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I have two 50 ohm characteristic impedance cables of which I need to shorten their length to compact my design. (put everything in to a box)

The cables I need to shorten are the GPS & GSM antenna cables.

I do not know if I can cut it from 12cm off the antenna and join it to the 50 ohm characteristic impedance . Currently each is about 3.5m.

Neither antennas have a LNA nor a SAW filters.

If I cut it off near the receiver and solder it to the 50ohm characteristic impedance cable coming off from my PCB, would that create any problems?

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A 50Ω cable is still a 50Ω cable, regardless of length. "50Ω" refers to the characteristic impedance, which is a function of the dielectric used in the cable, and its cross-sectional geometry.

Here's the problem: the solder joint you might make between two transmission lines won't have a 50Ω characteristic impedance. If you do it you will want to keep your connection as short as possible. Even then, by introducing this discontinuit, you will be introducing reflections on the cable which causes additional loss.

Maybe that's a problem, and maybe not. Depends on how efficient you need the transmission line to be. If you are just receiving you could try it and see. If you are also transmitting you could still try it and see, but depending on how robust your transmitter is it might be damaged. Probably it won't.

Or, you could join the cables with connectors. Coaxial connectors are designed to maintain the same characteristic impedance through the connection, avoiding the reflection problem.

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The length of a coaxial cable does not affect its impedance. If you cut a piece of 50 ohm cable anywhere, both pieces will be 50 ohm cables. For a uniform transmission line, the characteristic impedance is not a function of length; it will only depend on parameters such as the radii of the conductors and the type of insulation or dielectric used between the conductors.

References:

Characteristic impedance (Wikipedia)

Characteristic impedance and transmission lines (AllAboutCircuits)

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  • $\begingroup$ This is true but, if the cable is connected to something other than a 50 Ω impedance on one end, changing the length of the cable will affect the impedance presented to the other end. $\endgroup$ – Kevin Reid AG6YO Oct 13 '14 at 4:30
  • $\begingroup$ well could you kindly tell me how I could connect this wire to the other end of 50phm characteristic impedance cable coming off from the PCB after it is shortened? Should I proceed with solder? $\endgroup$ – Denis Oct 13 '14 at 5:38
  • $\begingroup$ @KevinReidAG6YO I doubt any 3.5m transmission line is used as an impedance transformer at GPS or GSM frequencies. That would be silly. $\endgroup$ – Phil Frost - W8II Oct 13 '14 at 16:34
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You would just be rotating around the smith chart, so the SWR as such will not change, just the angle of your impedance.

Just cut the transmission line and shorten it. The transmission line loss will cause more problems than the eventual impedance change.

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  • $\begingroup$ I understand. So, is it okay to use lead solder to join both ends? $\endgroup$ – Denis Oct 13 '14 at 7:05

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