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I am designing a four-layer board on which I have to run two 50 Ω traces, one on the top and one on the bottom side of the board. I have decided to use a coplanar wave guide for both the traces. I am skeptical about calculating the impedance of the trace on the bottom side since the adjacent plane is a power plane. I have attached the stack up image of the board.
Calculated impedance using APPCAD:
First I would ask why a coplanar waveguide? Given that you have a four layer board I would think using micro strips would be easier / better.
Based on your Stackup you are really talking about a conductor backed coplanar waveguide. In that case return current will flow on both your side conductors and the "reference" plane underneath them. I say "reference" to emphasize that on the bottom return current will flow in your vcc plane and your side conductors. In a micro strip it would flow just on vcc. This is because this path is the path of lowest impedance for the current to follow.
Now current flows in a loop so when it gets back to the source it must find a way back to gnd to complete the circuit so it will find a way. In a well decoupled board that path will be the nearest decoupling cap(s).
A good source to learn more is the handbook of black magic by Dr Howard Johnson, his website, Eric Bogatin's books or website, and Brian Waddel's transmission line book.
