Coaxial Cable coupling coefficient

Hi all,


suppose I want to make a 1:1 balun using a coaxial cable. So the primary would be the inner conductor, and the secondary, the outer conductor.

The question is, how do I determine Zp0e and Z0o or the coupling coefficient based on the cable data? Is there a back-of-the-envelope calculation?


thanks,
Aaron

aaron_do said:

So the primary would be the inner conductor, and the secondary, the outer conductor.

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I think something is missing here. Don't you need at least three conductors to do this?

You could get a rough low frequency approximation of leakage inductance if you knew the outer diameter of the inner conductor and the inner diameter of the shield. **broken link removed**.

Magnetizing inductance will depend on how you form the coax, and if you use a core material.

PlanarMetamaterials said:

I think something is missing here. Don't you need at least three conductors to do this?

Click to expand...

Why do I need three conductors? A 1:1 balun only has two windings.


thanks,
Aaron

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mtwieg said:

You could get a rough low frequency approximation of leakage inductance if you knew the outer diameter of the inner conductor and the inner diameter of the shield. **broken link removed**.

Magnetizing inductance will depend on how you form the coax, and if you use a core material.

Click to expand...

Thanks, but the link you included is only for the loop inductance. How can I find the leakage inductance?

regards,
Aaron

aaron_do said:

Why do I need three conductors? A 1:1 balun only has two windings.

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I'm definitely not a Balun expert, so I may just be misunderstanding the terminology used, but doesn't two windings imply at least 3 conductors? A quick online search shows a bunch of figures with at least three...

Why do I need three conductors? A 1:1 balun only has two windings.

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There are at least two different balun designs based on transmission line transformers, Guanella and Ruthroff type.

A single coaxial cable based transformer refers to the Guanella type and doesn't involve leakage inductance if it uses cable of the same characteristic impedance as input and output have. The magnetizing inductance and coupling of the coaxial outer conductor causes a balun asymmetry.

Adding a third winding can cancel the inductive asymmetry and changes the design to a Ruthroff balun.

FvM said:

There are at least two different balun designs based on transmission line transformers, Guanella and Ruthroff type.

A single coaxial cable based transformer refers to the Guanella type and doesn't involve leakage inductance if it uses cable of the same characteristic impedance as input and output have. The magnetizing inductance and coupling of the coaxial outer conductor causes a balun asymmetry.

Adding a third winding can cancel the inductive asymmetry and changes the design to a Ruthroff balun.

Click to expand...

Thanks for the info.

Seems my error was in not considering the common-mode voltage on the un-balanced side. Actually I used the word balun, but I really just meant any transformer. My main question is, what is the easiest way to approximate the coupling coefficient of a transmission line; coaxial cable for example?


thanks,
Aaron

My main question is, what is the easiest way to approximate the coupling coefficient of a transmission line; coaxial cable for example?

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In my understanding, transmission lines are characterized by characteristic impedances and electrical lengths. In case of "coupled transmission lines" or generally conductor geometries that involve more than one characteristic impedance, mutual impedances can be calculated.

Transmission line transformers are combining transmission line and transformers principles, they work as transmission line circuits at high frequencies and extend the frequency range downwards by a transformer core.

You should sketch the intended balun geometry to allow an exact analysis.