CH08-Magnetically Coupled Circuits

Mutual voltage

L1ML2+u*12--ui21+*1i2–u1

++u2

–j?L1j?MI??2M*j?MI1j?L2+--+*I?1I?-U?21++

U?2-

uLdi1di21?1dt?Mdtudi2di12?L2dt?Mdt?1?j?L?1I1?j?MI?2U?2?j?L?2I2?j?MI?1U8.2 Involving mutual inductance

circuits analysis

1. Series connection

+

j?MU?*I+

?*R2+

-d-

a

R1j?L1(series-

b-

c

j?L2U2?U1?U?U1?U2?I[Z1?ZM]?I[Z2?ZM]??I[R1?j?L1?j?M?R2?j?L2?j?M]?I[(R1?R2)?j?(L1?L2?2M)]?????aiding connection)

?equivalent inductance:L1?L2?2M＋

j?MU?*a

*j?L1b

d－cI?R1R2+

?j?L2U2-

+

U1?-

(Series-opposing connection)

U?I[(R1?R2)?j?(L1?L2?2M)]equivalent inductance:L1?L2?2M??2. Parallel connection

U??j?L??1I1?j?MI2U??j?MI??1?j?L2I2L2L?1L2?ML1?L2?2MU??j?L??1I1?j?MI2U???j?MI??1?j?L2I2L2L?1L2?ML1?L2?2M8.3 T equivalent circuit

一、T-connection

1

i1Mi22+??+uL1L12u2--3i1Mi22

+?+uL1L1?2u2--31