The　radio　frequency　(RF)　phase　shifter　with　finite　quantization　bits　in　analog　beamforming　(AB)　structure　forms　quantization　error　(QE)　and　causes　a　performance　loss　of　received　signal　to　interference　plus　noise　ratio　(SINR)　at　the　receiver　(called　Bob).　By　using　the　law　of　large　numbers　in　probability　theory,　the　closed-form　expression　of　the　SINR　performance　loss　is　derived　to　be　inversely　proportional　to　the　square　of　Sinc　(or　sin(x)/x)　function.　Here,　a　phase　alignment　method　is　applied　in　the　directional　modulation　transmitter　with　the　AB　structure.　Also,　the　secrecy　rate　(SR)　expression　is　derived　with　the　QE.　From　the　numerical　simulation　results,　we　find　that　the　SINR　performance　loss　gradually　decreases　as　the　number　L　of　quantization　bits　increases.　This　loss　is　less　than　0.3　dB　when　L　is　larger　than　or　equal　to　three.　As　L　exceeds　five,　the　SINR　performance　loss　at　Bob　can　be　approximately　trivial.　Similarly,　the　SR　performance　loss　gradually　reduces　as　L　increases.　In　particular,　the　SR　performance　loss　is　about　0.1　bits/s/Hz　for　L　=3　at　signal-to-noise　ratio　of　15　dB.　©　2013　IEEE.