Surfing on the net I was reading an article about extreme small HF antennas. I found it a strange design, but reading the article made me understand the design. In fact it's very simple, we connect a capacitor, in the form of a copper or aluminum tube, in series with an inductor. That makes a resonating circuit on a fixed frequency.
The formulas below explain how we can calculate the antenna called the Microvert. Designed by DL7PE
The length of the tube can be calculated using the formula below:
The capacitance of the tube can be calculated with:
To calculate the inductor to make it resonant is calculated using the formula below:
The coax inner wire is connected with the inductor. The outer conductor of the coax is used as a counterpoise. These has a certain length which can be calculated.
After this length we need a RF-choke to block the return current. The RF-choke can be made of the coax about 8 turns with a diameter from about 10cm
Original Microvert article (PDF) (English)