(1) The m should be an odd integer to eliminate the evenharmonics.（m应取奇数以消除偶次谐波）N=3UBoUact/smr(=3) is an oddinteger-Half-wave symmetryf(t)=-f(t-T/2)t/sNoevenharmonics120Ugot/s
12 (1) The mf should be an odd integer to eliminate the even harmonics. (mf应取奇数以消除偶次谐波) mf (=3) is an odd integer→ Half-wave symmetry f(t)=-f(t-T/2) No even harmonics
C00ESUgoN=6t/s181t/s20120°upot/s· mt (=6) is a even integer output voltage contains even harmonic components
• mf (=6) is a even integer →output voltage contains even harmonic components
N=3.5t/sUAOt/sUect/smf (=3.5)is a noninteger→output voltage containssubharmonics （次谐波)(of the fundamental frequency)which frequencies are lower than fundamental-frequency
•mf (=3.5) is a noninteger →output voltage contains subharmonics (次谐波) (of the fundamental frequency ) which frequencies are lower than fundamental-frequency
6) SidebandsTable 8-1 Generalized Harmonics of vAo for a Large mgmaharmonicsh0.20.40.60.81.011.00.20.40.60.8Fundamental0.6011.2421.151.0060.818my0.1310.2200.3180.0160.061m,±20.018m±40.3260.3700.3140.1810.1902m, ± 10.0240.0710.1390.2122m,± 30.0130.0332m,± 5fn = (jmf ± k)fi0.1133m,0.3350.1230.0830.1710.2030.1760.0620.1393m,±20.0440.1570.0470.1040.0123m,±40.0160.0443m,± 60.0080.1050.0680.1630.1574m, ± 10.0090.1320.1150.0120.0704m,± 30.1190.0340.0844m,±50.0170.0504m,±7Note: (VAo)n/;Va [= (VAN)r/;Val is tabulated as a function of ma
6) Sidebands harmonics
Example01In the following circuit, V.=300V, ma=0.8, m,=39, and thefundamental frequency is 47Hz. Calculate the rms values of thefundamental-frequency voltage and some of the dominantharmonics in VAo using Table 8-1Solution+The rms at any value of h is:+Va/2O1 Va(VAo)hVd= 106.07 (VAo )h?+x(VAo)h =J2 2Va/2Va/2VANVa /2N
Example 01 In the following circuit, Vd=300V, ma=0.8, mf=39, and the fundamental frequency is 47Hz. Calculate the rms values of the fundamental-frequency voltage and some of the dominant harmonics in vAo using Table 8-1 Solution The rms at any value of h is: ˆ ˆ d Ao h d Ao h V 2 (V ) 2 2 V 2 1 Vd (VAo )h (V ) = =106.07 TA+ TA- DADA+ + Vd/2 - + Vd - 0 io + vAN - N A + Vd/2 -