PhD Thesis - Cranfield University

Chapter 7
the inductor current (20kHz) suggest the use of conductors with a higher surface area rather
than cross sectional area in order to cope with skin-effects.
Considering the above constraints, the developed inductor was designed and fabricated using
an air-core bobbin with flat enamelled cooper conductors. Wheeler’s method [116] for multi-
layered inductors provides dimensioning guides for the physical coil construction. The
following design equations require arbitration of design parameters to achieve the required
electrical and physical objectives.
The coil inductance using Wheeler’s [116] method is given as,
2
0.
8(
ue
)( rN)
L = (7-64)
6r
+ 9l
+ 10b
To obtain number of turns,
1 ⎡ L(
6r
+ 9l
+ 10b
⎤
N = ⎢
⎥
(7-65)
r ⎣ ( 0.
8)(
ue
) ⎦
where,
L is the inductance in microhenries
u e is the effective permeability of the core in henry per metre
N is the number of turns
r is the mean radius in inches
d is the core diameter in inches
l is the core length in inches
b is the coil build in inches
Considering skin effect in the conductor at high frequency switching,
m
∆ c =
(7-66)
where
K
f
sw
∆ c is the penetration depth
K m is the material constant (For copper, K m ranges from 65 at 20 o C to 75 at 100 o C)
f sw is the switching frequency
196