I don't find any commercial antenna operating at 10MHz-50MHz. Why there is no horn antenna work at 10MHz, the size of the horn antenna is not so big.
Then I have to build a simple antenna connected with an RF signal generator with an SMA connector.
I guess the antenna I built is based on inductor loop wire, but the SMA connector has two nodes (a signal and a ground), how I can connect the SMA with the inductor loop wire with only one node ? Should I just leave the ground node of the SMA connector floating? Thanks.
You should give some additional informations. Are you planning a wide band transmitter or receiver antenna? A wide band receiver antenna might be made electrically small (with respective losses), a transmitter antenna effectively not. Tuning a small antenna to a different frequencies in the 10 - 50 MHz range is however feasible.