Applications Information
Quadrant II
Theory of Operation
VSIN+ Ð VSIN-
VCOS+ Ð VCOS-
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.
[
]
For q = 90.176¡ to 134.824¡:
VSIN = 0.748 ´ VBB
VCOS = -Tan(q Ð 90¡) ´ 0.748 ´ VBB
For q = 135.176¡ to 179.824¡:
V
SIN = Tan(180¡ Ð q) ´ 0.748 ´ VBB
VCOS = -0.748 ´ VBB
The disc (and pointer) respond to the vector sum of the
voltages applied to the coils. Ideally, this relationship fol-
Quadrant III
q = 180¡ + Tan-1
VSIN+ Ð VSIN-
VCOS+ Ð VCOS-
sine
cosine
[
]
lows a
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.
For q = 180.176¡ to 224.824¡:
VSIN = -Tan(q Ð 180¡) ´ 0.748 ´ VBB
VCOS = -0.748 ´ VBB
For q = 225.176¡ Ð 269.824¡:
VSIN = -0.748 ´ VBB
Degrees of Rotation
0°
45°
90°
135°
180°
225°
270°
315°
360°
Max (128)
VCOS = -Tan(270¡ Ð q) ´ 0.748 ´ VBB
+
SIN
Output
Min (0)
Quadrant IV
Max (128)
Ð
SIN
VSIN+ Ð VSIN-
VCOS+ Ð VCOS-
q = 360¡ Ð Tan-1
Output
Min (0)
[
]
Max (128)
For q = 270.176¡ to 314.824¡:
VSIN = -0.748 ´ VBB
+
COS
Output
Min (0)
VCOS = Tan(q Ð 270¡) ´ 0.748 ´ VBB
Max (128)
Ð
COS
Output
For q = 315.176¡ Ð 359.824¡:
VSIN = -Tan(360¡ Ð q) ´ 0.748 ´ VBB
VCOS = 0.748 ´ VBB
Min (0)
000
001
010
011
100
101
110
111
000
MUX bits (D9 Ð D7)
Figure 1. Major gauge outputs.
VCOS+
360/0°
Quadrant I
0.748VBB
VSIN+ Ð VSIN-
VCOS+ Ð VCOS-
q = Tan-1
q
[
]
IV
I
270°
VSINÐ
90°
VSIN+
For q = 0.176¡ to 44.824¡:
VSIN = Tanq ´ 0.748 ´ VBB
VCOS = 0.748 ´ VBB
0.748VBB
0.748VBB
II
III
For q = 45.176¡ to 89.824¡:
VSIN = 0.748 ´ VBB
0.748VBB
VCOS = Tan(90¡ Ð q) ´ 0.748 ´ VBB
180°
VCOS-
Graph 1. Major gauge response.
4
CHERRY [ CHERRY SEMICONDUCTOR CORPORATION ]
