An effective wide-band (10 to 60 MHz) active antenna element has been developed. The cost of one short (3 m), thin dipole with built-in amplifier and metal construction is less than 45 euro. It was shown both theoretically and experimentally that the upper limiting frequency is at least 60 MHz, the dynamic range is 90 dB/µV and the share of the amplifier noise to the background antenna temperature is about 10%. The developed active dipole was tested by building a 30-element antenna array and comparing its parameters with one of the subpart of the UTR-2 radio telescope having passive dipoles of 8.6 m in length and 1.8 m in diameter. The 3C461 ionospheric scintillation spectra observed in the experiments show that the sensitivities and noise-immunities of both antennas are close. This proves the availability using of a short cheap active dipole in new generation giant radio telescopes.