《电路》（英文版）10-3 Other resonant forms

810-3 Other resonant forms +jac+ R R +JOL R R R千C +jac R R,+ L o2L2R12+2L R j(aCc RR+0L R+0L L ato=00 c =0 or 0.C R,2+.2L Rn,2+a.2L2 L-RC 1 R 2 1 R LC L L LC

§10-3 Other resonant forms R j L j C R V I Y L   + = = + + • • 1 1 2 2 2 2 2 2 1 R L L j R L R j C R L L L     + − + = + + ) R L L j( C R L R R L L L 2 2 2 2 2 2 1     + + − + = + 0 2 2 2 = + = − R L L at C L r r r, r      2 2 2 R L L or C L r r r    + = 2 2 2 2 2 1 L R L C LC L RL C L r = − −  = 2 2 1 L R LC L  r = − ) 1 ( 0, LC RL →  r =

J c+ RL+jaL R OL C JaC R,2+2L2R,2+a2L2 R O a2+∥oC R+OL 2 when e>>1,OL >>RL r=-5+j(aC OL L L CR CR -L+jac-j L L +iac (>1) R

R j L Y j C L   + = + 1 2 2 2 2 2 2 R L L j R L R j C L L L     + − + = + ) R L L j( C R L R L L L 2 2 2 2 2 2     + + − + = 2 2 2 1 L RL when Q   ,    ( ) 2 2 2 2 L L j C L R Y L     = + − L j C j L CRL   1 = + − L j C j Req   1 1 = + −

Example:IfC=500PF,O=2兀×10,R=10,Q>1. Find c Solution: →L LC RL m×10)2×500×102÷50.7H 507×106 ≈10000 CR,500×102×10 (,=-.≈2兀×10°) L LO CR L C L O=ORC=R en q 12 (>1) 500×10 10 V507×106≈314

Example: If C=500PF, ,RL=10, Q>>1. Find Q. 6 2 10− r =   Solution: LC r 1  = H  50.7 (2 10 ) 500 10 1 6 2 1 2 =    = − C L r 2 1   = 10000 500 10 10 50.7 10 1 2 6     = = − − L eq CR L R L C Q = r ReqC = Req ) LC ( r 6 2 10 1  =    31 4 50 7 10 500 10 10 6 12 4 . . =   = − −

Find the resonant frequency L + 1∠0°4 2IC jOL X1+Icx 2Ic+Ic=1→Ic=1/3 jaC jOL Z=JOL or 0 jac 30C 30 c 3LC

Find the resonant frequency j C V j L I C   1 = 1+  • • 2 + = 1  = 1/ 3 • • • I C I C I C j C V j L   3 1 = + • C or L r r   3 1 = LC r 3 1  = ) 3 1 ( C Z j L  =  −

Find the resonant frequency or ar2 parallel resonance jOL,( jaC )iola OL L Joc JOL a2L1C11-a32L2C2 J jaL-joL, L2 C2+ jaL2-jo'L1L2C1=o (1-o2L1C1)(1-aL2C2) L+l L1+L2=2L1L2(C1+C2) VLL2(CI+C2) series resonance

Find the resonant frequency parallel resonance L C or L C r = r = − − 2 2 2 1 1 1 1 1   2 2 2 2 1 1 1 1 1 1 1 1 j C j L ) j C j L ( j C j L ) j C j L ( Z         + + + = 0 (1 )(1 ) 2 2 2 1 1 2 1 2 1 3 1 2 2 2 3 1 = − − − + − = L C L C j L j L L C j L j L L C       ( ) 1 2 1 2 2 L1 + L2 = L L C +C (series resonance ) L L (C C ) L L r 1 2 1 2 1 2 3 + +  = L1 L2 C1 C2 2 2 2 2 1 1 2 1 1 1 L C j L L C j L     − + − =