HA2556 Datasheet, PDF (13/20 Pages) Intersil Corporation – Wideband Four Quadrant Analog Multiplier (Voltage Output)

HA2556
DESIGN INFORMATION (Continued)
The information contained in this section has been developed through characterization by Intersil Semiconductor and is for use as
application and design information only. No guarantee is implied.
Let’s first examine the Balance Concept as it applies to the Signals may be applied to more than one input at a time as
standard multiplier configuration (Figure 2).
in the Squaring configuration in Figure 4:
Signals A and B are input to the multiplier and the signal W Here the Balance equation will appear as:
is the result. By substituting the signal values into the Bal-
ance equation you get:
(A) × (A) = 5 (W)
(A) × (B) = 5 (W)
And solving for W:
W = ^A-----^×₅-----^B-
A
V_X +
+
-
V_X -
HA-2556
X
V_OUT
A
W
+
1/5V
∑
A
V_X +
+
-
V_X -
HA-2556
X
V_OUT
A
W
V_Y +
+
Y
-
V_Y -
-
Z
V_Z +
+
-
V_Z -
1/5V
+
∑
FIGURE 4. SQUARE
B
V_Y +
+
Y
-
Z
V_Z +
+
-
-
V_Y -
V_Z -
Which simplifies to:
W = -^A-₅--²-
FIGURE 2. MULTIPLIER
Notice that the output (W) enters the equation in the feed-
back to the Z stage. The Balance Equation does not test for
stability, so remember that you must provide negative feed-
back. In the multiplier configuration, the feedback path is
connected to V_Z+ input, not V_Z-. This is due to the inversion
that takes place at the summing node just prior to the output
amplifier. Feedback is not restricted to the Z stage, other
feedback paths are possible as in the Divider Configuration
shown in Figure 3.
V_X+
HA-2556
V_OUT
+
V_X-
-
X
A
W
+
1/5V
∑
B
V_Y+
+
Y
-
Z
V_Z +
+
-
-
A
V_Y-
V_Z -
The last basic configuration is the Square Root as shown in
Figure 5. Here feedback is provided to both X and Y inputs.
V_X +
HA-2556
V_OUT
+
V_X -
-
X
A
W
1/5V
+
∑
V_Y +
+
Y
-
-
Z
V_Z +
+
-
A
V_Y -
V_Z -
FIGURE 5. SQUARE ROOT (FOR A > 0)
The Balance equation takes the form:
(W) × (–W) = 5 (–A)
Which equates to:
W = 5A
FIGURE 3. DIVIDER
Inserting the signal values A, B and W into the Balance
Equation for the divider configuration yields:
(–W) × (B) = 5V × (–A)
Solving for W yields:
W = -⁵-_B-^A--
Notice that, in the divider configuration, signal B must remain
≥0 (positive) for the feedback to be negative. If signal B is
negative, then it will be multiplied by the V_X- input to produce
positive feedback and the output will swing into the rail.
Application Circuits
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:
(ACos (ωτ) ) × (ACos (ωτ) ) = 5 (W)
And using some trigonometric identities gives the result:
W = -^A1--₀-²- ( 1 + Cos ( 2ωτ) )
Spec Number 511063-883
8-19