CS4172
Applications Information
Theory of Operation
Quadrant II
q
= 180¡ Ð Tan
-1
The SACD is for interfacing between a microcontroller or
microprocessor and air-core meter movements commonly
used in automotive vehicles for speedometers and
tachometers. These movements are built using 2 coils
placed at a 90¡ orientation to each other. A magnetized
disc floats in the middle of the coils and responds to the
magnetic field generated by each coil. The disc has a shaft
attached to it that protrudes out of the assembly. A point-
er indicator is attached to this shaft and in conjunction
with a separate printed scale displays the vehicleÕs speed
or the engineÕs speed.
The disc (and pointer) respond to the vector sum of the
voltages applied to the coils. Ideally, this relationship fol-
sine
lows a cosine equation. Since this is a transcendental and
non-linear function, devices of this type use an approxi-
mation for this relationship. The SACD uses a tangential
algorithm as shown in Figure 1. Only 1 output varies in
any 45 degree range.
[
V
SIN+
Ð V
SIN-
V
COS+
Ð V
COS-
]
For
q
= 90.176¡ to 134.824¡:
V
SIN
= 0.748
´
V
BB
V
COS
= -Tan(q Ð 90¡)
´
0.748
´
V
BB
For
q
= 135.176¡ to 179.824¡:
V
SIN
= Tan(180¡ Ð
q) ´
0.748
´
V
BB
V
COS
= -0.748
´
V
BB
Quadrant III
q
= 180¡ + Tan
-1
[
V
SIN+
Ð V
SIN-
V
COS+
Ð V
COS-
]
For
q
= 180.176¡ to 224.824¡:
V
SIN
= -Tan(q Ð 180¡)
´
0.748
´
V
BB
V
COS
= -0.748
´
V
BB
For
q
= 225.176¡ Ð 269.824¡:
V
SIN
= -0.748
´
V
BB
V
COS
= -Tan(270¡ Ð
q) ´
0.748
´
V
BB
Quadrant IV
q
= 360¡ Ð Tan
-1
Degrees of Rotation
0°
Max (128)
45°
90°
135°
180°
225°
270°
315°
360°
SIN
+
Output
Min (0)
Max (128)
SIN
Ð
Output
Min (0)
[
V
SIN+
Ð V
SIN-
V
COS+
Ð V
COS-
]
Max (128)
COS
+
Output
Min (0)
For
q
= 270.176¡ to 314.824¡:
V
SIN
= -0.748
´
V
BB
V
COS
= Tan(q Ð 270¡)
´
0.748
´
V
BB
For
q
= 315.176¡ Ð 359.824¡:
V
SIN
= -Tan(360¡ Ð
q) ´
0.748
´
V
BB
V
COS
= 0.748
´
V
BB
V
COS+
360/0°
0.748V
BB
Max (128)
COS
Ð
Output
Min (0)
000
001
010
011
100
101
110
111
000
MUX bits (D9 Ð D7)
Figure 1. Major gauge outputs.
Quadrant I
q
= Tan
-1
[
V
SIN+
Ð V
SIN-
V
COS+
Ð V
COS-
]
270°
V
SINÐ
q
IV
I
0.748V
BB
III
0.748V
BB
II
90°
V
SIN+
For
q
= 0.176¡ to 44.824¡:
V
SIN
= Tanq
´
0.748
´
V
BB
V
COS
= 0.748
´
V
BB
For
q
= 45.176¡ to 89.824¡:
V
SIN
= 0.748
´
V
BB
V
COS
= Tan(90¡ Ð
q) ´
0.748
´
V
BB
0.748V
BB
180°
V
COS-
Graph 1. Major gauge response.
4
CHERRY [ CHERRY SEMICONDUCTOR CORPORATION ]
