AD648

REV. E

–11–

LOG RATIO AMPLIFIER

Log ratio amplifiers are useful for a variety of signal conditioning

applications, such as linearizing exponential transducer outputs

and compressing analog signals having a wide dynamic range.

The AD648’s picoamp level input current and low input offset

voltage make it a good choice for the front end amplifier of the

log ratio circuit shown in Figure 30. This circuit produces an

output voltage equal to the log base 10 of the ratio of the input

currents I1 and I2. Resistive inputs R1 and R2 are provided

for voltage inputs.

Input currents I1 and I2 set the collector currents of Q1 and Q2,

a matched pair of logging transistors. Voltages at points A and B

are developed according to the following familiar diode equation:

VBE = (kT/q) ln (IC/IES)

In this equation, k is Boltzmann’s constant, T is absolute

temperature, q is an electron charge, and IES is the reverse

saturation current of the logging transistors. The difference of

these two voltages is taken by the subtractor section and scaled

by a factor of approximately 16 by resistors R9, R10, and R8.

Temperature compensation is provided by resistors R8 and

R15,

which have a positive 3500 ppm/

°C temperature coefficient.

The transfer function for the output voltage is:

VOUT = 1 V log10 (I2/I1)

Frequency compensation is provided by R11, R12, C1, and C2.

Small signal bandwidth is approximately 300 kHz at input cur-

rents above 100

µA and will proportionally decrease with lower

signal levels. D1, D2, R13, and R14 compensate for the effects

of the two logging transistors’ ohmic emitter resistance.

To trim this circuit, set the two input currents to 10

µA and

adjust VOUT to zero by adjusting the potentiometer on A3. Then

set I2 to 1

µA and adjust the scale factor such that the output

voltage is 1 V by trimming potentiometer R10. Offset adjust-

ment for A1 and A2 is provided to increase the accuracy of the

voltage inputs.

This circuit ensures a 1% log conformance error over an input

current range of 300 pA to l mA, with low level accuracy limited

by the AD648’s input current. The low level input voltage accu-

racy of this circuit is limited by the input offset voltage and drift

of the AD648.

Figure 30. Precision Log Ratio Amplifier