across a set of all measured immediate LCE values for a given range. The difference of the maximum and

minimum values is then halved and normalized with a division by the output voltage span of the measurement

(the difference of the maximum output voltage and minimum output voltage, typically at the two endpoints of the

data set), to express LCE as a percentage of the full-scale range:

LCE%= LCEmax−LCEmin

2× VLOGOUTmax−VLOGOUTmin ×100%

(6)

The LCE envelope can then be expressed in dB through the following relationship, where the factor of 20 is

associated with amplitude. For expression in terms of optical power, this factor is 10.

LCEdB=20log1−LCE%100%

(7)

7.1.1.2 Error Analysis Example

For an illustration of typical system error for a LOG200 implementation, consider the example use case defined

by the following conditions:

Table 7-1. Example Design Parameters

PARAMETER

SYMBOL

EXAMPLE VALUE

Maximum input current

Imax

200µA

Minimum input current

Imin

10nA

Output reference voltage

VREF

REF165 (1.65V)

Input reference current

II2

IREF (1µA)

Supply voltage

VS

10V (±5V)

Table 7-2lists the major error sources, and the typical values of each under the provided conditions. Typical

values are generally the sum of the mean value and one standard deviation. Calculations using these typical

values tend to be conservative, as the summation of uncorrelated errors tends to result in a larger compounded

total predicted error than the actual total error observed in a real system.

Table 7-2. Example Error Sources

PARAMETER

SYMBOL

TYPICAL VALUE

IREF reference current error

IREF_error

0.3%

REF165 reference error

REF165error

0.06%

Scaling factor error

Kerror

0.15%

Logarithmic conformity error

LCE

0.05%

Logarithmic amplifier output offset error

VOSO

1.3mV

These error terms are used to calculate actual values, as per the following equations:

IREF_actual=IREF× 1–IREF_error =1µA× 1–0.003 =0.997µA

(8)

VREF_actual=VREF165× 1+REF165error =1.65V× 1+0.0006 =1.65099V

(9)

Kactual=K× 1+Kerror =250mVdec× 1+0.0015 =250.375mVdec

(10)

LOG200

SBOSA28A – AUGUST 2023 – REVISED DECEMBER 2024

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