The thermal efficiency measured on surface of small antenna conductors is generally found to be much larger than the radiation efficiency measured outside the near-field region. The difference can reach 10 to 20 dB or more at some frequencies. High thermal efficiency means that the surfaces of the antenna conductors do not get excessively hot even with several hundred watts input. Low radiation efficiency with high thermal efficiency means that RF has ‘disappeared’ in the near-field region. Measurements made so far have discovered that this missing RF in part is converted into low temperature white noise with a flat spectrum up to about twice the carrier frequency. An additional discovery is that part of the ‘lost’ energy can become attached to any steady modulation sidebands on the transmitted signal so that in the ‘dissipative non-linear near- field region’ the carrier is more attenuated than some of the sidebands. The additional sideband energy appears to come from reduction of the white noise. The theory for this ‘near-field dissipation and frequency conversion’ effect was developed origi- nally to explain measurements made on the ‘Wideband Small Loop-monopole HF Transmitting Antenna’ announced at PIERS 2013 in Taipei [1]. It is compatible with and based on the ‘Physi- cal Model of Electromagnetism’ announced at PIERS 2011 in Morocco, [2] and extended in other subsequent papers [3–10]. The discovery of this small antenna ‘non-linear’ near-field effect would appear to have widespread implications, for example for antenna efficiency, Beverage antenna noise reduction, Maxwell’s Equations and the Chu Small Antenna Q Criterion [12]. This effect naturally links to an Elec- tromagnetic Theory of Everything as initiated in [2] and extended in and from [3–10].