SLVAEX3 October   2020 TPS8802 , TPS8804

 

  1.   Trademarks
  2. 1Introduction
  3. 2SNR Optimization
    1. 2.1 SNR Overview
    2. 2.2 Smoke Concentration Measurement
    3. 2.3 Amplifier and LED Settings
      1. 2.3.1 Photo Amplifier Gain
      2. 2.3.2 Photo Amplifier and AMUX Speed
      3. 2.3.3 LED Current and Pulse Width
    4. 2.4 ADC Sampling and Digital Filtering
      1. 2.4.1 ADC Sampling
      2. 2.4.2 Digital Filtering
  4. 3System Modeling
    1. 3.1 Impulse Response
      1. 3.1.1 Photodiode Input Amplifier Model
      2. 3.1.2 Photodiode Gain Amplifier and AMUX Buffer Model
      3. 3.1.3 Combined Signal Chain
    2. 3.2 Noise Modeling
      1. 3.2.1 Noise Sources
      2. 3.2.2 Output Voltage Noise Model
      3. 3.2.3 ADC Quantization Noise
    3. 3.3 SNR Calculation
      1. 3.3.1 Single ADC Sample
      2. 3.3.2 Two ADC Samples
      3. 3.3.3 Multiple Base ADC Samples
      4. 3.3.4 Multiple Top ADC Samples
      5. 3.3.5 Multiple ADC Sample Simulation
  5. 4SNR Measurements
    1. 4.1 Measurement Procedure
    2. 4.2 Measurement Processing
    3. 4.3 Measurement Results
      1. 4.3.1 Varying Amplifier Speeds
      2. 4.3.2 Varying Digital Filter and ADC Timing
      3. 4.3.3 Varying LED Pulse Length
      4. 4.3.4 Varying ADC Sample Rate
      5. 4.3.5 Real and Ideal System Conditions
      6. 4.3.6 Number of Base Samples
      7. 4.3.7 ADC Resolution
  6. 5Summary
  7. 6References

3.2.2 Output Voltage Noise Model

The PDO voltage noise density is calculated using the op-amp and resistor noise models, shown in Equation 13. Independent noise sources are combined by taking the root-sum-of-squares. Equation 14 simplifies the output noise by dividing the Equation 13 noise voltage density by the signal voltage calculated in Equation 5. Equation 14 is used to identify the dominant source of noise in the amplifier.

Equation 13. S P D O ( N O I S E ) = 2 × I N A M P 2 + 2 × I N R P H 2 × R P H 1 + s × R P H × C P H 2 + V N A M P 2 × 1 + s × R P H × C P H + 2 × C P D 1 + s × R P H × C P H 2 1 + 1 + s × R P H × C P H + 2 × C P D 1 + s × R P H × C P H × A s
Equation 14. S P D O N O I S E V P D O S I G = 1 I P D × I N A M P 2 2 + I N R P H 2 2 + V N A M P 1 + s × R P H × C P H + 2 × C P D 2 × R P H 2

The resistor noise and amplifier voltage noise is less than the amplifier current noise when RPH is greater than approximately 200 kΩ, based on measurements of the voltage and current noise density. In most applications, RPH is greater than 200 kΩ and the resistor noise and voltage noise are negligible.

The buffered photo RMS voltage noise is calculated in Equation 15 using the amplifier current noise as the only noise source. The amplifier current noise is assumed to be white. The buffered photo signal model in Equation 7 is used to calculate the buffered photo noise density in Equation 15. Integrating the noise density across the frequency spectrum calculates the RMS noise. The result demonstrates that the output noise increases with the amplifier gain and decreases with the root-sum of time constants.

Equation 15. V B U F N O I S E = ∫ 0 ∞ 2 × I N A M P × R P H × G P G A I N 1 + j × 2 × π × f × τ 1 × 1 + j × 2 × π × f × τ 2 2 × d f     = I N A M P × R P H × G P G A I N 2 × ( τ 1 + τ 2 )