Free　positioning　wireless　charging　for　consumer　electronics　allows　the　devices　to　be　charged　at　arbitrary　positions　and　angles　to　improve　user　experience.　However,　a　user-initiated　sudden　movement　of　the　device　during　charging　can　cause　hazards　due　to　the　abrupt　variation　of　the　coupling　coefficient.　To　solve　this　issue,　the　coupling　coefficient　variation　at　different　positions　should　be　mitigated,　which　is　also　good　for　the　design　and　high-efficiency　operation　of　power　electronics　converters.　This　article　proposes　a　design　methodology　to　employ　antiparallel　windings　to　smooth　the　coupling　coefficient　variation　over　different　positions　by　reducing　the　coupling　coefficient　at　central　positions　and　enhancing　it　at　boundary　positions.　Two　optimization　methods　are　proposed:　Turn-by-turn　optimization　and　winding-by-winding　optimization.　A　design　flow　is　offered.　The　hexagonal　coil　is　compared　with　the　square　coil　and　proved　to　achieve　better　performance　than　the　latter.　An　experimental　prototype　is　implemented　to　validate　the　effectiveness　of　the　proposed　design　methodology.　©　1982-2012　IEEE.