Physical limitations of ESA:CHU's limit A.Field of a vertically polarized dipole For the vertically polarized dipole,only TMno waves are required to consider a H=>AnP(cos0)hn(kR), INPUT ANTENNA STRUCTURE B=-() ∑Ar(m+1) hn(kR) XP(cos0)- kR For an arbitrary current distribution =j(月AP.oas and antenna structure,the field out 1 d side the sphere can be expressed in X一-[Rhn(kR)], terms of complete set of orthogonal, kRdR spherical waves P,(cos):Legendre polynomial of order n P(cos):The first associated Legendre polynomial h (kR):spherical Hankel function of second kind L.J.CHU,"Physical limitations of omni-directional antennas",Journal of applied physics,vol.19,Dec 1948Physical limitations of ESA: CHU’s limit a For an arbitrary current distribution and antenna structure, the field out side the sphere can be expressed in terms of complete set of orthogonal , spherical waves For the vertically polarized dipole, only TMn0 waves are required to consider A. Field of a vertically polarized dipole 1 (cos ) : Legendre polynomial of order n (cos ) : The first associated Legendre polynomial ( ) : spherical Hankel function of second kind n n n P P h kR   L.J.CHU, “Physical limitations of omni-directional antennas”, Journal of applied physics, vol.19, Dec 1948