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11
FN2477.7
April 25, 2013
Setting:
Values for
α to give a desired M root or power are as follows:
Sine Function Generators
Similar functions can be formulated to approximate a SINE
function converter as shown in Figure
22. With a linearly
changing (0V to 5V) input the output will follow 0° to 90° of a
sine function (0V to 5V) output. This configuration is
theoretically capable of ±2.1% maximum error to full scale.
By adding a second HA-2556 to the circuit an improved fit
may be achieved with a theoretical maximum error of ±0.5%
as shown in Figure
23. Figure
23 has the added benefit that it
will work for positive and negative input signals. This makes a
convenient triangle (±5V input) to sine wave (±5V output)
converter.
References
[1] Pacifico Cofrancesco, “RF Mixers and Modulators made
with a Monolithic Four-Quadrant Multiplier” Microwave
Journal, December 1991 pg. 58 - 70.
[2] Richard Goller, “IC Generates Nonintegral Roots”
Electronic Design, December 3, 1992.
for; 0V
≤ VIN ≤ 5V
Max Theoretical Error = 2.1%FS
where:
for; -5V
≤ VIN ≤ 5V
Max Theoretical Error = 0.5%FS
FIGURE 20. NONINTEGRAL POWERS - ADJUSTABLE
FIGURE 21. NONINTEGRAL POWERS - FIXED
ROOTS - FIGURE 19
POWERS - FIGURE 20
M
α
M
α
0.5
0
1.0
1
0.6
≈0.25
1.2
≈0.75
0.7
≈0.50
1.4
≈0.50
0.8
≈0.70
1.6
≈0.30
0.9
≈0.85
1.8
≈0.15
1.0
1
2.0
0
NC
V-
VIN
V+
NC
HA-2556
HA-5127
NC
VOUT
0V
≤ VIN ≤ 1V
1.0
≤ M ≤ 2.0
α
1-
α
+
-
14
15
16
9
13
12
11
10
1
2
3
4
5
7
6
8
Σ
+ -
REF
Y
X
Z
+
-
+
-
+
-
NC
V-
VIN
V+
NC
HA-2556
NC
VOUT
0V
≤ VIN ≤ 1V
1.2
≤ M ≤ 2.0
R3
R4
R1
R2
14
15
16
9
13
12
11
10
1
2
3
4
5
7
6
8
Σ
+ -
REF
Y
X
Z
+
-
+
-
+
-
V
OUT
1
5
---
R
3
R
4
-------
1
+
V
IN
2
R
3
R
4
-------
1
+
R
2
R
1
R
2
+
---------------------
V
IN
+
=
(EQ. 21)
1
α
–
1
5
---
R
3
R
4
-------
1
+
=
α
R
3
R
4
-------
1
+
R
2
R
1
R
2
+
---------------------
=
(EQ. 22)
NC
V-
VIN
V+
NC
HA-2556
NC
VOUT
R3, 644
R4, 1k
R2
R1
R6
R5
262
470
1410
14
15
16
9
13
12
11
10
1
2
3
4
5
7
6
8
Σ
+ -
REF
Y
X
Z
+
-
+
-
+
-
FIGURE 22. SINE-FUNCTION GENERATOR
V
OUT
V
IN
1
0.1284V
IN
–
()
0.6082
0.05V
IN
–
()
---------------------------------------------------
=
5sin
π
2
---
V
IN
5
---------
≈
(EQ. 23)
0.6082
R
4
R
3
R
4
+
---------------------
=
5 0.1284
()
R
2
R
1
R
2
+
---------------------
=
50.05
()
R
6
R
5
R
6
+
---------------------
=
;
(EQ. 24)
V
OUT
5V
IN
0.05494V
IN
3
–
3.18167
0.0177919V
IN
2
+
-------------------------------------------------------------------
5sin
π
2
---
V
IN
5
---------
≈
=
(EQ. 25)
HA-2556