An antenna unit provided with an antenna which comprises at least one turn forming a coil, wherein the antenna unit is further provided with an electronic circuit which is connected with the antenna wherein the electronic circuit is arranged to tune the antenna unit such that this antenna unit has an impedance which has at least substantially no imaginary component for a transmission signal supplied by a transmitting device, wherein the electronic circuit comprises connection contacts for connecting the antenna unit with said transmitting device, wherein the electronic circuit is arranged to draw the energy which the electronic circuit needs for its operation from the transmission signal which is supplied to the connection contacts and to utilize this energy to tune the antenna unit, wherein the electronic circuit is provided with a tuning circuit which forms a tuning capacity which is connected with the antenna, wherein the tuning circuit is arranged to be able to set the magnitude of the tuning capacity, characterized in that the electronic circuit is further provided with a supply circuit for taking up the energy from the transmission signal and a measuring and control circuit which comprises said tuning circuit, wherein the electronic circuit is so arranged that the measuring and control circuit receives the energy required for its operation from the supply circuit and wherein the measuring and control circuit is arranged to measure whether the antenna in combination with the tuning circuit comprises an impedance with an imaginary component and to control the tuning circuit such that any measured imaginary component is reduced, wherein the electronic circuit is further provided with a current circuit for generating a first signal which represents the phase of a current through the antenna, and a voltage circuit for generating a second signal which represents the phase of a voltage across the antenna and the tuning circuit, wherein the measuring and control circuit is provided with a control circuit and a phase comparator for comparing the first signal and the second signal, wherein the control circuit is arranged for, on the basis of a phase difference signal generated by the phase comparator that represents a phase difference between the first and second signal, controlling the tuning circuit such that said imaginary component is reduced, and wherein the electronic circuit is further provided with a transformation selection circuit comprising a first transformer with a first side and a second side, wherein the first side is connected to the connection contacts and the second side is connected to the tuning circuit. wherein the ratio between the number of turns on the first side of the first transformer and the number of turns on the second side of the first transformer is settable, wherein said setting can be carried out, for example, by hand or through a control signal, and wherein the transformation selection circuit further comprises a second transformer for drawing energy from the transmission signal towards the supply circuit, and wherein the current circuit is part of the measuring and control circuit or of the supply circuit, and the voltage circuit is part of the measuring and control circuit or of the transformation selection circuit.