# Circuit and Noise Analysis of Odorant Gas Sensors in an E-Nose

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## Abstract

**:**

## Introduction

- (1)
- The sensors in the array interfere with each other.
- (2)
- Different types of sensors are used, some of which have large heating current and power dissipation.
- (3)
- Some sensors require amplifiers with extremely high input impedance (e.g., higher than 10
^{11}Ohm) that makes them susceptible to interference. - (4)
- Some sensors have large dynamic current that produces electromagnetic disturbances to the output of other sensors in the same array.

- (1)
- The sensors are very sensitive to temperature and humidity.
- (2)
- The baseline of sensors shifts with time.
- (3)
- Large noise exists in sensor output.

## Typical gas sensors and their noise

#### Resistive gas sensors

_{s}. With pure air R

_{s}is high. With the presence of detectable gases, R

_{s}changes with the variation of gas concentration. Since V

_{C}is a fixed voltage, by measuring the voltage on the resistor R

_{L}, the change on R

_{s}as well as the gas concentration can be calculated.

#### Gas sensors with electromotive output

^{11}Ohm. As a result, it has the disadvantage of being vulnerable to external electromagnetic interferences in addition to the noise of the resistive gas sensor.

#### Sensors with dynamic heating

#### Gas sensors with current output

## Probability distribution function (pdf) of noise

^{−2 / 3}as a function of the total number N of the samples [10].

_{1}, X

_{2}, …, X

_{N}be independent and identically distributed on [0,1] with N the total number of samples. Let m be an integer and h = 1/m. Define the bins as

_{j}=v

_{j}/N and let v

_{j}be the number of observations in B

_{j}. Then the histogram estimation of probability distribution function f (x) is given as:

- 1)
- How to measure the error between f̂
_{n}(x) and the real probability distribution function f (x) ?, and - 2)
- What is the optimal h that makes the approximation of f̂
_{n}(x) to f (x) the best?

_{n}(x) and the real probability distribution function f (x). The function R (f, f̂; is given by:

**E**{·} is to calculate the expected value (mean). For the second question, it is obvious that the smaller the R (f, f̂;, the more closer will be f̂

_{n}(x) and f (x) (with the exception of only some point sets with zero measure). When R (f, f̂) reaches its minimum, the best approximation of f̂

_{n}(x) to f(x) is obtained. Since f(x) is unknown, R(f,f̂; cannot be calculated directly, but its minimum can be reached by making Ĵ(h) the minimum [10]. The function Ĵ(h) is given by:

## Power spectrum estimation of noise

_{1}, X

_{2}, …, X

_{N}, and N is the total number of data sets.

_{1}, X

_{2}, …, X

_{N}into K small non-overlapping sections. The length of each small section is M with KM = N. First, the power spectrum is estimated for each small section (also remove the mean of the small section before the DFT). Then, the power spectrum estimation will be the average of the K small sections. The disadvantage of this method lies in its losing of information on sensor's baseline shifting that is much smaller during the small section than that of the whole section. The advantage is its asymptotic consistent estimation of real power spectrum. With the increase of M, the variance of the averaged segmenting periodical graph approaches zero. By this manner, the power spectrum estimation of the small section j is given as:

_{1}, X

_{2}, …, X

_{M}. The total power spectrum estimation is given as:

## Experiment results

- (1)
- For the case of coloured noise with a single peak pdf, Figures 8(a) and 8(b) show the time-domain curve and the power-spectrum estimation curve, respectively. It shows that the power spectrum of noise mainly consists of two parts: one is the almost constant-magnitude part filling the whole frequency band, and the other is composed of some lower frequency components that may be caused by some inherent feature of the sensor and its circuit. Some of them have the same frequency as signal; it cannot be filtered out by just a simple low-pass filter.Figure 9 shows the curve of Ĵ(h) from Equation (4) with h = 1/m. It can be seen that when m = 10, i.e., h = 0.1, Ĵ(h) reaches its minimum that makes the risk function R (f, f̂; minimum. The h value at h = 0.1 makes the estimation of pdf to be optimal. Figure 10 gives the pdf estimation under this h value. It is close to a Gaussian distribution.
- (2)
- In the case of white noise with single peak, the noise in time domain and its power-spectrum estimation curve are shown in Figures 11(a) and 11(b), respectively. The pdf estimation is shown in Figure 11(c) with the optimal value at h = 1/75. It is similar to a Gaussian distribution. The envelop of the noise power spectrum is almost constant in the whole band. Thus, it is reasonable to consider this type of noise as normal white noise. For the sensors 3SH (current output) and TGS4160 (electromotive), their output signals are too weak and the gain of amplifier has to be large enough (about 6,000), or the input impedance is too high (more than 10
^{11}Ohm). The noise energy of these sensors is much bigger than that of the first type in Table 1, which implies that the noise in this type of sensor cannot be ignored.

- (3)
- For the coloured noise with double peak pdf, Figures 12(a) and 12(b) show the noise in time domain and its power spectrum estimation of sensor, respectively. Figure 12(c) is the estimation of pdf with the optimal value at h = 1/29. In comparison to the first type of sensors in Table 1, both have similar coloured noise power spectrum and many of their low frequency components have the same location in the frequency domain. This implies that the inherent features of the sensors are similar, as they are produced by the same manufacturer. The only obvious difference here is that its pdf has double peaks, while the first type has only one. The double peaks in its pdf imply the high appearance frequency of these two types of noise magnitude.

- (4)
- For some sensors such as TGS830, TGS2600, the remarkable difference exists in their zero frequency component of noise power spectrum between the periodical graphs and averaged segmenting periodical graph methods. This can be observed when comparing Figure 12(b) and Figure 13. No peak appears in the nearby zero frequency of the averaged segmenting periodical graph in Figure 12(b), which is opposite to its counterpart in Figure 13. It is due to the fact that the sensor baseline shifts slowly within the whole time period (the total 30,000 data sets), although in both methods the mean is removed. Whereas in each small section (5,000 data sets) the baseline changes little and results in almost no nearby zero frequency component. That indicates, of all sensors tested, the three types of sensors can work more stably and have much smaller baseline shift than other sensors.

## Conclusions

- Since the sensors only work with its corresponding circuits as a whole, the sensor noise here means the whole noise from the sensor and its amplifying circuit. The noise is related to the art of manufacture, the input impedance of amplifier and its gain. In our experiment, the optimal operating circuits and devices recommended by the manufacturers are adopted. So it is reasonable to believe those e-noses which use the same type of sensors have similar circuit structure and noise feature as we give here.
- The noise in the sensors of the e-nose can be categorized into coloured or white noise according to its power spectrum. The coloured noise can be regarded as the white noise plus some stronger low frequency components. The pdf of noise is of either single peak or double peaks.
- The noise of resistive gas sensor is coloured one.
- The white noise lies in either electromotive sensor or sensor with current output, which is due to either the weak signal or the high input impedance.
- To estimate the pdf of noise, we have used the optimal width (h) for bins in histogram that results in the closest estimation to the real pdf in the sense of smallest integrated mean squared error. The averaged segmenting periodical graph estimation of noise power spectrum is an asymptotic consistent estimator of the real power spectrum. The error of estimation is expected to be small enough considering the huge number of data sets.
- The baseline shift of sensor can be observed through comparing the periodical graph and the averaged segmenting periodical graph of noise. Of all the sensors tested, the three sensors TGS830, TGS2600, TGS2602 can work more stably and have smaller baseline shift than others. They almost have no baseline shift in each small section of 5,000 data sets (corresponding to 13 minutes or so). But in the whole period of 30,000 data (corresponding to 1.5 hours), there is still baseline shift.

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**Figure 8.**The noise (a) and its power spectrum estimation (b) of the first type of sensors in Table 1.

**Figure 11.**The noise (a), its power spectrum (b) and pdf estimation (c) of the second type of sensors in Table 1.

**Figure 12.**The noise (a), its power spectrum (b) and pdf estimation (c) of the third type of sensors in Table 1.

Single peak | Double peaks | |
---|---|---|

Power spectra | ||

Coloured noise | (1) TGS813 etc. | (3) TGS830 etc. |

White noise | (2) 3ETO etc. | N/A |

© 2005 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license ( http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Tian, F.; Yang, S.X.; Dong, K.
Circuit and Noise Analysis of Odorant Gas Sensors in an E-Nose. *Sensors* **2005**, *5*, 85-96.
https://doi.org/10.3390/s5010085

**AMA Style**

Tian F, Yang SX, Dong K.
Circuit and Noise Analysis of Odorant Gas Sensors in an E-Nose. *Sensors*. 2005; 5(1):85-96.
https://doi.org/10.3390/s5010085

**Chicago/Turabian Style**

Tian, Fengchun, Simon X. Yang, and Kevin Dong.
2005. "Circuit and Noise Analysis of Odorant Gas Sensors in an E-Nose" *Sensors* 5, no. 1: 85-96.
https://doi.org/10.3390/s5010085