Before doing anything else, I decided it would be a good idea to determine the appropriate width for a 50\(\Omega\) microstrip line. Proceeding without properly matched terminations would just complicate everything afterwards. There’s plenty of resources online describing the various approximations and formulas for calculating microstrip impedance, so I won’t go into detail here. I just used QUCS’s built in calculator to determine what width of copper tape I needed.
The values of interest for characteristic impedance calculations are the dielectric constant (\(\varepsilon_r\)), the substrate height (H), and the trace thickness (T). FR-4’s dielectric constant for 1.5 GHz and substrate height are easily found online. While I couldn’t get a manufacturer figure for the metal thickness of my copper tape, I assumed it was 1oz. copper, in which case the thickness is 0.036mm. The relative permeability for FR-4 is about 1 and \(H_T\), the distance between the trace and top ground plane, doesn’t really matter unless it’s small so I left it at its default large value. I’m not super concerned about loss so I left the trace conductivity, loss tangent, and roughness as is. As we can see, we want a trace width of ~2.97mm for a \(50\Omega\) line.
Implementation and Measurements
Building this is pretty straightforward. Just cut out a ~3mm strip of copper tape and stick it across the length of the board as straight as you can. Then solder on SMA connectors to both ends of the tape. That’s it!
With the VNA, I probed the S11 of my circuit, obtaining the trace below.
As we can see, the line is well matched at 1.5GHz with an S11 of -25dB. However, it does appear that the actual null is about 200MHz higher than desired. Looking at my circuit, my line does slightly widen at one end, making the impedance a bit lower than \(50\Omega\). An impedance measurement of \(47.3 + j5.23\Omega\) from my nanoVNA supports this. This is something easy to correct by being more careful when measuring and cutting in the future though.