Page 433 - Op Amps Design, Applications, and Troubleshooting

Logarithmic Amplifiers 409

Since resistors RI and R 2 are equal, we can replace the expression RI + R 2
with the expression 2JR. Making this substitution and simplifying gives us the fol-
lowing results.

Voltage gain is equal to the output voltage of an amplifier divided by its input
voltage, and the input voltage to our present circuit is v 2 - v^ therefore, we can
now obtain our final gain equation

This shows us that the gain of the instrumentation amplifier is determined by the
value of the external resistor R G. In the case of the circuit in Figure 11.2, the voltage
gain is computed as

This, of course, correlates to our earlier discovery that an input voltage of 0.1 volts
(2,1 V - 2 V) produces an output voltage of 2.1 volts.
Actual integrated instrument amplifiers may use either one or two external
resistors to establish the voltage gain of the amplifier. Some devices have internal,
precision resistors that can be jumpered into the circuit to obtain certain fixed
gains (e.g., 10,100, and 1000). Additionally, they will generally have other inputs
for such things as trimming offset voltage and modifying the frequency response
(frequency compensation).
The instrumentation amplifier is an important building block based on op
amps. An understanding of its general operation coupled with the data provided
by the manufacturer will allow you to use this device effectively.

11.3 LOGARITHMIC AMPLIFIERS

Although it is certainly possible to construct discrete amplifier circuits based on
op amps that produce outputs that are proportional to the logarithm or antiloga-
rithm of the input voltage, the design is very critical if stable performance is to be
expected. In many cases, it is more practical to utilize integrated log and antilog
amplifiers that perform these functions in a stable and predictable manner.