The equationfor determiningthe maximum flux densityof a given toroidal core is as follows:
E o 1 = a P P l i e dR M S v o l t s
E x 108
4.44xA"xNxF
B m a x=
Ae = cross-sect.area (cm2)
N = n u m b e ro f w i r e t u r n s
F
= frequency(Hertz)
The safety factor may be increasedby using the peak AC voltage in the equation. This is a standard
practiceamong many RF engineerswho design broadbandRF power transformers.
The above equation may be changedas shown below to make it more convenientduring calculationsof
Bmaxdt radio frequencies.
E o 1=. a P P l i e dR M S v o l t s
Ex102
4.44xAuxNxF
B m a x=
Ae = cross-sect.area (cm2)
N = n u m b e ro f w i r e t u r n s
F
= frequency (MHz)
The sample calculationbelow is basedon a frequencyof 7 MHz, a peak voltage of 25 volts and a primary
w i n d i n g o f 1 5 t u r n s .T h e c r o s s - s e c t i o n a lr e a o f t h e s a m p l ec o r e i s 0 . 1 3 3c m 2 .F r o m p r e v i o u sg u i d e l i n e s
w e k n o w t h a t t h e m a x i m u m f l u x d e n s i t ya t 7 M H z s h o u l db e n o t m o r e t h a n 5 7 g a u s s .
B m a x=
2 5x 1 0 0
4 . 4 4x 0 . 1 3 3x 1 5 x 7
= 40.3gauss
T h i s h y p o t h e t i c atl o r o i d c o r e w i l l h a v e a f l u x d e n s i t yo f 4 0 g a u s s a c c o r d i n gt o t h e a b o v e f o r m u l a a n d
w h e n o p e r a t e du n d e rt h e a b o v ec o n d i t i o n sT. h i s i s w e l l w i t h i n t h e g u i d e l i n e sa s s u g g e s t e da b o v e .
Temperaturerise can be the result of using an undersizedwire gauge for the amount of current involved
a s w e l l a s m a g n e t i ca c t i o n w i t h i n t h e c o r e . B o t h w i l l c o n t r i b u t et o t h e o v e r a l lt e m p e r a t u r er i s e o f t h e
transformer. This can be calculatedwith the following equation:
Rise('C) =
Temperature
Total Power Dissipation(Milliwatts) 1.833
I
AvailableSurfaceArea (cm2)
J
[
+ temperaturerise)is m o r e t h a n 1 0 0 " Cw h e n u s e d
lf the operatingtemperature(ambienttemperature
a largersizecore a n d / o r a h e a v i e rg a u g e w i r e
intermittently,
or more than 75'C if usedcontinuously,
shouldbe selected.
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