Signal Processing for Infrared Gas Sensors

This article discusses signal processing necessary for linearization, calibration, and temperature compensation of the whole range of infrared gas sensors from e2v Technologies as well as computations required for determining the concentration of target gas.

A software or external circuit will be required to perform signal processing and to store calibration information.

Sensor Outputs

The output signals for the gas sensors include the following:

• Reference detectors — Sinusoidal output is at the same frequency as the lamp pulses. This detector is employed for variations in optical degradation, source intensity, and temperature to a certain extent. The amplitude of this detector will not reveal any variations due to the target gas effects.
• Active detectors — Sinusoidal output is at the same frequency as the lamp pulses. When a target gas is present, there is a decrease in signal amplitude.
• Temperature Sensor — It gives a linearized DC output in relation to the temperature of the device.
• Thermistor — It gives an output in relation to the temperature of the device, which requires further linearization

Target Gas Concentration Calculation Overview

Continuous monitoring of the outputs of the reference and active detectors is crucial in obtaining their peak-to-peak outputs. The target gas concentration is calculated from the ratio of these normally averaged outputs carried out at regular periods. Following installation, the sensors will require the Zero and Span values (calibration) to be calculated, which should be stored in the non-volatile memory for future use. For linearization, “a” and “n” coefficients are used and it is based on the Beer-Lambert Law.

The steps to determine the target gas concentration is shown in the following data. Compensation is required for eliminating the effects of temperature. This is performed on the normalized ratio obtained from the measurements of sensor output, also known as the alpha compensation, and on the Span, also known as the beta compensation obtained during the calibration routine.

Normalized Ratio = Act/(Zero x Ref)
Normalized Absorbance = 1 − (Act/(Zero x Ref))

Table 1. Temperature compensation requirements

Alpha Beta
CO2 No* Yes
Hydrocarbons Yes Yes

*Alpha compensation can be used for increased accuracy over the concentration range.

The process for determining the concentrations of target gas for both hydrocarbon and CO2 devices is shown in Figure 1. Figure 1. Flow diagram of signal processing.

Calibration

During the calculation of target gas concentration, “Zero” and “Span” are used, which are determined by the calibration routine of the infrared gas sensor. It is important to determine the temperature at the time of calibration Tcal and to store it with the zero and span readings in the non-volatile memory.

• Calculate the “Zero”—This calculation is performed when the gas sensor is exposed to the zero test gas nitrogen in the absence of target gas. In this case, Zero = Act/Ref, where Act is the peak-to-peak output of the Active Detector in volts in zero test gas and ref is the peak-to-peak output of the Reference Detector in volts in zero test gas.
• Calculate the “Span”—This calculation is performed when the gas sensor is exposed to the calibration test gas. In this case, Span = [1 − Act/(Zero x Ref)]/[1 − exp(−aCn)], where Act is the Active Detector’s peak-to-peak output in volts in the calibration test gas, Ref is the Reference Detector’s peak-to-peak output in volts in the calibration test gas, Zero is the “Zero” value (stored in non-volatile memory) calculated during this calibration routine, a is the fixed linearization coefficient, C is the concentration of the applied calibration test gas in percentage volume, and n is the fixed linearization coefficient.

Temperature Compensation

Apart from the independence of lamp intensity, the use of the ratio of detector and active signals offers a level of temperature compensation. It is recommended to divide the alpha and beta coefficients into two ranges, assuming the value of Tcal to be nearly 20 °C:

• Positive (of Tcal) temperature compensation
• Negative (of Tcal) temperature compensation

Alpha Temperature Compensation

The alpha coefficient can be “interactively” recalculated in the software or entered as a fixed coefficient obtained after experimental testing.

Normalized Ratio(Comp) = Normalized Ratio x (1 + α (T − Tcal))

Where:

• Normalized Ratio = Act/(Zero x Ref)
• Act = the Active Detector’s peak-to-peak output in volts
• Zero = the “Zero” value calculated at the time of the calibration routine
• Ref = the Reference Detector’s peak-to-peak output in volts
• α = the “alpha” coefficient, either “alphaneg” or “alphapos”
• T = the actual temperature measured at the sensor in Kelvin
• Tcal = the temperature stored in non-volatile memory measured at the time of the calibration routine in Kelvin

Beta Temperature Compensation

The Beta temperature compensation is the evident variation in “Span” over temperature. The coefficient is entered as a fixed value.

Span(comp) = Span + (β x ((T − Tcal)/Tcal))

Where:

• Span = the Span value stored in non-volatile memory calculated at the time of the calibration routine
• β = the “beta” coefficient, either “betaneg” or “betapos”
• T = the actual temperature measured at the sensor in Kelvin
• Tcal = the temperature stored in non-volatile memory measured at the time of the calibration routine in Kelvin

Calculation of the Target Gas Concentration

C = (−ln [1 − ((1 − Normalized Ratio(comp))/Span(comp))]/a) (1/n))

Where a and n are the fixed linearization coefficients.

Interactive Alpha Calculation Method

This technique explains the use of an “interactive” method to calculate the alpha coefficient for the gas sensor, which has been installed, by recalculating the alpha coefficient with the help of software. This may be required to lessen the inherent sensor-to-sensor differences in the alpha coefficient.

The temperature compensation works by primarily setting default alpha (α) coefficients. The compensation is divided into two regions, which will have their own alpha coefficients (“alphaneg” and “alphapos”). They are:

• Positive (of Tcal) temperature compensation (“alphapos”)
• Negative (of Tcal) temperature compensation (“alphaneg”)

To determine the alpha value, there are two conditions that need to be met:

• Whenever the normalized Ratio (for "alphaneg") or Normalized Ratio (comp) (for "alphapos") readings increase to greater than the maximum value from the previous alpha recalculations.

• The difference between the current temperature and the calibration temperature is above 5 °C

Temperature Measurements

Thermistor

Using the following suitable third-order polynomial equation, the signal from the thermistor can be converted to temperature:

Temperature (K) = 375.120 − (54.122*V) + (13.349*V2) − (1.617*V3) (Twin Gas Devices only, for example, IRxxTT)
Temperature (K) = 395.47 − (74.94*V) + (19.68*V2) − (2.327*V3) (IRxxEx Devices only)

Where V is the voltage between the 10-kΩ resistor and the output of the thermistor

Temperature Sensor

Using the following equation, the signal from the temperature sensor can be converted to temperature:

Temperature (K) = ((V − 0.5)/0.01) + 273 (IR600 Series Devices only)
Temperature (K) = ((V − 0.424)/0.00625) + 273 (IRxxGx Devices only)

Where V is the voltage output of the temperature channel. This information has been sourced, reviewed and adapted from materials provided by SGX Sensortech (IS) Ltd.

For more information on this source, please visit SGX Sensortech (IS) Ltd.

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