08_MutualInductance

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Mutual Inductance and Transformer Circuits

with LTspice IV

University of EvansvilleJuly 27, 2009

In addition to LTspice IV, this tutorial assumes that you have installed the University of Evansville imulation Li!rary for

LTspice IV" This li!rary e#tends LTspice IV !y addin$ sym!ols and models that ma%e it easier for students &ith noprevious 'I(E e#perience to $et started &ith LTspice IV"

Mutual Inductance

)e &ill use LTspice IV to determine the mesh currents I*and I2in the phasor circuit sho&n in +i$ure *" This circuitincludes a pair of couple inductors &ith a mutual inductance ofj -"

+*2 0. V *2 -j/ -j -

j1 -j, -

I1

I2

+i$ure * E#ample (ircuit

The correspondin$ LTspice IV schematic is sho&n in +i$ure 2" The coupled_inductor_pair_1component from the03_coupled_inductorscomponent directory is used to represent the coupled inductor pair" There are three parametervalues that must !e set &hen usin$ a pair of coupled inductors" 3ou must set the self4inductance values 5L* and L26 and thevalue of mutual inductance 56" The method discussed in the 8( 8nalysis tutorial for simulatin$ phasor circuits is usedhere inductance values are eual to the inductive reactances, capacitance values are eual to the ne$ative reciprocal of the

capacitive reactances and the circuit is simulated at a freuency of : ; * rad


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the circuit $ives identical results" @ote that LTspice defines the current throu$h a volta$e source as positive &hen enterin$the positive terminal of the source" The current throu$h V* is therefore the ne$ative of the current throu$h (*" Thene$ative of a phasor can !e o!tained !y either addin$ or su!tractin$ *A0. from the phase an$le 5!y convention phasoran$les are in the ran$e from 4*A0. to B*A0., &e either add or su!tract *A0. so that the phase an$le of the result is &ithin thisran$e"6"

frequency: 0.16 Hz

I(C1): mag: 13.0158 phase: -4.38!" #e$%ce&curren'I(1): mag: .1043 phase: 14.036" #e$%ce&curren'

I(*1): mag: 13.0158 phase: 130.601" #e$%ce&curren'

Ta!le * imulation Cesults for +i$ure 2

8 second e#ample circuit &ith a pair of coupled inductors is sho&n in +i$ure "

+20 60. V

-

j/ -

j2 -

j1 -j -

I1 I2

+i$ure 8 econd utual Inductance E#ample (ircuit

The correspondin$ LTspice IV schematic is sho&n in +i$ure 1" @ote ho& the inductor pair is oriented and connected sothat the Ddots match those in +i$ure "

+i$ure 1 LTspice IV chematic (orrespondin$ to +i$ure

imulation results are sho&n in Ta!le 2" (urrent I*is euivalent to current I5C*6 and is "7A 86.565. 8" (urrent I2is

euivalent to current I5(*6 and is "/7 86.565. 8" These results a$ree &ith those o!tained from a theoretical analysis ofthe circuit"

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frequency: 0.16 Hz

I(C1): mag: 5.36656 phase: 86.5651" #e$%ce&curren'

I(1): mag: 3.5!!!1 phase: 86.5651" #e$%ce&curren'

I(*1): mag: 3.5!!!1 phase: -3.434" #e$%ce&curren'

Ta!le 2 imulation Cesults for +i$ure 1

Linear Transformers

Linear transformers are Fust a special case of a pair of coupled inductors" eparate linear transformer components areavaila!le in the UE li!rary, !ut the underlyin$ model is euivalent to that of a coupled inductor pair"

Ideal Transformers

The ideal transformer sho&n in +i$ure is modeled in the UE li!rary as sho&n in +i$ure /"

+

B

vp

G

B

vs

G

ip

is@

' @

s

B

vp

G

B

vs

G

ip

is

5@s


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+i$ure A LTspice IV chematic (orrespondin$ to +i$ure 7

frequency: 0.16 Hz

*($+): mag: 14.663 phase: 116.565" $+,'age

I(C1): mag: 8.44! phase: -153.435" #e$%ce&curren'

I(): mag: 8.44! phase: -153.435" #e$%ce&curren'

I(1): mag: 35.!!!1 phase: 6.5651" #e$%ce&curren'

I(*1): mag: 35.!!!1 phase: -153.435" #e$%ce&curren'

Ta!le imulation Cesults for +i$ure A

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