Handbook of Electrical Engineering

378 HANDBOOK OF ELECTRICAL ENGINEERING

This has the form:-
y 2 =a 21 Ic+a 22 Is ( 13. 11 )

Where

y 2 =−jωM 3 sI 3

a 21 =+jωMsc

a 22 =−(Rss+jωLs)

Rss=+Rs+Re

The solution of the simultaneous equations (13.10) and (13.11) for the two currentsIsandIcis:-

Is=

y 1 a 21 −y 2 a 11

a 12 a 21 −a 11 a 22

amps ( 13. 12 )

and

Ic=

y 2 a 12 −y 1 a 22

a 12 a 21 −a 11 a 22

amps ( 13. 13 )

Some simplifications can be made after comparing the various mutual and self-inductances.
The following assumptions are valid:-

Msc=Ls because the majority of the flux between the screen and the core couples

the screen and the core.

Let M=M 3 s≈M 3 c

AndMscM 3 sorM 3 cbecause of the relative dimensions and separation distances.

The denominator of (13.12) and (13.13) becomes:-

a 12 a 21 −a 11 a 22 =RssRcc+jω(RccLs+RssLc)+ω^2 (Ls(Ls−Lc))

In which the extreme right-hand term is very small in the range of frequencies of interest, and can
be ignored. Therefore the denominator becomes:-

a 12 a 21 −a 11 a 22 =RssRcc+jω(RccLs+RssLc)

TheIsnumerator of (13.12) becomes:-

y 1 a 21 −y 2 a 11 =(+ω^2 M(Ls−Lc)+jωMRcc)I 3

TheIcnumerator of (13.13) becomes:-

y 2 a 12 −y 1 a 22 =(−ω^2 M(Ls−M)+jωMRss)I 3