During the flight of a sounding rocket, it is not possible to keep an antenna pointed at the sky at all time. Since the electronic bay is located inside the nosecone, the antenna is facing the sky during the ascension but face the ground after the parachute deploys. The use of the traditional ceramic patch antenna is not ideal since the are directional.
The quadrifilar helix antenna is used since it is a less directional circularly polarized antenna.
Antenna frequency
The antenna is designed for the following bands:
GPS L1 : 1575.42 MHz
GLONASS L1 : 1598.0625-1609.3125 MHz
Galileo E1 1575.42 MHz
SBAS L1 : 1575.42 MHz
Design of the antenna
Since there are no exact formulas for designing this type of antenna, a numerical modelling approach is used. The NECPP python library is used for the optimisation of the antenna geometry and the 4nec2 software is used for the validation.
The antenna is composed of 2 loops of around one wavelength in length that are rotated. To achieve the circular polarisation, there must be a phase difference of 90˚ between the tow loops. One of the loops is made smaller and the other larger so they have an opposite reactance.
The following parameters are used as a starting point:
Length of one loop: One wavelength in air -> 190mm
Diameter of the antenna: 30mm
Number of turns: 0.5
The scypy library is used to optimize the antenna geometry for the highest circularly polarized gain.
The script is available here: https://github.com/le-Bark/QFH-Antenna
The first prototype of the antenna is built using a PCB as a support. The PCB contains a quarter wave folded balun, a 50 ohm micro-strip and a SMA connector.
The antenna is measured using a NanoVNA, the frequency response is as expected. The impedance of the antenna is 95+J2 ohm and will need to be matched on the next prototype.
The unmatched Antenna is then tested successfully using a U-Blox GPS module.

Active antenna
The design is based on the BGA524N6 LNA IC from Infineon. The LNA circuit is placed in the middle of the antenna on the support PCB.
To be continued…
Thanks for posting an antenna project. The quadrifilar helix can be optimized for an omni-directional pattern, which would suit your rocketry application well (given uncertain flight attitudes). Why are you optimizing for "upward" gain/directivity. Got any test plans for your hardware proto? /Glenn