  An in-situ calibration of a logarithmic periodic dipole antenna with a
frequency coverage of 30 MHz to 80 MHz is performed. Such antennas are part of
a radio station system used for detection of cosmic ray induced air showers at
the Engineering Radio Array of the Pierre Auger Observatory, the so-called
Auger Engineering Radio Array (AERA). The directional and frequency
characteristics of the broadband antenna are investigated using a remotely
piloted aircraft (RPA) carrying a small transmitting antenna. The antenna
sensitivity is described by the vector effective length relating the measured
voltage with the electric-field components perpendicular to the incoming signal
direction. The horizontal and meridional components are determined with an
overall uncertainty of 7.4^{+0.9}_{-0.3} % and 10.3^{+2.8}_{-1.7} %
respectively. The measurement is used to correct a simulated response of the
frequency and directional response of the antenna. In addition, the influence
of the ground conductivity and permittivity on the antenna response is
simulated. Both have a negligible influence given the ground conditions
measured at the detector site. The overall uncertainties of the vector
effective length components result in an uncertainty of 8.8^{+2.1}_{-1.3} % in
the square root of the energy fluence for incoming signal directions with
zenith angles smaller than 60{\deg}.
