VCA810_16 Datasheet, PDF (24/40 Pages) Texas Instruments – VCA810 High Gain Adjust Range, Wideband and Variable Gain Amplifier

VCA810
SBOS275G – JUNE 2003 – REVISED DECEMBER 2015
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Application Information (continued)
9.1.5 Low-Drift Wideband Log Amplifier
The VCA810 can be used to provide a 2.5-MHz (–3 dB) log amp with low offset voltage and low gain drift. The
exponential gain-control characteristic of the VCA810 permits simple generation of a temperature-compensated
logarithmic response. Enclosing the exponential function in an op-amp feedback path inverts this function,
producing the log response. Figure 39 shows the practical implementation of this technique. A DC reference
voltage, V_R, sets the VCA810 inverting input voltage. This configuration makes the amplifier output voltage
V_OA
=
−GV_R,
where
G
=
10^{-2 (VC}
+
1)
.
V_R
-10mV
V_OA = -GV_R
VCA810
V_C
R₁
470W
( ) ^VOL ^{= -}
1 + ^R1
R₂
1 + 0.5 Log(-V_IN/V_R)
R₂
330W
R₃
V_OL
OPA820
100W
V_IN
C_C
50pF
Figure 39. Temperature-Compensated Log Response
A second input voltage also influences V_OA through control of gain G. The feedback operational amplifier forces
V_OA to equal the input voltage V_IN connected at the operational amplifier inverting input. Any difference between
these two signals drops across R₃, producing a feedback current that charges C_C. The resulting change in V_OL
adjusts the gain of the VCA810 to change V_OA.
At equilibrium:
V_OA = V_IN = -V_R · 10^{-2(VC + 1)}
(6)
V
=
R
1
·
V
OL
C
The operational amplifier forces this equality by supplying the gain control voltage,
R
1
+
R
2
.
Combining the last two expressions and solving for V_OL yields the circuit’s logarithmic response:
( ( ^VOL ^{= -}
1
+
R₂
R₁
·
1 + 0.5·log
- ^VIN
V_R
(7)
An examination of this result illustrates several circuit characteristics. First, the argument of the log term, −V_IN/V_R,
reveals an option and a constraint. In Figure 39, V_R represents a DC reference voltage. Optionally, making this
voltage a second signal produces log-ratio operation. Either way, the log term’s argument constrains the
polarities of V_R and V_IN. These two voltages must be of opposite polarities to ensure a positive argument. This
polarity combination results when V_R connects to the inverting input of the VCA810. Alternately, switching V_R to
the amplifier noninverting input removes the minus sign of the log term argument. Then, both voltages must be of
the same polarity in order to produce a positive argument. In either case, the positive polarity requirement of the
argument restricts V_IN to a unipolar range. Figure 40 illustrates these constraints.
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