Equation 6 represents the sum of all the individual components of error normally associated with the log amp

when operating in the current input mode. The worst-case error for any given ratio of I1/I2 is the largest of the two

errors when I1 and I2 are considered separately. Temperature can also affect total error.

7.1.7.3 Errors RTO and RTI

As with any transfer function, errors generated by the function may be Referred-to-Output (RTO) or Referred-to-

Input (RTI). Log amps have a unique property that the error voltage at the output corresponds to a constant

percentage of the input, regardless of the actual input level.

7.1.7.4 Log Conformity

For the LOG114, log conformity is calculated in the same way as linearity and is plotted as I1/I2 on a semilog

scale. In many applications, log conformity is the most important specification. This condition is true because

bias current errors are negligible (5pA for the LOG114), and the scale factor and offset errors may be trimmed to

zero or removed by system calibration. These factors leave log conformity as the major source of error.

Log conformity is defined as the peak deviation from the best fit straight line of the VLOGOUT versus log(I1/I2)

curve. Log conformity is then expressed as a percent of ideal full−scale output. Thus, the nonlinearity error

expressed in volts over m decades is:

VLOGOUT nonlinear =0.375 Vdecade×2Nm

(7)

where

• N is the log conformity error, in percent

7.1.7.5 Individual Error Components

The ideal transfer function with current input is:

VLOGOUT IDEAL =0.375×log I1I2

(8)

The actual transfer function with the major components of error is:

VLOGOUT actual =0.375× 1±ΔK ×log I1I2 ±2Nm±VOSO

(9)

where:

• ΔK = gain error (0.4%, typical, as specified in the Electrical Characteristics table)

• IB1 = bias current of A1 (5pA, typical)

• IB2 = bias current of A2 (5pA, typical)

• m = number of decades over which the log conformity error is specified

• N = log conformity error (0.1%, typical for m = 5 decades; 0.9% typical for m = 7.5 decades)

• VOSO = output offset voltage (11mV, typical for ±5V supplies; 14mV, typical for +5V supplies)

To determine the typical error resulting from these error components, first compute the ideal output. Then

calculate the output again, this time including the individual error components. Then use Equation 10 to

determine the error in percent:

%error= VLOGOUT ideal −VLOGOUT typical

VLOGOUT ideal

×100%

(10)

For example, in a system configured for measurement of five decades, with I1 = 1mA, and I2 = 10μA:

VLOGOUT ideal =0.375×log 10−310−5 =0.75V

(11)

LOG114

SBOS301B – MAY 2004 – REVISED MARCH 2025

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