
FASTRAK MANUAL
Rev. G
D-3
JUNE 2012
Figure D-2 Black Box System
There are three sensing coils and three magnetic moments with the resultant matrix =
M
expressed by
M
= [
m
1
m
2
m
3
]. Position and orientation are described by the voltages induced
in the three receiver loops according to their sensitivity and orientation and given by the matrix
quantity
S
= [
s
1
s
2
s
3
]. Coupling between the Magnetic Linkage and Position and Orientation
sensitivity produces nine voltages giving rise to the input voltage matrix expressed as:
M
K
S
r
1
=
V
t
3
Equation D-1
Coupled through the Magnetic Linkage is a noise quantity N
i
, which is composed of incidental
link noise plus atmospheric noise. Additionally, system noise, generated as a function of the
black box electronics is given by N
b
. System noise (N
b
) is the sum of quantization, shot and
thermal noise and is referred to the input of the black box. These noise quantities are
algebraically added to the voltage equation for the input to the black box and expressed as:
N
+
N
+
M
K
S
r
1
=
V
b
i
t
3
Equation D-2
SIGNAL-TO-NOISE (S/N) RATIO
At the output of the black box, the signal (S) portion of the S/N ratio is the value of any
given position and orientation of the receiver. It could be considered as the input equation stated
above, minus the noise components, times the transfer function of the “black box.” The noise
portion (N) is the noise components of the input equation times the “black box” transfer function
and is observed as the deviation in the output parameters about the given position and