SBOSA28 august   2023 LOG200

ADVANCE INFORMATION  

  1.   1
  2. 1 Features
  3. 2 Applications
  4. 3 Description
  5. 4 Revision History
  6. 5 Pin Configuration and Functions
  7. 6 Specifications
    1. 6.1 Absolute Maximum Ratings
    2. 6.2 ESD Ratings
    3. 6.3 Recommended Operating Conditions
    4. 6.4 Thermal Information
    5. 6.5 Electrical Characteristics
    6. 6.6 Typical Characteristics
  8. 7 Detailed Description
    1. 7.1 Overview
    2. 7.2 Functional Block Diagram
    3. 7.3 Feature Description
      1. 7.3.1 High Speed, Logarithmic Current-to-Voltage Conversion
      2. 7.3.2 Voltage and Current References
      3. 7.3.3 Adaptive Photodiode Bias
      4. 7.3.4 Auxiliary Operational Amplifier
    4. 7.4 Device Functional Modes
  9. 8 Application and Implementation
    1. 8.1 Application Information
      1. 8.1.1 Logarithmic Transfer Function
        1. 8.1.1.1 Logarithmic Conformity Error
    2. 8.2 Typical Application
      1. 8.2.1 Optical Current Sensing
        1. 8.2.1.1 Design Requirements
        2. 8.2.1.2 Detailed Design Procedure
        3. 8.2.1.3 Application Curves
    3. 8.3 Power Supply Recommendations
    4. 8.4 Layout
      1. 8.4.1 Layout Guidelines
      2. 8.4.2 Layout Example
  10. 9 Device and Documentation Support
    1. 9.1 Device Support
      1. 9.1.1 Third-Party Products Disclaimer
    2. 9.2 Documentation Support
      1. 9.2.1 Related Documentation
    3. 9.3 Receiving Notification of Documentation Updates
    4. 9.4 Support Resources
    5. 9.5 Trademarks
    6. 9.6 Electrostatic Discharge Caution
    7. 9.7 Glossary
  11. 10Mechanical, Packaging, and Orderable Information

Package Options

Mechanical Data (Package|Pins)
Thermal pad, mechanical data (Package|Pins)
Orderable Information

8.1.1 Logarithmic Transfer Function

The LOG200 uses a differential amplifier to compare the voltage outputs of two logarithmic amplifiers. Logarithmic amplifiers rely on the feedback transistor relation of the base-emitter voltage (VBE) to the collector current IC, according to the principle:

Equation 1. VBE=kTqln⁡ICIS

where

  • k = the Boltzmann constant, 1.381 × 10-23 J/K
  • T = absolute temperature in kelvins (K)
  • q = the elementary charge, 1.602 × 10-19 C
  • IS = the transistor reverse saturation current

For the basic logarithmic amplifier implementation shown in Figure 8-1, the following expression holds:

Equation 2. VOUT=-VBE=-kTqln⁡IINIS
GUID-20230714-SS0I-GHWC-QDDS-TDPR8HLJHD15-low.svg Figure 8-1 Basic Logarithmic Amplifier

When a difference amplifier with reference voltage VREF is implemented to compare the outputs of two logarithmic amplifiers with input currents I1 and I2,

Equation 3. V O U T2 - V O U T1 = k T q ln ⁡ I 1 I S1 - k T q ln ⁡ I 2 I S2

As IS1 is approximately equivalent to IS2 by design, this equation is equivalent to:

Equation 4. V O U T2 - V O U T1 = k T q ln ⁡ I 1 I 2 = k T 0.434q log 10 ⁡ I 1 I 2
GUID-20230714-SS0I-JBMT-VPSM-PWC5NRVZF1TP-low.svg Figure 8-2 LOG200 Difference Amplifier

In the LOG200, the internal input resistors of the difference amplifier have a positive temperature coefficient to compensate for the temperature dependence of the above expression. The difference amplifier also gains up the nominal output, such that the output of the LOG200 is:

Equation 5. V L O G O U T = K × log 10 ⁡ I 1 I 2 + V R E F

where K is the device scaling factor, nominally 250 mV/decade (252 mV/decade for preview material). Thus, for each 1-decade or order of magnitude shift in the difference of I1 and I2, the device output is correspondingly shifted by 250 mV (such as by 250 mV for I1 = 10 µA and I2 = 1 µA, or by –500 mV for I1 = 10 nA and I2 = 1 µA).