For the introduction of the design, please read this article [1] written by JA6XKQ. For those who are interested in the details of the derivation and surface accuracy of the structure, you can refer to [2]. Another important thing is the supporting structures such as adding supporting rods behind the dish or additional inner meshes to prevent the heavy feed from deforming the structure. See [3] and [4]. Please refer to the excel sheet from JA6XKQ's website at [5] to obtain the specific dimensions.
Cantenna's diameter: 14.5cm, length: 18cm, probe's distance from the back (1/3 of the length): 6cm, probe's length: I started with 0.25*λ, and it is trimmed until a good SWR is obtained with a NanoVNA. These dimensions are based off from the design from Figure 3 at [6]. If you want to determine the diameter based on your desired edge taper, you can see page 3 at [7]. To compute the dimensions of the cantenna and a choke ring, refer to the excel sheet from SETI League at [8].
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