MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.334 Power Electronics
Problem Set 4
Issued: February 28, 2003
Due: March 7, 2003
Reading: KSV Chapter 7
Problem 4.1
KSV Problem 20.1
Problem 4.2
Partial data for a Philips TN23/14/7 ferrite ring core is illustrated in Fig. 1. The (Philips 3F3) material
permeability is 1800µ0, and the saturation flux density is approximately 0.32 T.
a. Please find the specific inductance, AL , of the core. AL is the number of nanohenries for a singleturn winding.
b. What is the inductance with a 7-turn winding?
c. Please find the dc current rating for a 7-turn winding. What is the smallest wire gauge that would
be acceptable for a 500 A/cm2 current density limit in the winding? Would such a 7-turn winding
fit in the core window?
d. What is the volt-second limit of such an inductor?
Problem 4.2
KSV Problem 20.10
Problem 4.3
Figure 2 shows a tapped-inductor boost converter. This approach is sometimes used to achieve larger
conversion ratios as compared to a conventional boost design. The inductor winding contains a total of
(N1+N2) turns. The switch is placed N1 turns from the left side of the inductor, as shown. The tapped
inductor can be viewed as a two-winding (N1:N2) transformer, in which the two windings are connected in
series. The inductance of the entire (N1+N2) turn winding is L.
a.
Sketch an equivalent circuit model for the tapped inductor that includes a magnetizing
inductance and an ideal transformer. Label the values of the magnetizing inductance and
turns ratio.
b.
Determine an analytical expression for the conversion ratio V2/V1 assuming that all
components are lossless, and that the converter operates in continuous conduction mode.
c.
Plot the conversion ratio as a function of duty ratio D for the case N1=N2, and compare to the
conventional non-tapped case (N2 = 0).
Problem 4.4
KSV Problem 20.7
Problem 4.5
Consider the magnetic circuit of Fig. 3(a). All legs are 1 cm wide, except for the right leg, which is 0.5
cm wide. You may neglect any nonuniformities in flux distribution at the corners.
a.
Find a magnetic circuit model for the device, and find the inductance of the winding.
A second winding is added, as shown in Fig. 3(b).
b.
Modify the circuit model of part a to include this second winding.
c.
Derive the matrix description for this magnetic circuit, and find the numerical values of L11,
L12, and L22. The matrix representation has the form:
 v1   L11
v  =  L
 2   12
L12  d  i1 
L22  dt i2 
Ferrite Ring Cores (Toroids)
Effective core parameters
Symbol
Parameter
Core
factor (C1)
(1 / A)
Value
1.81
Unit
mm-1
Ve
le
Ae
m
1722
55.8
30.9
~8.4
mm3
mm
mm2
g
∑
Effective volume
Effective length
Effective area
Mass of core
23.7 ± 0.7
13.1 ± 0.6
~0.3
7.5 ± 0.45
CBW307
Coating PA11
TN23/14/7 Ring Core
(Dimensions in mm)
Figure 1
Partial data for a toroidal ferrite core from Philips components.
N1
N2
+
V1
q(t)
C
R V2
-
Figure 2 A tapped-inductor boost converter.
Figure 3 A magnetic circuit. (a) single magnetic circuit. (b) coupled magnetic circuit.