========================FM_2_PM========================= _ _ _ _ _ _ _ _ _ _ _ _ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| | Pure sign wave _ _ __ __ _ _ _ _ _ _ | | | | | | | | | | | | | | [|[| | | | | | | | | | | | | | | | | | | | |||| | | | | | | | | | | | | | | | | | | | |||| | | | | | | | | | | | | | | | | | | | |||| | | | | | | |_| |_| |__| |_| |_| |_| |_|L||_| |_| |_| A Moving sign wave Frequency Modulate a 1kHz carrier with a 1Hz signwave Freq(t) = [ 1000 + sin(2*PI*t) ] Signal= sin( (Freq(t))*2*PI*t) <--FM format at time = 1/4 The Frequency is 1001 Hz at time = 3/4 The Frequency is 999 Hz Another way to think of it is Phase Modulation... Signal= sin( (1000)*2*PI*t +Phase(t)) <-- PM format the phase will be Integral of FM ... _ / Phase(t) = | 2*PI*sin(2*PI*t)*dt = -cos(2*PI*t) _/ So 1Hz peak FM over 1Hz will generate 1radian peak of PM And to convert FM to PM, just integrate and One Hz FM at One Hz equals One radian PM The PM will lag the FM which causes it. ^ /|\ Freq=1001Hz| Phase= +1radian __--|--__ __-----__ __/ | _\/_ \__ _/ | _/ \_ \_ _ _ / _ _ _ _ |/_ _ _ _ \_ _ _ _ _ \_ _ _ _ _ _ _ \ _/| \_ \_ _/ / __/ | \__ \__ __/ TIME __/ | \__ ___/___ ---- ----- ---- Phase= -1radian Freq=999Hz