87-1 Characteristics of sinusoids V sin ot y sin ot Vn-- amplitude(振幅 兀 a-- arg ument(幅角) T--period (T=1/f,OT=2丌,O=2m) f--frequency A more general form of the sinusoid @--angular frequency 丿 sin at u=Vm sin(at +9 (at +9)--arg ument V sin(at+gy 9--phase angle 「 v sin((or+9) leads(超前)V sin at by raa, orv sin at lags(滞后)nsin(or+9b9rad
§7-1 Characteristics of sinusoids f frequency T period − − − − V amplitude(振幅) m − − t − −argument(幅角) − −angular frequency t 2 V t m sin Vm 0 (T = 1/ f ,T = 2 , = 2f ) t 2 V t m sin V sin(t +) m 0 A more general form of the sinusoid phase angle ( t ) arg ument − − + − − =Vm sin(t +) sin sin( ) . sin( ) sin , or V t lags V t by rad V t leads V t by rad m m m m + + （滞后） （超前） =Vm sint
In either case, leading or lagging, we say that sinusoids are out ofphase (F#8), if phase angles equal they are said to be in phase(同相) U=220sim(314t-/6→U=220si314t-30°)y Two sinusoidal waves that are to be compared in phase must written as sine-waves, or both as cosine-waves. both waves must be written with positive amplitudes, and each must be of the same frequency. sin(5t-30°) leads v by-130 U2=V2mcos(5t+10°) orU1lgsU,b+130° Vm sin(5t +100) Normally, the difference in phase between two sinusoids is expressed by that angle which is less than or equal to 1800 in magnitude
In either case, leading or lagging, we say that sinusoids are out of phase（异相）, if phase angles equal they are said to be in phase（同相）. 220sin(314t / 6)V 220sin(314t 30 )V = − → = − Two sinusoidal waves that are to be compared in phase must written as sine-waves, or both as cosine-waves, both waves must be written with positive amplitudes, and each must be of the same frequency. sin(5 30 ) 1 1 =V m t − cos(5 10 ) 2 2 =V m t + sin(5 100 ) 2 =V m t + 130 130 1 2 1 2 + − or lags by leads by Normally, the difference in phase between two sinusoids is expressed by that angle which is less than or equal to 180o in magnitude
