Solution (c)台VoP。+N2Vo=I+I+1.081)12mVaNiRRVdN11VTVaDT5x10-5mripple2 LmVN22I7711V。 N,R:xD, xTV11=i,=0ü,VdVi(t) =i.(t) = I (0)o<t<tontonofF→(N,/N2)VVdI =I=Im(0)(10-9)onVmΦ(0)DE-mail:xj
E-mail: xjhuang@bjtu.edu.cn 1 ) 1 1 = 510-5 d m o m s s m mripple d 1 d V 11.1 L ( 1 + N2 V N 1+ 2 L Vd T Vd 1 DT = 2 L = 1 Vd I + N2 ) = 6(12 +1.081) V N1 R R Vd N V = I = I + I Po ' m 1 2 + N2 Vo = Vo(Vo Solution (c)
SolutioneN, VV.V.N2(c) I. =I +Ia+1.081)12VaRN, RVadN11T, Va1 VaDTT5×10-mrippleS2 Lm2VN2Lm1 +(+1.1V。N,To guarantees continuous mutual inductance current,we have Im>Imripple112+1.081)> 5×10-5x6U1Vdmaxdmax15×10-5:54.76×10-6(H)L126(1.081V11dmaxdmax
11.1 1 )( ) 12 1 1 6 11.1 1 1 ) 1 V L ( Vd max Vdmax m d max m = 54.7610-6 (H) (1.081+ + + 6( 12 +1.081) 510-5 Vd max L 5 10−5 Solution 1 ) 1 = 510-5 m o 1 d m s s m mripple d 1 d m V 11.1 L ( 1 + N2 V N 1+ 2 L Vd T Vd 1 DT = 2 L = 1 Vd I + N2 ) = 6(12 +1.081) V N1 R R Vd N V = I + I ' 1 2 (c) I = Po + N2 Vo = Vo(Vo To guarantees continuous mutual inductance current, we have Im>Imripple
3ReviewofbasicMagneticCircuitConceptsTermsF---maanetomotive force (磁势)H----maanetic field intensity(磁场强度A/m)B----flux density(磁通密度Wb/m2orTesla)p----flux (磁通);(磁链)Am----flux linkage(磁阻);reluctance(磁导率 H/m)μ----permeabilitySaturation(饱和)
Terms F-magnetomotive force (磁势) H-magnetic field intensity (磁场强度 A/m) B-flux density (磁通密度 Wb/m2 or Tesla) Φ-flux (磁通); λm-flux linkage (磁链) -reluctance (磁阻); μ-permeability (磁导率 H/m) Saturation(饱和) 3 Review of basic Magnetic Circuit Concepts
Basicrelationsa(t)= N (t)e(t) = u/1a,= Nom= Lmigmd(dtdt=NiN2N2A.llAmmLm8RΦ(t) = d(0) + 1e(t).dtmNiNR=Rm+Rd0RFaraday's law+B(t), Φ(t)V(t)B= μHterminal=ourcorecharacteristicscharacteristicsμ=4元×10-7(H / m)H(t), F(t)i(t)Ho—airAmpere' s lawpermeability(空The line integral of the气磁导率)fHdl =ZimagneticfieldintensityHPr—relativeZHlk=Nmi(磁场强度)equalsthepermeabilitytotal (enclosed) current:km
Basic relations Hdl = i k H k l k = N m i m m The line integral of the magnetic field intensityH (磁场强度)equals the total (enclosed) current: 0 −7 = 4 10 B = H = 0r (H / m) µ0—air permeability(空 气磁导率) µr—relative permeability g g g m m Ni l l = = m +g A A ( ) = Ni m + t 1 (t) = (0) + e( ) d N e(t) = d (t) = N d (t) dt dt 0 Faraday’ slaw V(t) B(t), ɸ(t) core characteristics H(t), F(t) Ampere’ slaw terminal characteristics i(t) m m m m m m Am l = Lm = N 2 N 2 ( ) = N = L i