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the X2 function by a series of straight-line segments.
An output voltage pro-
portional to the square root of an input voltage is obtained by placing the X2
DFG in the feedback loop of an amplifier.
b.
Generating the Square of an Input Voltage (Single Polarity)
A simplified diagram of the X2 DFG is shown in Figure l3a.
The DFG terminated on
the upper portion of the patching block accepts only negative inputs; the lower
DFG accepts only positive inputs.
If the input voltage has the wrong polarity,
the DFG output is zero.
Resistor R
f
(R52) is not associated with either DFG; it
can be used wherever required.
A typical use of the unit is illustrated in Figure l3b.
The unit is patched to
yield two independent squaring circuits.
In each case, the DFG is used as the in-
put element of an amplifier that has a 3550 ohm feedback resistor.
The voltage X
must be negative; the voltage Y must be positive.
Since the DFG's have a variable
input impedance, the voltages applied to the -IN and +IN terminations should not be
obtained from potentiometers.
The output amplifiers can be used to sum additional
inputs.
2
A programming symbol for the X
DFG is sho"m in Figure l3c.
c.
Generating the Square of an Input Voltage (Bi-Polar)
The X
2
X2
DFG's are connected as shown in Figure 14 to generate + 10 from an input
voltage X where -10
~
X
~
+10.
When X is negative, the upper DFG conducts and pro-
duces an output of +X2/l0 from amplifier 1; the lower DFG does not conduct.
When
X is a positive voltage, the lower DFG conducts and generates _X2/l0 at the output
of amplifier, 2.
This output is applied through resistor R f to the base of ampli-
fier 1.
This signal is inverted and appears at the output of amplifier 1 as +X 2 /lO.
Thus for an input of either polarity, the output of amplifier 1 is +X2/l0.
Circuits using the X2 DFG are summarized in the appendix.
8.
LOG X DFG AND 1/2 LOG X DFG
a.
General Description
The Log X DFG's are used in conjunction with a dc amplifier to produce an output
voltage that is proportional to the logarithm of the input signal voltage.
Common
base or natural logarithms and antilogarithms can be generated.
The output of the
DFG's is in the form of straight-line segments that closely approximate a loga-
rithmic curve for a single polarity input voltage.
The desired function is pro-
duced by summing the outputs of simple limiter circuits that use solid-state diodes
as voltage sensitive switches . .
The Dual Log X DFG, Model 16.126, consists of two independent logarithmic function
generators.
One generator accepts a positive input voltage, X, and produces a
negative output voltage Y
=
-5 loglOlOX.
The other generator accepts a negative
input voltage, -X, and produces a positive output voltage Y
=
+5 10glO IlOXI.
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