I want to make myself a antenna for 40m and 20m wavelength band, but i don't have enough space for a full scale dipole, and even for more compact configurations like delta-loop or inverted v, so i want to create a shortened dipole in configuration of a whole-length solenoid with small (compared to wavelength) diameter. It should work the same as a wire in terms of transmitting energy (J. S. Belrose article, QST, Sep 1953) but with increased inductance throughout whole length of it.
And if i recall correctly, that for a shortened dipole it's input impedance starts to have a reactive capacitive component which needs to be compensated with a "lengthening inductance".
So the question is, how much inductance i need to have to appropriately compensate for a shortened regular dipole? And what the active resistance will be so i can match the antenna? I'm having trouble finding the formulas for overall input impedance.
Thanks in advance.