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

3.3.2 Two ADC Samples

Using one ADC sample for the base voltage and one ADC sample for the top voltage results in the SNR calculated in Equation 17. The top signal is calculated using the Equation 9 buffered photo signal pulse sampled at time t. The signal noise is calculated using the Equation 15 buffered AMUX output noise voltage divided by the square root of two. Sampling the signal at the peak maximizes the SNR. The peak of the signal is approximately tLED, and by sampling the signal at time tLED, Equation 17 simplifies to Equation 18. Equation 18 provides the key insight that increasing tLED, τ1 and τ2 together by a constant factor improves the SNR by the square root of the factor.

Equation 17. S N R 2 = 2 × I P D × τ 1 + τ 2 I N × V B U F P U L S E ( t ) - V D C
Equation 18. S N R 2 ≅ 2 × I P D × τ 1 + τ 2 I N × 1 + τ 1 τ 2 - τ 1 × e   - t L E D τ 1 + τ 2 τ 1 - τ 2 × e - t L E D τ 2

Improving the SNR by increasing tLED, τ1 and τ2 comes at the cost of increased power consumption. Because low power consumption is essential for smoke alarms, it is desirable to optimize the SNR without increasing power consumption. The LED pulse energy consumption is calculated in Equation 19. Dividing Equation 18 by Equation 19 results in Equation 20, the SNR per unit energy (SNRE). The photodiode current is proportional to the LED current, therefore the SNRE is relatively unaffected by changes in LED current.

Equation 19. E L E D = t L E D × V L E D × I L E D
Equation 20. S N R E 2 ≅ 2 × I P D × τ 1 + τ 2 I N × t L E D × V L E D × I L E D × 1 + τ 1 τ 2 - τ 1 × e - t L E D τ 1 + τ 2 τ 1 - τ 2 × e - t L E D τ 2

Equation 20 is maximized in two steps. First, tLED is held constant and the optimal τ1 and τ2 are numerically calculated using a nonlinear programming solver fminsearch in MATLAB. Setting τ1 and τ2 to 0.31 times the LED pulse length maximizes the SNR. Next, tLED is varied with τ1 and τ2 set to 0.31 times tLED. The SNRE increases as tLED, τ1 and τ2 decrease, therefore the SNRE is maximized when tLED is minimized. This result explains why shorter pulse lengths with higher LED currents can have a higher SNR than longer pulse lengths with lower LED currents. If τ1 and τ2 are equal and fixed while tLED is varied, the optimal solution for tLED is 1.8 τ1.

Common methods set τ1 and τ2 below 0.2 tLED to allow the signal to settle before taking the measurement or set τ1 above tLED to integrate the photodiode signal. Both of these methods do not have as high of an SNR compared to when τ1 and τ2 are set to 0.31 tLED. Setting τ1 and τ2 to 0.2 tLED compared to 0.31 tLED has 14% higher amplitude and 25% higher noise. Setting τ1 and τ2 to tLED compared to 0.31 tLED has 58% lower amplitude and 44% lower noise.