The latest revision of the path antennas arrived. The network analyzer indicates that the patch resonance frequency is no correctly centered at 1.420 GHz, but the impedance matching is still incorrect. Working backwards from an input impedance of 86-40j Ohms with a 147.6 Ohm quarter-wave TL yields an impedance of 208+97j at the patch edge. Changing the TL impedance to 112.8 Ohms (20 mils) reduces the input impedance to 50.2-23.4j. The imaginary part can then be canceled out with a 2.7nH series inductor. I've submitted the revised board to OSH Park.
The patch antenna boards have arrived. The measured resonant frequency is 1.311 GHz, so I've adjusted the patch size proportionately and sent the revised boards off to OSH Park. I also added mounting holes on the off chance that the center frequency is correct this time.
So, after reviewing the antenna design and characterizing the FR4 material, it has become apparent to me that my initial log-periodic design is simply incorrect. The substrate permittivity only affects the feed line line impedance and does not change the phase velocity of the radiators. As a result the antenna simply does not work, and would need to be twice as large to operate correctly. A board that large would be prohibitively expensive for a single antenna, so I've decided to pivot to a patch-based array design that is dual polarized. This effectively gives me two antennas in the same footprint and should also improve better beam symmetry. My prototype patch layout is shown below.
Once I've verified the resonant frequency of the patch, and the port isolation, I'll complete the array layout. The final design will contain four patches in a grid layout with combiners and impedance matching to produce the broadside radiation pattern. The final board dimensions are expected to be 8 in. x 8 in.
I assembled the board with components I had on hand to test the LNA and noticed some issues. The LNA circuit itself works correctly and produces about 19dB of gain. The antenna itself, however, does not appear to operate correctly. I suspect this is a result of the difference between the OSH Park prototype boards and their "After Dark" process. In an effort to preserve my sanity, I've ordered some simple characterization boards to compare the two processes. The boards have three open-ended transmission lines to allow for measuring the permittivity at different frequencies.