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INSTRUCTION MANUAL
AL-RE101
LOOP ANTENNA
SECTI ON 5
-
ANTENNA THEORY
1912 1 E l T o ro R d
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Si l vera do, Ca lifo rni a 9 26 76
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(9 49) 459 -96 00
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co m-p o wer. com
Rev101617
5.2.1
Derivation of Antenna Conversion Factor Equation
The formulae below demonstrates the derivation of
Equation (6)
for
determination of the loop antenna conversion factors (ACF).
Equation (6a)
was introduced earlier as
Equation (3).
It is borrowed from
basic magnetic loop theory, and establishes the relationship between the
physical parameters of the loop antenna, the magnetic flux density
present within the loop coil, and the open circuit voltage developed
across the loop terminals.
During actual measurements, the antenna terminals are terminated by
the input impedance of the measuring instrument
(R
L
)
.
The measured
voltage
(V
L
)
is proportional to the impedance of the loop coil
(R
C
) + (jX
C
)
and
(R
L
)
. This relationship is demonstrated in
Equation (6b)
, and then
rearranged in
Equation (6c)
and
Equation (6d)
.
EQUATION (6a)
A
ƒ
N
= number of turns in loop coil =
36 turns
= area of coil =
0.0139 meters
= frequency
(in Hz)
= magnetic flux density
(in Tesla)
2
=
π
r
,
where
r
= coil radius
=
0.0665 meters
2
where:
= open-circuit loop terminal voltage
(in Volts)
e
i(V)
B
(T)
e
=
2
π
NA
ƒ
B
(Volts)
i(V)
(T)
EQUATION (6b)
e
i(V)
+ R
C
+ jX
C
R
L
=
V
L(V)
R
L
where:
e
i(V)
R
C
j
X
C
R
L
= open-circuit loop terminal voltage
(in Volts)
= load resistance
[or input impedance of measurement instrument]
(in ohms)
= loop coil resistance
=
10Ω
= loop coil reactance
(2
π
ƒL)
(in ohms)
L
= inductance of the loop coil
=
0.00034 H
L
EQUATION (6c)
=
e
i(V)
V
L(V)
R
C
R
L
1
+
X
C
R
L
+
j
=
R
C
R
L
1
+
( )
2
X
C
R
L
+
( )
2
e
i(V)
V
L(V)
EQUATION (6d)
V
L(V)
= voltage across R
(in Volts)
L
