# Investigation and Optimization of the Performance of an Air-Coil Sensor with a Differential Structure Suited to Helicopter TEM Exploration

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}(diameter is 0.5 m), 71 kHz, 20 (the varying magnetic field strength is 1 nT/s), and 5.43 nV/m

^{2}, respectively. These data are superior to those of the traditional induction sensor 3D-3. Finally, a field experiment is performed with a fabricated sensor to show a valid measurement of the time-varying magnetic field of a helicopter TEM system based on the designed ACS.

## 1. Introduction

^{2}, respectively. Although the equivalent areas of such sensors satisfy the requirement of helicopter TEM, their bandwidth is narrow, thus limiting the detection depth in helicopter TEM exploration. The MTEM-AL sensor developed by Phoenix Geophysics (Canada) has an equivalent area of 100 m

^{2}, and its bandwidth can reach up to 50 kHz. Given such parameters, the sensor from Phoenix can satisfy the requirement of helicopter TEM exploration. However, its diameter is as large as 2.1 m, which cannot meet the ACS size requirement of a helicopter TEM system. Therefore, a custom ACS with optimized specifications for helicopter TEM exploration should be developed.

## 2. Equivalent Electrical Model of an Air-Core Coil

**Figure 1.**(

**a**) Air-core coil with a differential structure; (

**b**) typical design of an air-core coil (l—length of the air-core coil, D—diameter of the air-core coil, d—diameter of wire, and n—number of turns).

**Figure 2.**Schematic of the air-core coil, where r, L, and C are the resistance, inductance, and capacitance of the air-core coil, respectively.

_{t}depends on the resistance r of the air-core coil and has a temperature T with a coefficient equal to the Boltzman factor k

_{B}= 1.38 × 10

^{−23}W·s/K.

^{2}, and the self-thermal noise V

_{t}only goes up by $\sqrt{nD}$. Therefore, the optimum values of D and n for an air-core coil can be determined by considering the required SNR. The discussed parameters of the air-core coil determine the electrical equivalent parameters (i.e., resistance, inductance, and capacitance), which are critical to the selection of the operational amplifier for a differential pre-amplifier.

## 3. Equivalent Schematic of ACS with Noise Source

_{11}and R

_{22}, are connected to the air-core coil in parallel as a matched resistor to adjust the working state of the air-core coil in accordance with the requirement of helicopter TEM exploration. Easy gain control is realized by changing the value of one single resistor R

_{5}, which can amplify the low amplitude sensed signal in the order of few mV to the operational range for further processing in several volts.

_{en}consists of three components (i.e., input voltage noise V

_{n}, input current noise I

_{n}, and Nyquist noise ${T}_{n}=\sqrt{4kT{R}_{tot}}$ of all resistors in Figure 3) [11,12]. All these noise contributions can be combined to obtain V

_{en}as expressed below.

_{i,tot}is the impedance of all resistors that input current noise flow through, and T denotes the environmental temperature at all resistance R

_{t,tot}.

_{n}from amplifiers U

_{1}and U

_{3}can be obtained as

_{n1}and e

_{n3}are the input voltage noise of amplifiers U

_{1}and U

_{3}, respectively, and G is the gain of amplifier U

_{1}.

_{n}Z

_{i,tot}generated by the input current noise of amplifiers U

_{1}and U

_{3}flowing through the three stages of ACS can be expressed as

_{n1}and i

_{n3}are the input current noise of amplifiers U

_{1}and U

_{3}, respectively.

_{n}produced by all resistors included in Figure 3 can be obtained as

_{t,en}can be calculated as ${V}_{t,en}=\sqrt{2}\cdot {V}_{en}$ depending on the complete symmetrical structure of the pre-amplifier.

## 4. Specification Optimization of the ACS

#### 4.1. Geometry Optimization of the Air-Core Coil

#### 4.2. Optimization for Electrical Specification of the Pre-Amplifier

_{n}, input current noise I

_{n}, and Nyquist noise T

_{n}.

_{n}, input current noise I

_{n}, and Nyquist noise T

_{n}, the noise source contribution map is expressed as in Figure 8 to analyze the contributions of such noises to the EIN.

_{n}($\text{1.28nV/}\sqrt{\text{Hz\hspace{0.17em}}}$) and T

_{n}($\text{1.31\hspace{0.17em}nV/}\sqrt{\text{Hz\hspace{0.17em}}}$) both primarily generate the EIN. When the frequency increases to higher than 10 kHz, the impedance of the distribution parameters increases along with the EIN. Reducing V

_{n}and T

_{n}is helpful to minimize the EIN of the picked up ACS.

## 5. Experiment

#### 5.1. Realization of ACS

^{2}, and its mass is 2.5 kg with a ring wooden frame. By contrast, the length, resultant effective area, and mass of the 3D-3 are 0.6 m, 50 m

^{2}, and 16 kg, respectively. These data show that compared with the 3D-3, the designed ACS is more suitable for helicopter TEM exploration.

Parameters | Symbol | Value |
---|---|---|

Diameter of air-core coil | D | 0.5 m |

Diameter of wire | d | 0.5 mm |

Number of turns | n | 28 |

Wooden frame density | ρ | 730 kg/m^{3} |

Resistivity of wire | ρ_{r} | 1.7 × 10^{−8} Ω/m |

Length of air-core coil | l | 0.045 m |

Resistance of air-core coil | r_{1} | 3.23 Ω |

Inductance of air-core coil | L_{1} | 243.7 μH |

Capacitance of air-core coil | C_{1} | 113 pF |

Resistor | R_{4} = R_{6}; R_{5}; R_{7} = R_{8}; R_{9} = R_{10}; R_{11} = R_{22} | 1.5 kΩ; 100 Ω; 22.6 kΩ; 1 kΩ; 1.3 kΩ |

Gain of pre-amplifier | G | 672 |

Operational amplifier | U_{1}, U_{2}, U_{3} | AD797 |

#### 5.2. Frequency Response Comparison of ACS and 3D-3 Sensor

^{2}, which is larger than that of the ACS, the 3 dB bandwidth can only go up to 28 kHz. Hence, the 3 dB bandwidth of the designed ACS is as high as 71 kHz, which meets the requirement of helicopter TEM exploration, with enough gain stability. The 3D-3 sensor is suitable for low frequency detection applications.

#### 5.3. EIN of ACS

^{2}. The normalized value equivalent to the square root of the integration of EIN

^{2}in 3 dB bandwidth is described below.

^{2}), respectively.

^{2}.

#### 5.4. Field Experiment

**Figure 13.**Cross-section maps of different survey lines detected by the (

**a**) ACS-based helicopter TEM system and (

**b**) the AeroTEM system.

## 6. Conclusions and Prospects

^{2}(diameter is 0.5 m), 71 kHz, 20 (exciting field strength is 1 nT/s), and 5.43 nV/m

^{2}, respectively. The conformity between the experimental and simulation results confirms the optimization theory. Finally, a field experiment was performed with a fabricated sensor to show the reliability of a helicopter TEM system based on the designed ACS.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Chen, C.; Liu, F.; Lin, J.; Wang, Y.
Investigation and Optimization of the Performance of an Air-Coil Sensor with a Differential Structure Suited to Helicopter TEM Exploration. *Sensors* **2015**, *15*, 23325-23340.
https://doi.org/10.3390/s150923325

**AMA Style**

Chen C, Liu F, Lin J, Wang Y.
Investigation and Optimization of the Performance of an Air-Coil Sensor with a Differential Structure Suited to Helicopter TEM Exploration. *Sensors*. 2015; 15(9):23325-23340.
https://doi.org/10.3390/s150923325

**Chicago/Turabian Style**

Chen, Chen, Fei Liu, Jun Lin, and Yanzhang Wang.
2015. "Investigation and Optimization of the Performance of an Air-Coil Sensor with a Differential Structure Suited to Helicopter TEM Exploration" *Sensors* 15, no. 9: 23325-23340.
https://doi.org/10.3390/s150923325