Derivation of some expansions of near-field gain of antennas in lossy medium

To estimate SAR (specific absorption rate) of the wireless devices operated in HF band, the behavior of the near-field gain in the near-field region of the reference antennas operated in the tissue-equivalent liquid is required. Some asymptotic expansions of the near-field gain of the reference antennas are derived by using an integral form of the transmission coefficient between the antennas and expansion theorem.