7
FN2477.7
April 25, 2013
The last basic configuration is the Square Root as shown in
Figure
5. Here feedback is provided to both X and Y inputs.
The Balance equation takes the form of Equation
11:Which equates to Equation
12:The four basic configurations (Multiply, Divide, Square and
Square Root) as well as variations of these basic circuits
have many uses.
Frequency Doubler
For example, if ACos(
ωτ) is substituted for signal A in the
Square function, then it becomes a Frequency Doubler and
the equation takes the form of Equation
13:And using some trigonometric identities gives the result in
Square Root
The Square Root function can serve as a precision/wide
bandwidth compander for audio or video applications. A
compander improves the Signal-to-Noise Ratio for your
system by amplifying low level signals while attenuating or
compressing large signals (refer to Figure 17; X0.5 curve). This provides for better low level signal immunity to noise
during transmission. On the receiving end, the original signal
may be reconstructed with the standard Square function.
Communications
The Multiplier configuration has applications in AM Signal
Generation, Synchronous AM Detection and Phase
Detection to mention a few. These circuit configurations are
shown in Figures
6, 7 and
8. The HA-2556 is particularly
useful in applications that require high speed signals on all
inputs.
HA-2556
1/5V
X
Y
VOUT
Z
VX+
VX-
VY+
VY-
VZ+
VZ-
W
A
∑
+
-
+
-
A
+
-
+
-
FIGURE 5. SQUARE ROOT (FOR A > 0)
W
()
W
–
()
×
5A
–
()
=
(EQ. 11)
W5A
=
(EQ. 12)
ACos
ωτ
()
ACos
ωτ
()
×
5W
()
=
(EQ. 13)
W
A2
10
------- 1Cos 2
ωτ
()
+
()
=
(EQ. 14)
HA-2556
1/5V
X
Y
VOUT
Z
VX+
VX-
VY+
VY-
VZ+
VZ-
∑
W
ACos(
ωΑτ)
CCos(
ω
Cτ)
CARRIER
AUDIO
W
AC
10
-------- Cos
ω
C
ω
A
–
()τ Cos ω
C
ω
A
+
()τ
+
()
=
+
-
+
-
A
+
-
+
-
FIGURE 6. AM SIGNAL GENERATION
HA-2556
1/5V
X
Y
VOUT
Z
VX+
VX-
VY+
VY-
VZ+
VZ-
∑
W
AM SIGNAL
CARRIER
LIKE THE FREQUENCY DOUBLER YOU GET AUDIO CENTERED AT DC
+
-
+
-
A
+
-
+
-
FIGURE 7. SYNCHRONOUS AM DETECTION
AND 2FC.
HA-2556
1/5V
X
Y
VOUT
Z
VX+
VX-
VY+
VY-
VZ+
VZ-
∑
W
ACos(
ωτ)
ACos(
ωτ+φ)
W
A2
10
------- Cos
φ
() Cos 2ωτ φ
+
()
+
()
=
DC COMPONENT IS PROPORTIONAL TO COS(f)
+
-
+
-
A
+
-
+
-
FIGURE 8. PHASE DETECTION
HA-2556