oU1@mid.individual.net>,
Trevor Wilson <trevor@SPAMBLOCKrageaudio.com.au> wrote:

Here's a question that stumped me back in the old slide rule days:

A coaxial cable, having an inner diameter of 0.0254mm (0.001") and using
an insulator with a dielectric constant of 2.56, is yo have a
characteristic impedance of 2,000 Ohms. What must be the outer conductor
diameter?

Almost sounds like an OLD ("slide rule") homework problem....

**Correct. It was.

I thought someone would have come up with an answer before now. It's not
an overly difficult calculation.

Well, just for grins... using the formula

Z0 = 138 log10 ((Dd/Dc)*(1/sqrt(eR)))

it seems to transform to

Dd = 10^(Z0/138) * sqrt(eR) * Dc

with Z0 = 2000, eR = 2.56, and Dc = .001, we'd get approximately

Dd = 10^14.5 * 1.6 * .001

Dd = 1.6 * 10^11.5

Dd = 5.1 * 10^11

or about half a trillion inches. That's if I didn't screw up
something using my slide rule (yes, I have a nice 10" Hemmi here at
my desk) or slip a decimal point somewhere along the way.

This seems a bit impractical for a coaxial cable. The
transmission-line cutoff frequency would be ridiculously low, and
construction of a matching section would be, well, interesting, to say
the least. And, I rather doubt that the classic formula is actually
applicable for impedances (and diameters) this large.

A solid cylinder of dielectric material this large would probably
insist on collapsing under its own gravitational self-attraction,
leaving you with a neutron star or a black hole.

 

[Trevor Wilson]

On 11/04/2018 9:42 AM, Dave Platt wrote:

In article <fj4r7gF4b4oU1@mid.individual.net>,
Trevor Wilson <trevor@SPAMBLOCKrageaudio.com.au> wrote:

Here's a question that stumped me back in the old slide rule days:

A coaxial cable, having an inner diameter of 0.0254mm (0.001") and using
an insulator with a dielectric constant of 2.56, is yo have a
characteristic impedance of 2,000 Ohms. What must be the outer conductor
diameter?

Almost sounds like an OLD ("slide rule") homework problem....

**Correct. It was.

I thought someone would have come up with an answer before now. It's not
an overly difficult calculation.

Well, just for grins... using the formula

Z0 = 138 log10 ((Dd/Dc)*(1/sqrt(eR)))

it seems to transform to

Dd = 10^(Z0/138) * sqrt(eR) * Dc

with Z0 = 2000, eR = 2.56, and Dc = .001, we'd get approximately

Dd = 10^14.5 * 1.6 * .001

Dd = 1.6 * 10^11.5

Dd = 5.1 * 10^11

or about half a trillion inches. That's if I didn't screw up
something using my slide rule (yes, I have a nice 10" Hemmi here at
my desk) or slip a decimal point somewhere along the way.

This seems a bit impractical for a coaxial cable. The
transmission-line cutoff frequency would be ridiculously low, and
construction of a matching section would be, well, interesting, to say
the least. And, I rather doubt that the classic formula is actually
applicable for impedances (and diameters) this large.

A solid cylinder of dielectric material this large would probably
insist on collapsing under its own gravitational self-attraction,
leaving you with a neutron star or a black hole.

**According to my calculations (performed ca. 1973) the answer is around
1.59 X 10^20 inches. My instructor ticked my answer as the correct one.

Or, for a more useful figure, 427 light years. That's one big coax. A
few hundred Metres would likely require more mass in it's construction
than exists in our galaxy (maybe the entire universe). I haven't tried
to work that out.

--
Trevor Wilson
www.rageaudio.com.au