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Author Topic: Coax at LF  (Read 781 times)
W6BP
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Posts: 530




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« Reply #15 on: March 28, 2019, 07:43:37 PM »

At typical LF/HF/VHF frequencies, you can ignore the dielectric loss of typical cables, and just look at conductor losses.

My old rule of thumb for FR-4 (not a great dielectric loss-wise) printed circuit boards was that the dielectric loss would exceed skin effect loss somewhere around or north of 500 MHz, so this would seem to be consistent with what you've said.

But this raises a question whose answer I've not yet found. If dielectric loss isn't the dominant loss mechanism below UHF, why do ladder line or open-line feed have a lower loss at sub-UHF? Those feeders tend to have small-diameter wires with a relatively modest outer surface area, while, with, say, RG8X coax, the outer surface of the inner conductor and the inner surface of the outer conductor have greater area. Wouldn't that produce higher skin effect losses in the balanced line than the coax? 

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W9IQ
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Posts: 3040




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« Reply #16 on: March 29, 2019, 03:19:28 AM »

But this raises a question whose answer I've not yet found. If dielectric loss isn't the dominant loss mechanism below UHF, why do ladder line or open-line feed have a lower loss at sub-UHF? Those feeders tend to have small-diameter wires with a relatively modest outer surface area, while, with, say, RG8X coax, the outer surface of the inner conductor and the inner surface of the outer conductor have greater area. Wouldn't that produce higher skin effect losses in the balanced line than the coax?  

The reason that ladder line, et al has lower loss is simply because of its higher impedance. For a given power level, this reduces the current that is flowing in either direction in the transmission line. Since resistive losses are based on I2R, the loss due to skin effect is greatly reduced despite the typically higher RF resistance of the conductors in a ladder line compared to a coax.

For example, compare a matched 50 ohm coax line verses a matched 450 ohm line, each with 100 watts applied. The I2 values are 2 and 0.22 amps2 respectively. The 450 ohm line could therefore have approximately 9 times (2/0.22) the RF resistance before its losses equalled the 50 ohm coax. This can be simplified to say that the allowable losses to achieve loss parity is the ratio of the two impedances (450/50).

The ladder type lines do have conductive losses that are beyond skin effect. They also exhibit proximity effect that tends to crowd the current on the side of the wires closest to the other wire. This enhances the conductive losses slightly.

- Glenn W9IQ
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- Glenn W9IQ

I never make a mistake. I thought I did once but I was wrong.
W6BP
Member

Posts: 530




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« Reply #17 on: March 29, 2019, 03:24:02 AM »

But this raises a question whose answer I've not yet found. If dielectric loss isn't the dominant loss mechanism below UHF, why do ladder line or open-line feed have a lower loss at sub-UHF? Those feeders tend to have small-diameter wires with a relatively modest outer surface area, while, with, say, RG8X coax, the outer surface of the inner conductor and the inner surface of the outer conductor have greater area. Wouldn't that produce higher skin effect losses in the balanced line than the coax?  

The reason that ladder line, et al has lower loss is simply because of its higher impedance. For a given power level, this reduces the current that is flowing in either direction in the transmission line. Since resistive losses are based on I2R, the loss due to skin effect is greatly reduced despite the typically higher RF resistance of the conductors in a ladder line compared to a coax.

For example, compare a matched 50 ohm coax line verses a matched 450 ohm line, each with 100 watts applied. The I2 values are 2 and 0.22 amps2 respectively. The 450 ohm line could therefore have approximately 9 times (2/0.22) the RF resistance before its losses equalled the 50 ohm coax. This can be simplified to say that the allowable losses to achieve loss parity is the ratio of the two impedances (450/50).

The ladder type lines do have conductive losses that are beyond skin effect. They also exhibit proximity effect that tends to crowd the current on the side of the wires closest to the other wire. This enhances the conductive losses slightly.

- Glenn W9IQ

(Slaps head) Of course. Thanks, Glenn.
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G3RZP
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Posts: 1148




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« Reply #18 on: March 29, 2019, 04:24:24 AM »

If you do the math - which I've forgotten, I haven't used calculus for many years - minimum loss is around 75 ohms. Maximum power handling is around 32 ohms. 50 ohms is the geometric mean.  In WW2 British radar, the minimum loss at 75 ohms meant that 75 ohms was pretty well standard for UK military gear until about the mid 1950s, while the US used the 'compromise' value of 50 ohms from pretty well the beginning. Sadly, the British spoiled things somewhat by using the 'Pye' coax connector - a horribly unreliable thing which according to G3DVV, caused more H2S failures in the RAF than any other component! You may not like PL259s, but compared to the 'Pye'plugs, they are marvels! The Germans used - and for some years into the 1950s - 60 ohms. The Rohde and Schwarz 'Polyskop' and some other R & S equipment of that era used 60 ohm 'Desifix' hermaphroditic connectors.
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G8HQP
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Posts: 905




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« Reply #19 on: March 29, 2019, 04:37:40 AM »

Quote from: KE7YD
If your really that curious, Times conveniently included the attenuation formula at the end.
That formula may only be correct in the region from 10MHz upwards, or at least where the RF current stays within the surface silvering.

Quote from: W9IQ
My statement was for coax of the same impedance.
OK, but it wasn't what you actually said.

From Wikipedia (https://en.wikipedia.org/wiki/Coaxial_cable#Choice_of_impedance)
Quote
he best coaxial cable impedances in high-power, high-voltage, and low-attenuation applications were experimentally determined at Bell Laboratories in 1929 to be 30, 60, and 77 Ω, respectively. For a coaxial cable with air dielectric and a shield of a given inner diameter, the attenuation is minimized by choosing the diameter of the inner conductor to give a characteristic impedance of 76.7 Ω. When more common dielectrics are considered, the best-loss impedance drops down to a value between 52–64 Ω. Maximum power handling is achieved at 30 Ω.

The arithmetic mean between 30 Ω and 77 Ω is 53.5 Ω; the geometric mean is 48 Ω. The selection of 50 Ω as a compromise between power-handling capability and attenuation is in general cited as the reason for the number.
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W9IQ
Member

Posts: 3040




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« Reply #20 on: March 29, 2019, 04:39:30 AM »

If you do the math - which I've forgotten, I haven't used calculus for many years - minimum loss is around 75 ohms. Maximum power handling is around 32 ohms. 50 ohms is the geometric mean. 

The power handling and losses will be affected by the type of dielectric and the type of conductors involved. Many people will quote the early 1900's research that was done that experimentally showed that the lowest loss was 77 ohms and the highest power handling was 30 ohms. But these were for copper conductors with an air dielectric. If you run the low loss calculations for PE dielectrics, for example, you will find it to range from 50 to 65 ohms. Of course, you need to state that this is for a given inner diameter of the shield conductor in order to make the comparison meaningful. Otherwise the highest impedance coax would yield the lowest loss when all other pertinent parameters are equal.

- Glenn W9IQ
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- Glenn W9IQ

I never make a mistake. I thought I did once but I was wrong.
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