Environmental Engineering Reference
In-Depth Information
w
I
p
N
s
q
I
s
U
s
g
Figure 12.6 CWT with dimensions for analysis
By definition, the primary turns
N
p
¼
1 and primary current
I
p
¼
I
0
sin(w
e
t
).
From the data listed the toroid core area,
A
c
¼
W
l
L
¼
5
10
3
m
2
.
Assuming infinite conductor conductivity on the CWT inner diameter and infinite
core permeability, the core flux is
m
0
N
p
A
c
2
g
f
¼
I
p
m
p
N
p
A
c
2
g
l
p
¼
N
p
f
¼
I
p
¼
L
p
I
p
m
p
N
s
N
p
A
c
2
g
l
s
¼
N
s
f
¼
I
p
¼
MI
p
dt
MI
p
¼
w
e
MI
0
cos
ð
w
e
t
Þ
d
U
s
¼
l
s
¼
Where l
p
and l
s
define the primary and secondary flux linkages respectively
for the case of a CWT with toroidal core with negligible flux leakage. Therefore,
substituting values listed above into (Ex12.3.1.4) yields the following value for
secondary voltage,
U
s
, when the primary frequency is 15 kHz:
2pm
0
f
p
N
p
N
s
A
c
2
g
U
s
ð
f
¼
15 kHz
Þ¼
I
0
¼
211
:
4V
pk
¼
149
:
5V
rms
When the primary frequency is 50 kHz, by examination of (Ex12.3.1.5), the
secondary voltage becomes
U
s
(
f
¼
50 kHz)
¼
498.3 V
rms
.
Before concluding this section, it is very instructive to note that better
matching can be obtained by placing a resonating capacitor,
C
r
, across the CWT
secondary. It is also now established that improved efficiency of a gapped core
inductor can be obtained by different geometry of secondary winding, and more-
over, a multi-turn secondary can further boost the CWT output voltage so that
