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I have a passive GNSS antenna with a 6" 1.13mm shielded coaxial cable that connects to a u.FL connector. From the u.FL connector I have a 2" microstrip transmission line to the RF input of my GPS receiver. Altium's built in impedance calculator shows the trace impedance at 34 ohms not 50 ohms. Other calculations of stripline based on on strip height above ground plane, freq, dielectric material... also show similar impedance.

How does that affect power received at the GNSS receiver? I presume there will not be max power transfer since the impedance are different.

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You will lose some power, but probably not an unacceptable amount - especially if the input of the receiver is in the 40 to 50 Ohm range. I get a gamma of -0.19 for coax to ms which is less than 0.2 dB power xfer loss - not the end of the world :).

However if the receiver input were, say 100 ohms, you'd get a gamma of about 0.5 there and lose 1/4 of your power.

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The different impedance of Coaxial cable and antenna feed, will create the mismatch at antenna feed-point. This mismatch will create power loss that will reduce antenna gain significantly. You can use some transformer to transform 50-ohm cable impedance to 34-ohm antenna feed impedance.

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    \$\begingroup\$ aybe I am splitting hairs here, but it will reduce antenna realized gain not gain. Transformer is also maybe not the approach here for mismatch - lumped components may be better - a weighting is needed between cost, loss, size, etc. \$\endgroup\$ – user94729 Mar 6 '18 at 5:11

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