This work investigates the design of a paper-substrate dipole antenna and its magnetic coupling to a UHF RFID chip. The magnetic coupling is realized by means of a heterogeneous transformer, the primary winding of which is implemented on the same paper-substrate of the antenna. The secondary winding, instead, is directly fabricated on the Si RFID chip, thus does not require for galvanic contacts between chip and antenna. The transformer insertion loss can be reduced to the device Maximum Available Gain (MAG) if a proper impedance termination of the primary (Z_S,opt) and secondary (Z_L,opt) windings is adopted. For the considered heterogeneous transformer the MAG is quite low and around -0.6 dB. Following this idea, a bow-tie dipole antenna is designed to meet Z_S,opt at the operating frequency of 868 MHz. The antenna size is reduced by exploiting a meander line. As a result, the designed dipole features an overall length of about 40 mm. To the authors knowledge this is the first bow-tie antenna the design of which has been optimized for the magnetic RFID coupling concept.