Analytical determination of load resistance value for MQ-series gas sensors: MQ-6 as case study

The MQ-series gas sensors are attractive candidates in the area of gas concentration sensing due to their high sensitivity and low cost. Even though the sensor circuit sensitivity and sensor power dissipation level both depend on load resistance, the process of the load resistance selection has not been well researched, hence the need for this study. The derivation of model equations for determining the sensor circuit sensitivity and sensor power dissipation is presented. The derived equations were used to investigate a typical scenario of MQ-6 gas sensor under the influence of liquified petroleum gas (LPG). The variation of sensitivity with load resistance and that of power dissipation with sensor resistance were parametrically investigated. The load resistance that yields maximum sensor circuit sensitivity with the maximum sensor power dissipation less than the set threshold is the candidate resistance for the sensor circuit. The 20 kΩ load resistance recommended for MQ -6 in the datasheet was authenticated in this study, yielding the maximum possible sensor circuit sensitivity and tolerable sensor power dissipation of 0.195 mV/ppm and 3.125 × 10 −4 W, respectively.


INTRODUCTION
The MQ-series gas sensors are attractive candidates in the area of gas concentration sensing due to their high sensitivity and low cost. The metal oxide (MOXs) semiconductor gas Sensors, comprising MQ-series and others, have wide applications in gas concentration sensing and detection due to their high sensitivity and low cost [1,2]. The MOX semiconductor gas sensor consists of a micro AL2O3 ceramic tube, a sensitive layer of tin dioxide (SnO2), and Nickel-Chromium alloys which serve as a heater coil. This sensor has 6 pins, 4 out of which are for signal and electrodes, while the remaining 2 are for heating coils [3][4][5]. The tin dioxide (SnO2) semiconductor is the sensor gas-sensitive portion [3,4,6,7] which has low conductivity in clean air [8]. The principle of operation of these sensors is based on the variation of their resistance when they come in contact with the gas to be sensed [7,9,10]. The magnitude of the sensor output signal depends on the concentration and nature of the gas [6,8,11] and the type of metal oxide used for the sensor sensing surface [2,12,13]. The sensor is made up of two elements, namely the heating and sensing elements. These elements are normally powered independently either from the same or separate voltage source. The heater voltage will allow it to generate the required heat for maintaining the sensor in the active state while the sensor voltage will allow the sensor to convert the sensed gas concentration to an appropriate voltage level across the load resistor connected in series with the sensing element [5,9,12,14]. Because of the characteristic of the sensing element a simple electrical equivalent circuit can be used to convert the sensed gas concentration to a corresponding signal usually voltage across the load resistor [5,8,9,11].
To calibrate MOX semiconductor gas sensors the following sensor parameters must be known: sensor activation voltage ( CC ), sensor electrical equivalent circuit output voltage ( R ), the sensor resistance for referent gas concentration and environmental conditions (temperature and humidity) ( ) [15], the sensor resistance ( S ) and load resistance ( L ) [3]. The value of O is not explicitly given in the sensor datasheet; therefore, it has to be determined experimentally [3]. In practice O must be determined for every sensor to be used because it is practically impossible to have similar gas sensors with the same value of O [16]. This is because it is also, practically impossible to secure the reproducibility and stability of this class of sensors as a result of the impossibility of keeping the consistency of the manufacturing environment, therefore, there is usually some variation in the sensor behaviour from one sensor to another and from one production batch to another [7,10]. After the determination of O value, the sensor resistance at different gas concentrations value for various gases and different environmental conditions (temperature and relative humidity (RH)) can be determined [2]. It should be noted that the sensor circuit sensitivity and the sensor power dissipation are both functions of the load resistance.
Even though the sensor circuit sensitivity and sensor power dissipation level both depend on load resistance, the process of resistance selection has not fully investigated, and hence the need for this study. The air quality using MQ-2 gas sensor was monitored as reported in [17], using the 20 kΩ load resistance as given in the sensor datasheet. The air quality monitoring system developed by [3] consisted of three sensors which include an MQ-7 gas sensor. However, a default manufacturer circuit with a load resistance of 1 KΩ was employed in the study, which is outside the range of value (5-47 kΩ) recommended in the datasheet with no justification. MQ-2 gas sensor was used by [18] for air quality monitoring with a load resistance value of 5 KΩ which is subjected to variation depending on the gas concentration to give room for sensitivity adjustment [19]. Four MOX sensors, consisting of MQ-2, MQ-3, MQ-6, MQ-135, were used in [4] for the development of a real-time olfaction monitoring system with a 10 kΩ load resistance for each of the sensors without considering their characteristics. An air pollution monitoring system using a single MQ-2 gas sensor for sensing both CO and smoke was developed in [20], using a 20 kΩ load resistance recommended in the sensor datasheet. The clean air sensor resistance parameter for MQ-5 gas sensor was computed in [1], by placing the sensor in fresh air while measuring the sensor output voltage with the 20 kΩ load resistance. However, the selection of load resistance was not justified. MQ-2 and MQ-7 were used for sensing flammable gases and carbon monoxide respectively in a death-defying gas intelligent sensor system [5]. The load resistance used for both MQ-2 and MQ-7 sensors was 1 kΩ which is outside the range (5-47 kΩ) recommended in the sensor datasheet.
In different microcontroller-based LPG leakage concentration monitoring and control systems proposed by [21][22][23][24][25][26][27][28], the leakage gas concentration was sensed in these systems using MQ-4 [28], MQ-6 [22,23,26,27], MQ-5 [24] and MQ-2 [21,25] gas sensors. The selection of the load resistance in all these systems sensor circuits was not considered. It was pointed out in [12,29] that the value of the load resistor should be selected in such a way as to optimize the alarm threshold value and keep the sensor power dissipation below the maximum allowable value. For some sensors, the manufacturer provides data on the value of load resistance to be used so that the resolution would be sufficient around the alarm point. It was pointed out in [21] that the load resistance should be wisely selected to improve sensor performance because a lower value will result in less sensitivity while a higher value will give less accuracy.
In most of the reviewed works, there is no concrete justification for the selection of the load resistance for the MQ-series gas sensor circuit aside from the claim that the selected value is as given in the sensor datasheet. Therefore, considering the dependence of the sensor circuit sensitivity and sensor power dissipation on the load resistance this study was carried out to investigate the dependence of these parameters on the load resistance and justify the selection of the resistance value. Using the sensor electrical equivalent circuit and a hypothetical sensitivity curve, the sensor model equations were developed. From the developed model equations, the equations for the determination of the sensor circuit sensitivity and sensor power loss were derived. The derived equations were used for a particular case of MQ-6 gas sensor under the influence of LPG to plot the graphs of sensor circuit output sensitivity versus load resistance and sensor power dissipation versus sensor resistance from which the trend of variation of sensitivity and sensor power dissipation with the load and the sensor resistance was respectively studied. The appropriate value of load resistance for maximum sensitivity and maximum power loss was determined. The load resistance that yielded maximum sensor circuit sensitivity with the maximum sensor power dissipation less than the set threshold is the candidate resistance for the sensor circuit. The value of the load resistance (20 kΩ.) recommended in MQ-6 datasheet was analytically authenticated in this study.

MODELLING OF MQ-SERIES GAS SENSOR CIRCUIT DYNAMICS
The electrical equivalent circuit diagram for MQ-series gas sensors is as shown in Figure 1. CC , RL , L and S are as earlier defined and H is the heater resistance. From Figure 1, the current, I flowing through and is given by; The output voltage across the load resistor, , is given by; From (2) the resistance is; Also, the relationship between the sensor resistance and the gas concentration under a specified environmental condition (temperature and RH) can be obtained from the sensor sensitivity curve present in each of the MQseries sensor's datasheet. A hypothetical plot of the sensor resistance ratio, versus the corresponding gas concentration in parts per million (ppm) on the logarithmic scale is shown in Figure 2.
where ( 1 , 1 ) and ( 2 , 2 ) are the coordinates of any two different points on the straight line of Figure 2.
From (4) = 10^( log 10 ( ) − log 10 ( )) From (4) the sensor resistance can be expressed in terms of the parameters obtained from the sensitivity curve of Figure 2 as shown in (7).

LOAD RESISTANCE FOR MAXIMUM SENSITIVITY AND SENSOR POWER DISSIPATION
It can be seen from (2) that the output voltage from the sensor circuit that is is a function of CC , and , but CC is always constant, therefore, varies only with the value of and . Also, from (7) is a function of , and but is constant, has a range for a given gas and also has a range for a given class of MQ-series gas sensors. But it should be noted that has a unique value for each member in the class which is normally determined using (3) by empirically measure the value of at a specified value of and environmental conditions. Based on this, it can be inferred that is a function of , and . From the MQ-series gas sensor datasheet, the range of and for a particular series of sensors is always specified. The requirements for the selection of are high output voltage span which will lead to high sensor circuit sensitivity and moderate sensor power dissipation [12]. It should be noted that out of the three parameters on which the value of sensor circuit output voltage ( ) depends, namely , and , it is only that can be easily adjusted by the circuit designer to meet the voltage span and power dissipation requirements. This is because , and are strictly dependent on the inherent characteristics of the gas and sensor material respectively. The sensor output voltage range was determined as follows, from (2) the minimum and maximum output voltage can be expressed as shown in (9-12).
is the maximum value of sensor resistance and using (7) is as shown in (10).
where is the minimum value of gas concentration in ppm.
is the minimum value of sensor resistance and using (7) is as shown in (12) = 10 ( log 10 ( )+log 10 ( )+log 10 ( )) where is the maximum value of gas concentration in ppm. The voltage span was obtained from (9) and (11) and is as expressed in (13) The sensitivity of the sensor circuit is the ratio of the magnitude of its output voltage span to the corresponding change in the magnitude of the gas concentration and is mathematically expressed in (14).
∆ = − in ppm The value of that gives the maximum sensitivity for a particular sensor with a given value of can be obtained by plotting against and determine the value of corresponding to the maximum point of the resulting curve. At maximum sensitivity = √ [32], therefore, the formula for the power dissipated by the sensor at maximum sensitivity was obtained by multiply the square of the current through the sensor obtained in (1) with the sensor resistance and is as expressed in (15). Therefore, for a determined value of and given value of , graph of against can be plotted to enable one study the trend of the variation of power dissipated by the sensor with and also, determine the maximum value of the sensor dissipated power at maximum sensitivity. It should be noted that this maximum value must not be greater than the set threshold value given in the sensor manufacturer datasheet [29].

MQ-6 GAS SENSOR CASE STUDY
The MQ-6 gas sensor was selected at random out of many available MQ-series gas sensors. This type of gas sensor is capable of sensing seven gases as listed on the sensitivity curve of Figure 3. Out of these gases, the sensor has a high sensitivity for both LPG and Methane but for this study, LPG was considered. The appropriate value of was determined by first determined the numerical values of the slope , intercept , and and substitute them into the appropriate equation as follows: Figure 3. Sensitivity characteristics graph for MQ-6 gas sensor [30,31] The slope was determined by considered two coordinates (200, 2) and (10000, 0.4) on the LPG gas curve on the sensitivity graph of Figure 3. Substituting these coordinates in (5) (14) with the value of equal to 5V. After the parameter substitution, (14) was used to plot the graph of versus for value of increasing from 10 kΩ to 60 kΩ in step of 5 kΩ and the plot yielded the graph of Figure 4. Also, using (15), the graph of the sensor dissipated power versus the sensor resistance was plotted for the obtained value of for the maximum sensitivity and a given value of . The graph was plotted for different values of varying from 10-60 kΩ in step of 5 kΩ and is as shown in Figure 5. To test the applicability of this study, the recommendation of =20 kΩ for the MQ-6 sensor in the datasheet [31] was authenticated. The equation that relates and is given in (16).
= 10 ((log10( 2 )− (log10( )+log 10( ))−2 log 10( ))/2) Substituting =20 kΩ and the value of other parameters into (16) gives the value of to be 23.065 Ω. The value of obtained can be confirmed as follows: From the LPG sensitivity curve, for to be equal to the gas concentration must be 1000 ppm. Substitute = −0.4114, = 17.15, =23.065 kΩ and = 1000 ppm into (7) gives Rs=23.065 kΩ. This implies that for this sensor =23.065 kΩ. This shows that the value of for the sensor used in the datasheet is 23.065 Ω and for the maximum sensitivity to be obtained must be equal to 20 kΩ which is validated as seen in Figure 6. The plot of the sensor dissipated power against for =23.065 kΩ and =20 kΩ is as shown in Figure 7. From Figure 7, the maximum power dissipated and the value of for maximum power dissipation can be obtained.

RESULTS AND DISCUSSION
The data presented in Table 1 were obtained from Figure 4. As can be seen from the figure, the maximum obtainable sensor circuit sensitivity remains fairly constant for different values of from 10-60 kΩ, but the maximum value occurred at different values of for each of the . The value of increases when falls between 10 kΩ and 50 kΩ but remain constant when is between the value of 55 kΩ and 60 kΩ. From this analysis, it is obvious that the obtained value of sensor circuit sensitivity is a function of both the and but it should be noted that is solely depend on the sensor characteristics it is only that can be adjusted by the circuit designer to achieve the required sensitivity.

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The data of Table 2 were extracted from Figure 5. It is very clear from the table that the sensor power dissipation decreases as the value of and increases. The highest obtained sensor power dissipation was 7.198 × 10 −4 W which is far less than the maximum limit of 15 × 10 −3 W [29]. As can be seen from Tables 2, the values of and are approximately equal, which implies that the law of maximum power dissipation is obeyed.
It can be deduced from Tables 1 and 2 that the behaviour of the MQ-6 gas sensor is consistent in terms of maximum sensor circuit sensitivity and sensor power dissipation when is between 10-60 kΩ. The manufacturer of this category of sensor should work toward achieving a high value of because sensor power dissipation decreases with an increase in without affecting the sensor circuit sensitivity. The applicability of this study is confirmed as shown in Figures 6 and 7, where =23.065 kΩ; the maximum sensor's circuit sensitivity and power dissipation are approximately 0.195 mV/ppm and 3.125 × 10 −4 W (far less than the maximum limit of 15 × 10 −3 W [29]), respectively for =20 kΩ.

CONCLUSION
The sensor circuit dynamics was modelled and the developed model equations were used for determining, for a given : (i) sensor circuit sensitivity as a function of load resistance and (ii) sensor power dissipation as a function of sensor resistance. The highest sensor power dissipation obtained when Ro = 10 kΩ was 7.198 × 10 −4 W (<< the maximum limit of 15 × 10 −3 W). It can be deduced from the study that the MQ-6 gas sensor has consistent behaviour in terms of maximum sensor circuit sensitivity and sensor power dissipation when 10 kΩ< <60 kΩ. The manufacturer of this category of sensor should increase the value of as the level of sensor power dissipation is inversely related to the former. Finally, the 20 kΩ load resistance recommended for MQ-6 in the datasheet was also validated in this study because it gives maximum sensor circuit sensitivity and tolerable sensor power dissipation.