Design of a Matching Network for a High

sensors Article

Design of a Matching Network for a High-Sensitivity Broadband Magnetic Resonance Sounding Coil Sensor Yang Zhang † , Fei Teng † , Suhang Li, Ling Wan and Tingting Lin *

ID

College of Instrumentation & Electrical Engineering, Lab of Geo-Exploration Instrumentation of Ministry of Education, Jilin University, Changchun 130026, China; [email protected] (Y.Z.); [email protected] (F.T.); [email protected] (S.L.); [email protected] (L.W.) * Correspondence: [email protected] (T.L.); Tel.: +86-135-0081-8835 † These authors contributed equally to this work. Received: 9 September 2017; Accepted: 23 October 2017; Published: 27 October 2017

Abstract: The magnetic resonance sounding (MRS) technique is a non-invasive geophysical method that can provide unique insights into the hydrological properties of groundwater. The Cu coil sensor is the preferred choice for detecting the weak MRS signal because of its high sensitivity, low fabrication complexity and low cost. The tuned configuration was traditionally used for the MRS coil sensor design because of its high sensitivity and narrowband filtering. However, its narrow bandwidth may distort the MRS signals. To address this issue, a non-tuned design exhibiting a broad bandwidth has emerged recently, however, the sensitivity decreases as the bandwidth increases. Moreover, the effect of the MRS applications is often seriously influenced by power harmonic noises in the developed areas, especially low-frequency harmonics, resulting in saturation of the coil sensor, regardless of the tuned or non-tuned configuration. To solve the two aforementioned problems, we propose a matching network consisting of an LC broadband filter in parallel with a matching capacitor and provide a design for a coil sensor with a matching network (CSMN). The theoretical parameter calculations and the equivalent schematic of the CSMN with noise sources are investigated, and the sensitivity of the CSMN is evaluated by the Allan variance and the signal-to-noise ratio (SNR). Correspondingly, we constructed the CSMN with a 3 dB bandwidth, passband gain, normalized equivalent input noise and sensitivity (detection limit) of 1030 Hz, 4.6 dB, 1.78 nV/(Hz)1/2 @ 2 kHz and 3 nV, respectively. Experimental tests in the laboratory show that the CSMN can not only improve the sensitivity, but also inhibit the signal distortion by suppressing power harmonic noises in the strong electromagnetic interference environment. Finally, a field experiment is performed with the CSMN to show a valid measurement of the signals of an MRS instrument system. Keywords: magnetic resonance sounding; coil sensor; LC filter

1. Introduction Compared to other geophysical methods, the use of MRS technology can directly determine the water content of the subsurface [1–3]. The method has become a competitive approach for non-invasive investigations of groundwater resources in recent years [4]. The basic principle of this method is that the transmitting loop is energized for a certain time τ by a pulse of alternating current I0 to stimulate a precession of the protons around the geomagnetic field. When the pulse is terminated, the protons produce a free induction decay (FID) signal with a fixed bandwidth, which depends on the pulse moment q = I0 × τ and can be detected by the pickup loop. The FID signal envelope is characterized by E0 (q) and T2 *(q), which are the initial amplitude and the average relaxation time of the signal, respectively [5]. After fitting the E0 (q) and T2 *(q) values using the Sensors 2017, 17, 2463; doi:10.3390/s17112463

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processed FID signal, the water content and pore size of the rock could be determined via the inversion process [6]. MRS is a large-scale method, with the investigated volume approximated by a cube of 1.5 × d, where 100 < d < 150 m is the side of a square loop [7]. To date, the MRS technology has been successfully applied in searching for underground water resources in arid regions and detecting seawater intrusion [8–12]. Therefore, it is of paramount importance to obtain reliable FID signals with suitable receiving sensors for MRS applications. Coil sensors are widely used in biomedical and geological survey instruments because of their excellent sensitivity, low fabrication complexity, robustness and low cost [13–16]. To optimize the coil sensor designs and improve the sensitivity, numerical methods have been developed [17–19]. An air-core induction magnetometer for detecting low-frequency fields was developed by optimizing the minimum coil size based on a specific type of amplifier and a fixed cut-off frequency [17]. Lin et al. designed a high-sensitivity cooled coil system (77 K) by optimizing the coil diameter and the conductor thickness for ultra-low-field nuclear magnetic resonance in laboratory and field conditions [18,19]. Nevertheless, the high sensitivity coil must be combined with a matching circuit that can achieve optimum performances for applications, especially in MRS, whose detection signal is on the order of nanovolts (10−9 V). The tuned design was initially used for the MRS coil sensor design because it can provide additional sensitivity with narrower bandwidth; however, the FID signals may be distorted through the tuned coil sensor because of the narrowband characteristics. The signal distortion is not acceptable, and this design is therefore seldom used in MRS. In the case of the non-tuned design, the sensor can obtain valid signals because of the broad bandwidth; however, the sensitivity is lower than that of the tuned design. Moreover, the FID signals sampled by the broadband sensor can be better suited for the post digital signal processing methods [20–22]. Lin et al. described a non-tuned coil system for the MRS application that involved minimizing the preamplifier equivalent input noise to improve the sensitivity [23]. However, the sensitivity of their MRS coil system is still lower than that of the tuned design. None of the tuned and non-tuned configurations has the advantages of both high sensitivity and broad bandwidth. Hence, our first goal is to propose a method to design a broadband MRS coil sensor with high sensitivity. In addition, the fact that low-frequency harmonics always cause preamplifier saturation in developed areas, regardless of which configuration for the MRS coil sensor design is selected is a serious problem. Although the uses of a notch filter and “figure-eight” shaped coil are effective methods of suppressing environmental noise, including power harmonic noises [24,25], low-frequency harmonics with large amplitude prevent additional applications of the above-described MRS technique. Lin et al. proposed a real-time anti-saturation technology that provides a new method for obtaining effective FID signals [26]. This method can inhibit the post-amplifier saturation distortion, but it cannot solve the problem of preamplifier saturation. Therefore, a specific coil sensor with a novel technology for MRS applications in strong electromagnetic noise environments should be developed. To improve the sensitivity of the system and suppress the signal distortion, we designed a matching network consisting of an LC broadband filter in parallel with a matching capacitor. Based on the characteristics of the pickup coil, the matching capacitor is selected to increase the gain in the passband of the filter and improve the sensitivity of the sensor system. The rest of this paper is organized as follows: Section 2 analyses the characteristics of the tuned and non-tuned coil sensors and the origins of the coil sensor nonlinear distortion and then introduces the design method of the matching network of the CSMN. Section 3 presents the equivalent schematic of the CSMN with noise sources. Section 4 evaluates the sensitivity of the CSMN system using the Allan variance. In Section 5, the effectiveness of the method is verified by laboratory and field experiments. Finally, Section 6 provides the conclusion of this study and recommendations for future research.

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2. High-Performance CSMN In this section, the advantages and disadvantages of the tuned and non-tuned configurations for the coil sensor are described in detail. The origins of the nonlinear distortion of the traditional MRS coil sensor are analysed. Finally, we introduce the design method of the matching network used for the CSMN. 2.1. Characteristics of the Tuned and Non-Tuned Coil Sensors The tuned and non-tuned configurations illustrated in Figure 1 are the most widespread configurations used for the MRS coil sensor design. The schematic of the tuned design (Figure 1a) Sensors 2017, 17, 2463 3 of 16 consists of three parts (i.e., coil, tuned capacitor and preamplifier). We take the resonance frequency 2330 Hz as an performFinally, simulation analysis; themethod relevant are as follows: MRSexample coil sensor to are analysed. we introduce the design of theparameters matching network used=for L = 0.8 mH, Rs 4 the Ω, CSMN. C = 5.8 µF and the gain of the preamplifier is 0 dB. The amplitude-frequency characteristics the tunedof design shown in the red curve (Figure 1c). The magnitude is 9.48 dB 2.1.of Characteristics the Tuned are and Non-Tuned Coil Sensors at a resonance frequency of 2330 Hz. Therefore, this hasmost thewidespread advantages of high The tuned and non-tuned configurations illustratedconfiguration in Figure 1 are the configurations the MRS the coil sensor design. The schematic of the with tuned the design (Figure 1a) of the tuned sensitivity and the abilityused to for maintain signal-to-noise ratio (SNR) resonance consists of threeHowever, parts (i.e., coil, tuned capacitor and preamplifier). the resonance frequency FID signal. capacitor and inductor. this configuration may leadWe to take a distorted broadband 2330 Hz as an example to perform simulation analysis; the relevant parameters are as follows: L = The maximum when T2 * is 30 ensure that all FID signals 0.8 bandwidth mH, Rs = 4 Ω,of C =the 5.8 signal μF and is the105 gainHz of the preamplifier is 0ms dB.[7]. The To amplitude-frequency the tuned design are shown in the red curve 1c). Themust magnitude is 9.48 dBthan 105 Hz. measured bycharacteristics the sensorofare undistorted, the bandwidth of (Figure the sensor be greater at a resonance frequency of 2330 Hz. Therefore, this configuration has the advantages high error, thus, Inaccurate values of the tuned capacitor and inductor cause the centre frequencyofoffset sensitivity and the ability to maintain the signal-to-noise ratio (SNR) with the resonance of the we should leave margins. Therefore, the bandwidth of to the sensorbroadband is usually tunedadequate capacitor and inductor. However, this configuration may lead a distorted FIDset to 200 Hz Thedesign maximum bandwidth of the 105 Hz when T 2* is 30 msits [7].narrow-band To ensure that allis lower than or more. Thesignal. tuned is rarely used forsignal the is MRS sensor because signals measured by the sensor are bandwidth of the sensor must be greater 200 Hz. TheFID non-tuned design (Figure 1b)undistorted, has onlythe two parts without the tuned capacitor C; its than 105 Hz. Inaccurate values of the tuned capacitor and inductor cause the centre frequency offset amplitude-frequency characteristics are shown in Figure 1c (the blue curve), exhibiting a very flat full error, thus, we should leave adequate margins. Therefore, the bandwidth of the sensor is usually set to 200 Hz orand more.0The design is rarely for the MRS sensor because narrow-band is FID signals frequency bandwidth dBtuned magnitude. This used configuration, which can its measure valid than digital 200 Hz. signal The non-tuned design because (Figure 1b) twobandwidth, parts without is thecurrently tuned and facilitatelower the post processing ofhas theonly broad the most capacitor C; its amplitude-frequency characteristics are shown in Figure 1c (the blue curve), commonly used structure; however, its sensitivity is lower than that in the tuned case. The sensitivity exhibiting a very flat full frequency bandwidth and 0 dB magnitude. This configuration, which can measure valid FID signals andthe facilitate the post digital signal processing because ofIntheMRS broadapplications, of a coil sensor directly determines performance of an MRS instrument. bandwidth, currently the enables most commonly used structure; however, its sensitivity is lowerlocated than increasing the sensor issensitivity the system to detect thinner or deeper aquifers. that in the tuned case. The sensitivity of a coil sensor directly determines the performance of an MRS In addition, the preamplifier of the coilincreasing sensor using the sensitivity tuned orenables non-tuned configurations may be instrument. In MRS applications, the sensor the system to detect thinner orelectromagnetic deeper located aquifers. In addition, the preamplifier the coil sensor using the tuned or saturation saturated in strong noise environments. Theofreasons for the preamplifier non-tuned configurations be saturated in strong electromagnetic noise environments. The distortion will be analysed in the may following section. reasons for the preamplifier saturation distortion will be analysed in the following section.

Figure 1. Schematics of the coil sensors with tuned and non-tuned configurations. (a) The tuned

Figure 1. Schematics of non-tuned the coil design; sensors tuned and non-tuned configurations. (a) The tuned design; (b) The (c) with The amplitude-frequency characteristic curves of tuned and non-tuned configurations. design; (b) The non-tuned design; (c) The amplitude-frequency characteristic curves of tuned and non-tuned configurations.

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2.2. The Coil Sensor Sensor Nonlinear Distortion Distortion 2.2. 2.2. The The Coil Coil Sensor Nonlinear Nonlinear Distortion The power power harmonic noises noises generated by by the power power line or or AC power power grid are are the most most serious The The power harmonic harmonic noises generated generated by the the power line line or AC AC power grid grid are the the most serious serious interference sources in developed areas. Here, we show a group of power harmonic noises (Figure 2) interference interference sources sources in in developed developed areas. areas. Here, Here, we we show show aa group group of of power power harmonic harmonic noises noises (Figure (Figure 2) 2) collected on on aalawn lawnofofChangchun ChangchunCity Citybyby a 100 m × 100 m square coil that is directly connected to collected a 100 m × 100 m square coil that is directly connected to the collected on a lawn of Changchun City by a 100 m × 100 m square coil that is directly connected to the analogue-to-digital (A/D) acquisition card. shownininFigure Figure 2a,the the amplitudeof of the harmonic harmonic analogue-to-digital (A/D) acquisition card. AsAs shown the analogue-to-digital (A/D) acquisition card. As shown in Figure2a, 2a, theamplitude amplitude ofthe the harmonic noises is so high that it reaches 180 mV, especially the low-frequency harmonics (the part noises high thatthat it reaches 180 mV, especially the low-frequency harmonics harmonics (the part surrounded noises isissoso high it reaches 180 mV, especially the low-frequency (the part surrounded by the red circle in Figure 2b), whose amplitudes are hundreds of times greater than by the red circle in Figure 2b), whose amplitudes are hundreds of times greater than those of the other surrounded by the red circle in Figure 2b), whose amplitudes are hundreds of times greater than those of the other high-frequency harmonics. The low-frequency harmonics with large amplitude is high-frequency harmonics. The low-frequency harmonics with large amplitude oneamplitude of the main those of the other high-frequency harmonics. The low-frequency harmonics with is large is one of the main reasons fornonlinear the coil sensor nonlinear distortion. reasons for the coil sensor distortion. one of the main reasons for the coil sensor nonlinear distortion.

Figure 2. power harmonic noise waveforms. (a) Time waveform; (b) Frequency domain Figure 2. The The power harmonic noise waveforms. (a) domain Time domain waveform; (b) Frequency Figure 2. The power harmonic noise waveforms. (a) Time domain waveform; (b) Frequency domain waveform. domain waveform. waveform.

Moreover, we find that the circuit structure of the traditional MRS data acquisition system with Moreover, structure of of thethe traditional MRS data acquisition system withwith the Moreover,we wefind findthat thatthe thecircuit circuit structure traditional MRS data acquisition system the coil sensor (the part surrounded by the red dotted line in Figure 3) is another reason for the coil coil (the part surrounded by thebyred line inline Figure 3) is another reason reason for the for coilthe sensor the sensor coil sensor (the part surrounded thedotted red dotted in Figure 3) is another coil sensor nonlinear distortion. As shown in Figure 3, the bandpass filter after the preamplifier is nonlinear distortion. As shown Figurein3,Figure the bandpass filter afterfilter the preamplifier is ineffective sensor nonlinear distortion. As in shown 3, the bandpass after the preamplifier is ineffective because the distortion of the coil sensor has already occurred. because the distortion of the coil sensor has already occurred. ineffective because the distortion of the coil sensor has already occurred. The coil sensor The coil sensor

A A Pickup Pickup coil coil

Preamplifier Preamplifier

A A

Bandpass Bandpass filter filter

Second stage Second stage amplifier amplifier

ADC ADC A/D A/D converter converter

Figure 3. The traditional MRS data acquisition system. Figure 3. 3. The traditional traditional MRS MRS data data acquisition acquisition system. system. Figure

2.3. Design of the Matching Network 2.3. Design Design of of the the Matching Matching Network Network 2.3. To improve the sensitivity of the broadband coil sensor and suppress the low-frequency Toimprove improvethethe sensitivity ofbroadband the broadband coil and sensor and suppress the low-frequency To sensitivity the suppress the low-frequency harmonics, we propose a newofcircuit structurecoil ofsensor the MRS data acquisition system, asharmonics, shown in harmonics, we propose a new circuit structure of the MRS data acquisition system, as shown in we propose a new circuit structure of the MRS data acquisition system, as shown in Figure 4. The Figure 4. The CSMN (the part is surrounded by the red dotted line in Figure 4) is designed by adding Figure 4. The CSMN (the part isby surrounded by the redindotted lineisindesigned Figure 4)by is designed adding CSMN (the part the red dotted line Figure adding anbyLC filter an LC filter withisa surrounded matching capacitor between the pickup coil 4) and the preamplifier compared with an LC filter with a matching capacitor between the pickup coil and the preamplifier compared with with a matchingbroadband capacitor between the pickup coil and theMRS preamplifier compared the traditional the traditional non-tuned coil sensor in an instrument (Figurewith 3). The matching the traditional broadband non-tuned coil sensor in an MRS instrument (Figure 3). The matching broadband non-tunedincoil sensorwith in an instrument (Figure matching capacitor capacitor connected parallel anMRS LC filter (the blue part 3). in The Figure 4) composes the connected matching capacitor connected in parallel with an LC filter (the blue part in Figure 4) composes thethe matching in parallelaswith an LC (thesensor. blue part in Figure 4) composes the matching network as core of network the core of filter the new network as the core of the new sensor. the new sensor.

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The coil sensor The coil sensor

A A Pickup Pickup coil coil

Matching Matching capacitor capacitor

LC filter LC filter

Preamplifier Preamplifier

A A

Bandpass Bandpass filter filter

Second stage Second stage amplifier amplifier

ADC ADC A/D A/D converter converter

Figure 4. The new MRS data acquisition system. Figure 4. The Figure 4. The new new MRS MRS data data acquisition acquisition system. system.

We consider an LC filter with a bandwidth of 1500 Hz and a centre frequency of 2330 Hz as an We consider an LC filter with a bandwidth of 1500 Hz and awhich centre frequency ofthree 2330 Hz as an example to introduce matching network’s design theof We consider an LCthe filter with a bandwidth of 1500 method, Hz and a centreincludes frequency 2330 following Hz as an example to introduce the matching network’s design method, which includes the three following steps: example to introduce the matching network’s design method, which includes the three following steps: steps: (1) The The topology topology of of the the LC LC bandpass bandpassfilter filter (1) (1) The topology of the LC bandpass filter Toeffectively effectivelysuppress suppress low-frequency harmonics, ofLC thefilter LC filter 500 less To thethe low-frequency harmonics, the the gaingain of the at 500atHz is Hz lessisthan To effectively suppress the low-frequency harmonics, the gain ofto the LC filter at 500and Hz reduce is less than −30 dB, and the gain at 100 Hz is less than −50 dB. In addition, simplify design −30 dB, and the gain at 100 Hz is less than −50 dB. In addition, to simplify design and reduce cost, than −30 dB, and the gain at Hz 3-order is less than −50 dB. bandpass In addition, to simplify and 5. reduce cost, the topology of 100 π-type LCbandpass passive filter, as showndesign Figure (Note we usewe theuse topology of π-type 3-order LC passive filter, as shown in Figure 5.in(Note that other cost, we use the topology of π-type 3-order LC passive bandpass filter, as shown in Figure 5. (Note that other circuit structures can also be selected, such as T-type 5-order filter, as long as the design circuit structures can also be selected, such as T-type 5-order filter, as long as the design indicators can that other circuit structures can also be selected, such as T-type 5-order filter, as long as the design indicators be met.) can be met.) indicators can be met.)

Rs Rs Vi Vi

C2 C2

L2 L2

L1 C1 L1 C1

L3 C3 L3 C3

Vo RL Vo RL

Figure Figure5.5.ππtype type33order orderLC LCpassive passivebandpass bandpassfilter. filter. Figure 5. π type 3 order LC passive bandpass filter.

(2) (2) The The approximate approximatefunction functionand andthe thecalculation calculationof ofthe theparameters parametersof ofthe thefilter filter (2) The approximate function and the calculation of the parameters of the filter To Toavoid avoidFID FIDdistortion, distortion, we wechoose choosethe theButterworth Butterworth function, function, which which has has the the advantage advantage of of To avoid FID distortion, we choose the Butterworth function, which has the advantage of relative passband. As Asmentioned mentionedabove, above, selected bandwidth = 1500 Hz relative flatness flatness in in the passband. thethe selected bandwidth BWBW = 1500 Hz and relative flatness inF0the As LC mentioned above, selected bandwidth BW frequency =and 1500 Hzcutoff and and centre frequency Fpassband. 2330 of the LCleads filter the −3cutoff dB low cutoff and centre frequency = 2330 of Hz the filter toleads thethe −3to dB low frequency high 0 = Hz centre frequency LCand filter leads the dB low+cutoff frequency and high cutoff high cutoff frequency of FHz = of F0the −Hz BW/2 = and−3 BW/2 = 3080The Hz, respectively. frequency of FL =FF0 0=−2330 BW/2 1580 FH1580 = F0 Hz +toBW/2 =F3080 respectively. relative centre L = H = FHz, 0 frequency of F L = F0 − BW/2 = 1580 Hz and FH = F0 + BW/2 = 3080 Hz, respectively. The relative centre 1/2 1/2 The relativeand centre and the factor can calculated = (FLHz × and FH ) Q ==F2206 Hz= frequency thefrequency quality factor canquality be calculated as Fbe m = (FL × FH) as F=m2206 m /BW frequency the quality factor asTable Fm = 1, (FLwe ×values FHcan ) 1/2Kfind =1 2206 Hznormalized and = FKm2values /BW = and = and Fm /BW = 1.47, respectively. 1.47,Qrespectively. From Table 1,can we be cancalculated findFrom the normalized = Kthe 3 = K = 1, Q and = 2. In 1.47, respectively. From Table 1, we can find the normalized values K 1 = K3 = K = 1, and K2 = 2. In Kaddition, 1, andthe K2 thermal = 2. In addition, to reduce the thermal noise R ofL the we choose to =reduce noise of the preamplifier, we choose = R preamplifier, = 50 Ω. According to the 1 = K3 = K addition, to reduce the thermal noise of the preamplifier, we choose R L = R = 50 Ω. According to the Rnormalized Ω. According to the normalized values and the value empirical formula, we calculate the and the empirical formula, we calculate of each parameter as follows: L1 L = R = 50 values normalized and the empirical formula, we calculate the value ofQK/(2πRF each parameter as) μF follows: L2 1= value eachvalues parameter asmH, follows: = L = R/(2πKQF ) = 2.46 mH, L = QRK /(2πF = 10.6 mH, = L3 =ofR/(2πKQF m) = 2.46 L2 = L QRK 2 /(2πF m ) = 10.6 mH, C 1 = C 3 = m ) = 2.12 and C m m 1 3 2 2 =C1/(2πRQK L3 = R/(2πKQF m) = 2.46 mH, L2 = QRK2/(2πFm) = 10.6 mH, C1 = C3 = QK/(2πRFm) = 2.12 μF and C2 = = 2.12 µF and C2 = 1/(2πRQK2 Fm ) = 0.491 µF. 2Fm) = 0.491 m )μF. 1 = C3 = QK/(2πRF 1/(2πRQK2Fm) = 0.491 μF. Table Table1.1.Normalized Normalizedvalues valuesof ofππtype type33order orderLC LCfilter. filter. Table 1. Normalized values of π type 3 order LC filter. π π Bessel Chebyshev Bessel Butterworth Butterworth Chebyshev

π K1 K KK1 2 1 K2 KK2 3 K3 K3

Bessel Butterworth 0.337 1.000 0.337 1.000 0.337 1.000 0.971 2.000 0.971 2.000 0.971 2.000 2.203 1.000 2.203 1.000 2.203 1.000

Chebyshev 1.633 1.633 1.633 1.436 1.436 1.436 1.633 1.633 1.633

Theamplitude-frequency amplitude-frequency characteristic designed is shown in Figure 6 (the The characteristic curve curveof ofthe theLC LCfilter filter designed is shown in Figure 6 The amplitude-frequency characteristic curve of themeet LC filter designed is shown in Figure 6at(the red curve). The test results show that the LC filter can the design indicators with a gain 500 (the red curve). The test results show that the LC filter can meet the design indicators with a gain at red results that LCdB, filter can meet theofdesign indicators withflat a gain at 500 Hz curve). of −53.5The dB,test a gain at show 100 Hz of the −95.4 a bandwidth 1580 Hz and a very passband. Hz of −53.5 dB, a gain at 100 Hz of −95.4 dB, a bandwidth of 1580 Hz and a very flat passband.

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However, the gain within passband of the filter of −6.02 dB is problematic because the FID signal 500 Hz of −53.5 dB, a gain at 100 Hz of −95.4 dB, a bandwidth of 1580 Hz and a very flat passband. will be attenuated by half through the filter, thereby increasing the difficulty of signal detection However, 6.02 dB is problematic However, the the gain gain within within passband passband of of the the filter filter of of − −6.02 problematic because because the the FID FID signal signal (even reducing the detection depth). The solution for this attenuation problem will be introduced in will will be be attenuated attenuated by by half half through through the the filter, filter, thereby thereby increasing increasing the the difficulty difficulty of of signal signal detection detection the next step. (even (even reducing reducing the the detection detection depth). The solution for this attenuation attenuation problem problem will will be be introduced introduced in in the next step. the next step.

Figure 6. The amplitude-frequency characteristic curves of the filter. (a) The LC filter; (b) The LC filter connected with the pickup coil; (c) The LC filter connecting in parallel with a matching Figure 6.6. The The amplitude-frequencycharacteristic characteristic curves filter. (a) The LC filter; (b)LC Thefilter LC Figure curves of of thethe filter. (a) The LC filter; (b) The capacitor andamplitude-frequency the pickup coil. filter connected with the pickup coil; (c) The LC filter connecting in parallel with a matching connected with the pickup coil; (c) The LC filter connecting in parallel with a matching capacitor and capacitor the pickup coil. pickupand coil. (3) the Selection of the matching capacitor

As an example, we takecapacitor a 100 m × 100 m square pickup coil with one turn, which can be (3) Selection of the matching (3) Selection of the matching capacitor equivalent to a series circuit of an inductor (L = 0.8 mH) and a resistor (Rs = 4 Ω). The As an example, we take a 100 m × 100 m square pickup coil with one turn, which can be amplitude-frequency curve of square the LCpickup filter connected with the which pickupcan coil is shown in As an example, wecharacteristic take a 100of m× m withand one equivalent to a series circuit an100 inductor (L = 0.8coil mH) aturn, resistor (Rs =be 4equivalent Ω). The Figure 6b (the blue curve). It can be seen that the curve is obviously distorted and the gain in the to a series circuit of an inductor (L curve = 0.8 mH) resistor (Rs = 4with Ω). the Thepickup amplitude-frequency amplitude-frequency characteristic of theand LC afilter connected coil is shown in passband of the filter the is attenuated. characteristic curve LCItfilter withthe thecurve pickup is shown in Figureand 6b (the Figure 6b (the blueofcurve). canconnected be seen that is coil obviously distorted the blue gaincurve). in the To solve the above problem, our idea is to connect a matching capacitorofinthe parallel with the LC It can be seen that the curve is obviously distorted and the gain in the passband filter is attenuated. passband of the filter is attenuated. filterTotosolve cancel the influence of our the pickup coil on the post-stage circuit. The new passive filter To solve the the above above problem, problem, our idea idea is is to to connect connect aa matching matching capacitor capacitor in in parallel parallel with with the the LC LC connected to the matching capacitor and the pickup coil is shown in Figure 7 (the matching capacitor filter to cancel the influence of the pickup coil on the post-stage circuit. The new passive filter connected filter to cancel the influence of the pickup coil on the post-stage circuit. The new passive filter is the located within the red dotted line). find that the effect matching of the pickup coil on the to matching the pickup coilWe is shown located connected to thecapacitor matchingand capacitor and the pickup coilinisFigure shown7in(the Figure 7 (the capacitor matchingiscapacitor amplitude-frequency characteristic bethe cancelled when the reactance of theamplitude-frequency equivalent inductor within the red dotted findcan that the pickup coil on is located within theline). red We dotted line). Weeffect findofthat the effect of the the pickup coil on the and the matching capacitor is zero at the centre frequency (F 0 = 2330 Hz). The value of the matching characteristic can be cancelled when the the equivalent and the matching amplitude-frequency characteristic canthe be reactance cancelled of when reactanceinductor of the equivalent inductor capacitor C can be calculated as: capacitor is zero atcapacitor the centreisfrequency Hz). The(F value of the matching capacitor C can be 0 = 2330 and the matching zero at the(Fcentre frequency 0 = 2330 Hz). The value of the matching calculated capacitor Cas: can be calculated as: 1 1  5.8μF (1) 2 CC= = 5.8µF (1) 2 F001)2 ×LL (2πF C  5.8μF (1) 2

 2 F0  C2

L2

C

C2 L1 C1

L2

C

L1 C1

Rs L

Rs

LV

i

Vi

L

L3 C3 L3 C3 RL RL

Vo Vo

Figure 7. 7. The circuit structure structure of of the the LC LC bandpass bandpass filter filter connecting connecting aa matching matching capacitor. capacitor.

Figure 7. The circuit structure of the LC bandpass filter connecting a matching capacitor.

The amplitude-frequency amplitude-frequencycharacteristic characteristic curve ofnew the passive new passive filter connected to the The curve of the filter connected to the matching matching and capacitor and the pickup coil in is shown in Figure 6 (the greenThe curve). The gain of the new capacitor the pickup coil is characteristic shown Figure 6 (the curve). the new filter at The amplitude-frequency curve of green the new passive gain filterofconnected to the filter at 500 Hz and at 100 Hz is −40 dB and −73.8 dB, respectively, and the gain in the passband is 4.6 500 Hz and at 100 Hz is − 40 dB and − 73.8 dB, respectively, and the gain in the passband is 4.6 dB, matching capacitor and the pickup coil is shown in Figure 6 (the green curve). The gain of the new dB, which eliminates the attenuation. bandwidth The bandwidth offilter the filter has changed, and−the dB and low which the of respectively, the hasand changed, and 3 dB−3low filter ateliminates 500 Hz and atattenuation. 100 Hz is −40The dB and −73.8 dB, the gain inthe the passband is 4.6 and high frequencies are 1730 Hz 2760 and 2760 Hz, respectively. In the fact,bandwidth the bandwidth (BW = 1030 high cutoffcutoff frequencies areattenuation. 1730 Hz and Hz, respectively. In fact, Hz) dB, which eliminates the The bandwidth of the filter has changed, and(BW the =−31030 dB low Hz) is adequate for detecting the FID signals in most areas. Moreover, according to actual needs, we and high cutoff frequencies are 1730 Hz and 2760 Hz, respectively. In fact, the bandwidth (BW = 1030 can design a larger or smaller bandwidth based on the above design method. Hz) is adequate for detecting the FID signals in most areas. Moreover, according to actual needs, we can design a larger or smaller bandwidth based on the above design method.

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isSensors adequate for2463 detecting the FID signals in most areas. Moreover, according to actual needs, we7can 2017, 17, of 16 Sensors 2017, 17, 2463 7 of 16 design a larger or smaller bandwidth based on the above design method. Note Notethat thatthe thematching matchingnetwork networkisissensitive sensitivetotothe theparameters parametersofofthe thepickup pickupcoil. coil.The Theequivalent equivalent Note that the matchingresistance network isofsensitive to the ofinfluence the pickup coil. equivalent inductance and equivalent the pickup pickup coilparameters haveaagreat great influence on theThe performance inductance and equivalent the coil have on the performance of inductance and equivalent resistance of the pickup coil have a great influence on the performance of of the matching network. We analyse the characteristics of the matching network with different the matching network. We analyse the characteristics of the network with different the matching network. We analysevia the characteristics of the The matching network with results different inductances and different resistances Monte Carlo simulation. Monte Carlo analysis of inductances and different resistances via Monte Carlo simulation. The Monte Carlo analysis results inductances and different resistances via Monte Carlo simulation. The Monte Carlo analysis the equivalent inductance (Figure 8) 8) show that only the amplitude-frequency ofofthe of the equivalent inductance (Figure show that only the amplitude-frequencycharacteristics characteristicsresults the of thewith equivalent (Figure 8) show that only the amplitude-frequency characteristics of the filter LL==0.8 mH curve) isis correct, whereas the filter with 0.8inductance mH(the (thegreen green curve) correct, whereas the results results of of other other values values are are distorted. distorted. filter with L = 0.8 mH (the green curve) is correct, whereas the results of other values are distorted. The TheMonte MonteCarlo Carloanalysis analysisresults resultsof ofthe theequivalent equivalent resistance resistance (Figure (Figure 9) 9)show showthat thatthe thegain gainin inthe the The Monte Carlo analysis results of the equivalent resistance (Figure 9) show that the gain in the passband increases as the resistance reduces. passband increases as the resistance reduces. passband increases as the resistance reduces.

Figure8.8.Monte MonteCarlo Carloanalysis analysisof ofthe theequivalent equivalentinductance inductanceof ofthe thepickup pickupcoil. coil. Figure Figure 8. Monte Carlo analysis of the equivalent inductance of the pickup coil.

Figure 9. Monte Carlo analysis of the equivalent resistance of the pickup coil. Figure 9. 9. Monte Carlo analysis analysis of of the the equivalent equivalent resistance resistance of of the the pickup pickup coil. coil. Figure Monte Carlo

Therefore, we designed a new coil sensor with a matching network. To make effective use of Therefore, wevalue designed a new coil sensor with a matching network. To make effective use of the Therefore, CSMN, thewe of the matching capacitor using formula formake different equivalent designed a new coil sensor with aby matching network.1 To effective use of the CSMN,ofthe value ofcoil the matching capacitor by using formula 1 for different equivalent parameter the pickup should be adjusted. the CSMN, the value of the matching capacitor by using formula 1 for different equivalent parameter parameter of the pickup coil should be adjusted. of the pickup coil should be adjusted. 3. Equivalent Circuit of the CSMN with Noise Sources 3. Equivalent Circuit Circuit of of the the CSMN CSMN with with Noise Noise Sources Sources 3. Equivalent In this section, equivalent circuits of the CSMN with the noise source are analysed. Figure 10 In this this section, equivalent circuits of the CSMN CSMN withsources. the noise noise source source are are analysed. analysed. Figure Figure 10 10 In equivalent circuits the with the presents thesection, schematic diagrams of the of CSMN with noise presents the the schematic schematic diagrams diagrams of of the the CSMN CSMN with with noise noise sources. sources. presents 3.1. The Proposed CSMN 3.1. The The Proposed Proposed CSMN CSMN 3.1. As shown in Figure 10, the CSMN consists of three stages, namely, the air core coil, a matching As shown shown Figure 10, the three namely, the core coil, coil, matching As inlow Figure 10, theCSMN CSMNconsists consists of three stages, namely, the air air detect core matching network and ain noise preamplifier. The airof core coilstages, is used to effectively theaaFID signal, network and a low noise preamplifier. The air core coil is used to effectively detect the FID signal, network and a low noise preamplifier. The air core coil is used to effectively detect the FID signal, which is indicated by the variations of the magnetic field. A low noise preamplifier is designed to which is aindicated the avariations of rejection the magnetic lowcontrol noise preamplifier designed the to achieve high gainbyand high noise ratio.field. Easy A gain is realized byischanging achieve a high gain and a high noise rejection ratio. Easy gain control is realized by changing the value of two resistors R1 and R2, which can amplify the low amplitude signal to a few nV. The value of two resistors R1 and R which can amplify the low amplitude to in a few nV.4.The matching network consisting of2, an LC filter and a matching capacitor issignal shown Figure As matching network consisting of an LC filter and a matching capacitor is shown in Figure 4. As

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which is indicated by the variations of the magnetic field. A low noise preamplifier is designed to achieve a high gain and a high noise rejection ratio. Easy gain control is realized by changing the value of two2017, resistors Sensors 17, 2463R1 and R2 , which can amplify the low amplitude signal to a few nV. The matching 8 of 16 network consisting of an LC filter and a matching capacitor is shown in Figure 4. As mentioned above, mentioned above, the matching network circuit designtomakes to detect FID signals the matching network circuit design makes it possible detect it allpossible FID signals withinallthe passband within the passband filterdistortion. bandwidth without distortion. filter bandwidth without Coil Rs ent

Matching network Z2 ent2

Preamplifier eni ini Pre-A

Z1 Z3 ent1 ent2

L

entr

es

R1

R2

Figure 10. The proposed CSMN circuits with equivalent noise sources. Figure 10. The proposed CSMN circuits with equivalent noise sources.

Considering the gain G(f) of the matching network, the noise floor of the setup is used to Considering the gain G(f ) of the matching network, the noise floor of the setup is used to estimate estimate the CSMN SNR, such that: the CSMN SNR, such that: SNR ese(s (f f))GG(( f ))/e / enn((f )f ) SNR((ff )== (2) (2) where in in thethe coil,coil, andand en (f )endenotes the total equivalent voltage noise where eess(f (f)) is the the output outputsignal signalinduced induced (f) denotes the total equivalent voltage at the input of the preamplifier. This total noise is calculated from all the individual noise sources noise at the input of the preamplifier. This total noise is calculated from all the individual noise depicteddepicted in Figurein10 and consists of three of components (i.e., input voltage eni ,noise inputenicurrent sources Figure 10 and consists three components (i.e., input noise voltage , input 1/2 of all in noise ini ,noise and Nyquist et =noise (4kTRetot )1/2 of all Figure in 10)Figure [17,27].10) We[17,27]. assumeWe these three current ini, and noise Nyquist t = (4kTR tot)resistors resistors assume noise components to be uncorrelated. All these noise contributions can be combined to obtain en as these three noise components to be uncorrelated. All these noise contributions can be combined to expressed obtain en asbelow. expressed below. q en =

e2ni2 + (ini Zi )22 + (4kTRtot2 )2

(3) (3) where Zi is the impedance of all resistors that input current noise flows through, T is the environmental
23 W · flows where Zi isofthe impedance of kallis the resistors that factor input current T is the 1.38 · 10−noise s/K . ethrough, temperature resistance Rtot , and Boltzmann ni and ini represent 23 environmental temperature of resistance Rtot, noise and kofisthe thepreamplifier, Boltzmann factor the input voltage noise and the input current respectively. （1.38 10 W  s/K）. eni and iIn ni represent voltage and thecomponents input current of thewith preamplifier, respectively. summary,the theinput values for thenoise individual of noise the CSMN the matching network Incalculated summary,as:the values for the individual components of the CSMN with the matching can be q
2 network can be calculated as: ini Zi = (ini Z )2 + ini Req , (4)

en = eni +(ini Zi ) +(4kTRtot )

Z =i ((( jωL + Rs )k2Z1 ) + Z2 )k2Z3 , ni Z i = (ini Z ) +(ini Req ) , 1 Z1 = jωL1 k , jω (C + C1 )

Z =(((j L+Rs ) || Z1 )  Z 2 ) || Z3 , Z2 = jωL2 +

1 , jωC2

jωC3

Req = R1 k R2 ,

1 Z =j L2 + where ω is the angular frequency, ω = 2πf.2 jC2

(6) (5) (7)

1 , 1 j (3C Z3 = R L k jωL k  C1,)

Z1 =j L1 ||

(5) (4)

(6) (8) (9)

,

(7)

The Nyquist noise et produced by all resistors included can be obtained as: s Tn =

 √ 2  √ 1 2 q 2 G 4kTR 4kTR Z3s = R || j  L || L ,+ L 3 Z + Z 4kTR eq Rs + jωL R L jC3

Req  R1 || R2 , where ω is the angular frequency, ω = 2πf. The Nyquist noise et produced by all resistors included can be obtained as:

(8) (10)

(9)

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2

 G 4kTRs   4kTRL  2 (10) Tn   Z   Z   4kTReq   Rs  of   are j  L R The above electrical parameters the CSMN analysed, respectively. The CSMN with low L    





input noise can be achieved by adopting an operational amplifier with reasonable input voltage noise The above electrical and input current noise. parameters of the CSMN are analysed, respectively. The CSMN with low input noise can be achieved by adopting an operational amplifier with reasonable input voltage noise and input current noise.Specification of the Preamplifier 3.2. Optimization for Electrical To optimize the CSMN, we investigated the noise en contributions of the CSMN by using different 3.2. Optimization for Electrical Specification of the Preamplifier operational amplifiers. Two low noise operational amplifiers (i.e., INA163 and AD745) are adopted. To optimize CSMN, low-distortion we investigated the noise en contributions the low CSMN using INA163, which is athe low-noise, instrumentation amplifier, has aofvery inputbyvoltage 1/2 1/2 different operational amplifiers. Two low noise operational amplifiers (i.e., INA163 and AD745) are noise Vn = 1 nV/(Hz) @ 2 kHz and a relatively high input current noise In = 0.8 pA/(Hz) @ 2 adopted. INA163, which is a low-noise, low-distortion instrumentation amplifier, has a very low kHz. Conversely, AD745, which is an ultralow-noise, high-speed preamplifier has a slightly higher input voltage voltage noise noiseVVnn==2.9 1 nV/(Hz) relatively lower high input = 6.9 0.8 input nV/(Hz)1/21/2@@2 2kHz kHzand and aa relatively input current current noise noise IInn = 1/2 @ 2 kHz. Conversely, AD745, which is an ultralow-noise, high-speed preamplifier has a 1/2 pA/(Hz) fA/(Hz) @ 2 kHz than INA163. The two resistors R1 and R2 are set to 1 Ω and 100 Ω, respectively. 1/2 @ 2 kHz and a relatively lower input current slightly input voltage noise Vn to = 2.9 All otherhigher electrical parameters are set the nV/(Hz) values calculated in Section 2, as shown in Table 2. The 1/2 noisenoise In = 6.9 @ 2 by kHz thanINA163 INA163.and TheAD745, two resistors R1 and are R2 are set to 1 Ωasand 100 Ω, total en fA/(Hz) of the CSMN using respectively, calculated, shown in respectively. All other electrical parameters are set to the values calculated in Section 2, as shown in Figure 11. Table 2. The total noise en of the CSMN by using INA163 and AD745, respectively, are calculated, as Table 2. Electrical parameters of the proposed CSMN. shown in Figure 11. Parameters

L Table Rs 2.CElectrical L1 parameters C1 L2 of the C2 proposed L3 C3 RL CSMN.

R1

R2

Value 5.8 2.46 2.12 100 Parameters L1 C1 10.6L2 0.491C22.46 L2.12 3 C50 3 R 1 L 0.8 Rs 4 C R1L unit of inductance the unit of capacitance (µF); Value The 0.8 4 5.8 (mH); 2.46 2.12 10.6 0.491the unit 2.46of resistance 2.12 (Ω). 50 1 The unit of inductance (mH); the unit of capacitance (μF); the unit of resistance (Ω).

R2 100

Figure 11. 11. The The total total noises noises of of two two sensors sensors calculated calculated using using AD745 AD745 and and INA163. INA163. Figure

The whole frequency bandwidth can be divided into two regions (i.e., 1/f and broadband The whole frequency bandwidth can be divided into two regions (i.e., 1/f and broadband regions) [28,29]. In the 1/f region, the total noise exhibits the characteristics of a 1/f slope that regions) [28,29]. In the 1/f region, the total noise exhibits the characteristics of a 1/f slope that decreases as frequency increases and reaches the minimum value at the corner frequency. For decreases as frequency increases and reaches the minimum value at the corner frequency. For AD745, AD745, the corner frequency is 200 Hz, which is higher than that of IN163 (i.e., 100 Hz). The the corner frequency is 200 Hz, which is higher than that of IN163 (i.e., 100 Hz). The broadband region broadband region corresponds to higher frequencies than the corner frequency, in which the total corresponds to higher frequencies than the corner frequency, in which the total noise is flat and is the noise is flat and is the mainly usable bandwidth of the MRS instrument system. In the broadband mainly usable bandwidth of the MRS instrument system.1/2In the broadband region, the total noise of region, the total noise of AD745 is as low as 3.66 nV/(Hz) , and IN163 produces a smaller noise (1.76 AD745 is1/2as low as 3.66 nV/(Hz)1/2 , and IN163 produces a smaller noise (1.76 nV/(Hz)1/2 ) than that nV/(Hz) ) than that of AD745. Accordingly, IN163 is chosen as the preamplifier of the CSMN. of AD745. Accordingly, IN163 is chosen as the preamplifier of the CSMN. To measure the total noise en of the CSMN, an inductor is designed and connected to a resistor To measure the total noise en of the CSMN, an inductor is designed and connected to a to simulate a pickup coil, whose equivalent inductance and resistance are 0.8 mH and 4 Ω, resistor to simulate a pickup coil, whose equivalent inductance and resistance are 0.8 mH and respectively. The CSMN is developed by adopting the matching network mentioned above and the 4 Ω, respectively. The CSMN is developed by adopting the matching network mentioned above preamplifier IN163. The dynamic signal analyser 35670A is employed in the shielding room to and the preamplifier IN163. The dynamic signal analyser 35670A is employed in the shielding room to minimize interference outside the room. Figure 12 displays the results. The total noise en in the 1/f minimize interference outside the room. Figure 12 displays the results. The total noise en in the 1/f

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region is very high. The the increase inin frequency until it reaches 20 region The 1/f 1/fnoise noisesharply sharplydecreases decreaseswith with the increase frequency until it reaches HzHz and then decreases Hz. The The total total noise noiseeenn tends tends 20 and then decreasesgradually graduallyininthe theregions regionsbetween between 20 20 Hz Hz and 100 Hz. 1/2 1/2 in the broadband region. to be bestable stableafter afterthe thecorner cornerfrequency frequency100 100 Hz and low 1.78 nV/(Hz) to Hz and is is asas low asas 1.78 nV/(Hz) The agreement agreementbetween betweenthe theexperimental experimentaland and theoretical calculated results shows reliability of The theoretical calculated results shows the the reliability of the the CSMN model noise sources. CSMN model withwith noise sources.

Figure12. 12.The Thetotal totalnoise noiseeenn of of the the proposed proposed CSMN. Figure CSMN.

We evaluate the bandwidth noise of the CSMN at one stacking time according to the total noise We evaluate the bandwidth noise of the CSMN at one stacking time according to the total noise floor measured above. The value equivalent to the square root of the integration of the noise floor in floor measured above. The value equivalent to the square root of the integration of the noise floor in 3 dB bandwidth is described as follows: 3 dB bandwidth is described as follows: r en _ band  Z en 22 (11) B en en _band = (11)



B

where B is the bandwidth. The minimum bandwidth of the system is 200 Hz, which allows one to where is the bandwidth. The minimum bandwidth the system is 200ofHz, allowsnoise one to obtain Bthe valid FID signals [7,30]. Consequently, theofvalue equivalent thewhich bandwidth is obtain the valid FID signals [7,30]. Consequently, the value equivalent of the bandwidth noise is calculated as 25.2 nV, which represents the amplitude of this sensor system noise when the calculated represents the noise amplitude of noise this sensor noise when thethat bandwidth bandwidthasis25.2 200 nV, Hz.which We assume that this is white with asystem Gaussian distribution reduces 1/2 is 200 Hz. We assume that this noise is white noise with a Gaussian distribution that reduces 1/2 a) to (Na) times when averaged Na times (i.e., Na stacking times). In addition, we utilize to the(NAllan times when averagedthe Na optimum times (i.e.,averaging Na stacking times). addition,sensor we utilize the Allan variance to variance to describe time of theInproposed system. The sensitivity of describe the optimum averaging time of the proposed sensor system. The sensitivity of the CSMN can the CSMN can be redefined and predicted based on the Allan variance and the SNR in the next be redefined and predicted based on the Allan variance and the SNR in the next section. section. 4. Sensitivity of the CSMN 4. Sensitivity of the CSMN Signal averaging is usually an effective method for improving the sensitivity. In terms of a Signal averaging is usually an effective method for improving the sensitivity. In terms of a perfectly stable system, the signal could be averaged infinitely in theory, and infinite averaging should perfectly stable system, the signal could be averaged infinitely in theory, and infinite averaging lead to extremely sensitive measurements. However, all real systems are stable only for a limited time should lead to extremely sensitive measurements. However, all real systems are stable only for a because of temperature drifts, etc. Consequently, every real system has an optimum averaging time limited time because of temperature drifts, etc. Consequently, every real system has an optimum that can be described using the Allan variance [31,32]. averaging time that can be described using the Allan variance [31,32]. We utilize the Allan variance to analyse the stability of the new MSR instrument with the CSMN We utilize the Allan variance to analyse the stability of the new MSR instrument with the leading to a detection limit (i.e., the sensitivity) for the FID signal. For a formal description of the CSMN leading to a detection limit (i.e., the sensitivity) for the FID signal. For a formal description of stability of our MRS instrument, we assume a recorded set of N time-series data x. The N elements of the stability of our MRS instrument, we assume a recorded set of N time-series data x. The N the time-series data can be divided into M subsets containing k elements, where M = N/k. Next, each of elements of the time-series data can be divided into M subsets containing k elements, where M = N/k. these subgroups is averaged, and if i denotes the subgroup number, then the subgroup average value Next, each of these subgroups is averaged, and if i denotes the subgroup number, then the subgroup Ai (k) can be calculated: average value Ai(k) can be calculated: 1 k Ai (k ) = ∑ k x(i−1)k+m , i = 1, . . . , M (12) k1 Ai (k )= m=1 x(i -1) k  m , i  1,..., M (12)



k m1

The Allan variance is given by:

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The Allan variance is given by: M 1 M (A Ai ((kk)) − A ))22  i ((k ( A k )) i i ∑ 22M M i 1

2  (k )= 1 σ2A(k) =

A

(13) (13)

i =1

To obtain the optimum averaging time of our new system by Allan variance, 1000 continuous To obtain the optimum averaging time of our new system by Allan variance, 1000 continuous tests (N = 1000) and 1 second acquisition intervals are used. In Figure 13, the black curve is the Allan tests (N = 1000) and 1 second acquisition intervals are used. In Figure 13, the black curve is the Allan variance plot as a function of the integration time. The minimum of the Allan variance representing variance plot as a function of the integration time. The minimum of the Allan variance representing the optimum integration time of 90 s is determined by the intersection of the grey dashed line and the optimum integration time of 90 s is determined by the intersection of the grey dashed line and the the red dashed line. red dashed line.

Figure 13. Allan Allan variance varianceofofthe the new system a function of integration Theand grey red Figure 13. new system as aasfunction of integration time. time. The grey redand dashed dashed lines are used to obtain the maximum available averaging time of 90 s. lines are used to obtain the maximum available averaging time of 90 s.

The Allan variance is proportional to the sensitivity measurement of a given system; therefore, The Allan variance is proportional to the sensitivity measurement of a given system; we can use the Allan variance plot and SNR to redefine and predict the sensitivity of the MRS therefore, we can use the Allan variance plot and SNR to redefine and predict the sensitivity of instrument. First, the broadband noise en-band of the sensor is calculated or measured over the effective the MRS instrument. First, the broadband noise en-band of the sensor is calculated or measured over bandwidth. Second, we use the Allan variance to determine the optimum averaging time Na. Third, the effective bandwidth. Second, we use the Allan variance to determine the optimum averaging the new broadband noise is reduced to en-band/(Na)1/2 after Na averaging1/2 times. Finally, given that the time Na . Third, the new broadband noise is reduced to en-band /(Na ) after Na averaging times. signal is valid in MRS application when the SNR is greater than 2, the sensitivity of a sensor is Finally, given that the signal is valid in MRS application when the SNR is greater than 2, the sensitivity calculated as follows: of a sensor is calculated as follows: √ eess = / NNa a (14)  22eenn_band (14) _ band / In addition, sensitivity of the system with the LCthe filterLC canfilter be obtained In addition,the thehigher higher sensitivity of CSMN the CSMN system with can be according obtained to the formula with the (4.6gain dB) G in (4.6 the passband the matching according to the(2)formula (2)gain withGthe dB) in the of passband of the network. matching network.

√ es _ CSMN =22e en n_band G, es_CSMN _ band / / NN a a/ /G,

(15) (15)

Therefore, sensitivity measurement measurementisis3.12 3.12nV nVwhen when optimum averaging number Therefore, the sensitivity thethe optimum averaging number andand the the broadband noise 90 and respectively. broadband noise are are 90 and 25.225.2 nV, nV, respectively. 5. Experiment Experiment 5. In this performance of the that could the coil the sensor distortion In this section, section,the the performance of CSMN the CSMN that inhibit could inhibit coilnonlinear sensor nonlinear and the high first verified in the laboratory. a field experiment performed to distortion andsensitivity the high is sensitivity is first verified in the Finally, laboratory. Finally, a fieldisexperiment is show the valid measurement of the FID signals with the CSMN. performed to show the valid measurement of the FID signals with the CSMN. 5.1. Experiment Experiment for for Suppressing Suppressing the the Signal Signal Distortion Distortion 5.1. To verify verify the the performance performance of of the the CSMN CSMN system, system, aa comparative comparative experiment experiment between between the the new new To MRS data acquisition system (Figure 4) based on the CSMN and the traditional MRS data acquisition MRS data acquisition system (Figure 4) based on the CSMN and the traditional MRS data acquisition

system (Figure 3) was conducted in laboratory under the same conditions. The technical indices of the systems are as follows. (1) The new MRS system: the LC filter bandwidth is 1030 Hz, the gain within the passband is 4.6 dB, the preamplifier (INA163) gain is 40 dB, the active bandpass filter has

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system (Figure 3) was conducted in laboratory under the same conditions. The technical indices of the systems are as follows. (1) The new MRS system: the LC filter bandwidth is 1030 Hz, the gain Sensors 2017, 17, 2463 12 of 16 within the passband is 4.6 dB, the preamplifier (INA163) gain is 40 dB, the active bandpass filter has a bandwidth of 1000 Hz, and the overall magnification of the new system is 4000. (2) The traditional a bandwidth of 1000 Hz, and the overall magnification of the new system is 4000. (2) The traditional system: the overall magnification of the system is 4000, with a preamplifier (INA163) gain of 40 dB system: the overall magnification of the system is 4000, with a preamplifier (INA163) gain of 40 dB and an active bandpass filter with bandwidth of 1000 Hz. and an active bandpass filter with bandwidth of 1000 Hz. Both systems were tested in the laboratory according to the schematic diagram shown in Figure 14. Both systems were tested in the laboratory according to the schematic diagram shown in Figure A programmable signal source (AFG3021B, Tektronix, Johnston, OH, USA) is used to generate an 14. A programmable signal source (AFG3021B, Tektronix, Johnston, OH, USA) is used to generate an exponential decay signal with E = 500 mV, T * = 150 ms and fL = 2330 Hz. The programmable exponential decay signal with E0 =0 5006 mV, T2* =2 150 ms and fL = 2330 Hz. The programmable signal signal source is connected to a6 2 × 10 times voltage attenuator. Hence, a simulated FID signal with source is connected to a 2 × 10 times voltage attenuator. Hence, a simulated FID signal with a 250 nV a 250 nV amplitude is produced in the signal coil (the blue one in Figure 14). In addition, a signal amplitude is produced in the signal coil (the blue one in Figure 14). In addition, a signal generator generator (HDG2102B, Qingdao Hantek Electronic Co., Qingdao, China) is connected to the noise coil (HDG2102B, Qingdao Hantek Electronic Co., Qingdao, China) is connected to the noise coil (the red (the red coil in Figure 14) to produce a low-frequency power harmonic noise with fixed amplitude coil in Figure 14) to produce a low-frequency power harmonic noise with fixed amplitude at 500 Hz. at 500 Hz. The pickup coil (the green coil in Figure 14) is closely placed in parallel with the signal The pickup coil (the green coil in Figure 14) is closely placed in parallel with the signal coil and the coil and the noise coil. As the three coils have the same configuration, an integrated signal that noise coil. As the three coils have the same configuration, an integrated signal that contains a contains a decaying FID signal with E0 = 250 nV, T2 * = 150 ms, fL = 2330 Hz and a low-frequency decaying FID signal with E0 = 250 nV, T2* = 150 ms, fL = 2330 Hz and a low-frequency power power harmonic noise of 500 Hz can be induced. The inductance of every coil is 0.8 mH, and the harmonic noise of 500 Hz can be induced. The inductance of every coil is 0.8 mH, and the pickup coil pickup coil is connected in series with a 4 Ω resistor to simulate a 100 m × 100 m receiving coil with is connected in series with a 4 Ω resistor to simulate a 100 m × 100 m receiving coil with one turn. The one turn. The programmable signal source is set to external trigger mode, and the signal generator is programmable signal source is set to external trigger mode, and the signal generator is set to set to continuous operation mode. As shown in Figure 14, the specific working process is as follows: continuous operation mode. As shown in Figure 14, the specific working process is as follows: the the controller triggers the programmable signal source to generate the simulated signal through the controller triggers the programmable signal source to generate the simulated signal through the synchronous circuit; meanwhile, the A/D converter is activated and acquires data. synchronous circuit; meanwhile, the A/D converter is activated and acquires data.

Traditional system

Magnetic core

Noise coil

Passive filter system Signal coil

Signal generator (Generating harmonic noise)

Pickup coil

Voltage attenuator

A/D converter Controller Synchronous circuit Programmable signal source

Figure Figure 14. 14. Schematic Schematic diagram diagram of of the the test test in in the the laboratory. laboratory.

We We adjust adjust the the signal signal generator generator so so that that the the amplitude amplitude of of the the 500 500 Hz Hz noise noise is is 10 10 mV mV and and then then perform the comparative experiment between the new system and the traditional system using perform the comparative experiment between the new system and the traditional system using the the method described above. Both groups are stacked 90 times. Similarly, the amplitude of the noise method described above. Both groups are stacked 90 times. Similarly, the amplitude of the noise is is adjusted 200 mV mV and and 300 300 mV mV for for the the experiments. experiments. adjusted to to 150 150 mV, mV, 200 The 0 and T2* are extracted after the experiments, as shown in Table 3. The The key key parameters parametersEE 0 and T2 * are extracted after the experiments, as shown in Table 3. traditional system and the new system can obtain the effective E0 and T2* when the amplitude of the The traditional system and the new system can obtain the effective E0 and T2 * when the amplitude of noise is 10 mV or 150 mV. In addition, the signal accuracy sampled by the new system is higher than the noise is 10 mV or 150 mV. In addition, the signal accuracy sampled by the new system is higher that theoftraditional system because of the lower background noise and thanof that the traditional system because of the lower background noise andhigher highersensitivity sensitivityof of the the new new coil coil sensor sensor system. system. However, E0 and T2* when the amplitudes of However, the the traditional traditional system system cannot cannot obtain obtain the the effective effective E 0 and T2 * when the amplitudes of the In contrast, contrast, the the new new system system can can still still extract extract the the effective effective E E0 and T2* the noise noise are are 200 200 mV mV and and 300 300 mV. mV. In 0 and T2 * at the noise amplitude of 200 mV and 300 mV. When the noise amplitude is 200 mV, the data after the preamplifiers are sampled, as shown in Figure 15. The time-domain signal (Figure 15a) sampled with the traditional system is distorted because of preamplifier saturation. To obtain a better view of the saturation region, the signal from 10 to 30 ms in Figure 15a is enlarged in Figure 15b In contrast,

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at the noise amplitude of 200 mV and 300 mV. When the noise amplitude is 200 mV, the data after the preamplifiers are sampled, as shown in Figure 15. The time-domain signal (Figure 15a) sampled with the traditional system is distorted because of preamplifier saturation. To obtain a better view of the saturation region, the signal from 10 to 30 ms in Figure 15a is enlarged in Figure 15b In contrast, Sensors 2017, 17, 2463 13 of 16 the time-domain signal sampled with the new system is valid without preamplifier saturation, as in Figuresignal 15c. sampled with the new system is valid without preamplifier saturation, as theshown time-domain

shown in Figure 15c.

Table 3. The experimental results in laboratory.

Table 3. The experimental results in laboratory. Traditional System New System Noise Amplitude Traditional System New System T2 * (ms) E0 (nV) T2 * (ms) E0 (nV) Noise Amplitude E0 (nV) T2* (ms) E0 (nV) T2* (ms) 10 mV 245.2 155.6 249.3 152.6 10 mV 245.2 155.6 249.3 150 mV 243.8 154.3 248.5 152.6 153.8 154.3 248.5 200 mV 150 mV * 243.8 * 246.9 153.8 155.2 * 246.9 300 mV 200 mV * * * 246.3 155.2 153.4 300 mV * * 246.3 Remark: The * means that the valid key parameters can’t been extracted because of 153.4 the preamplifier saturation. Remark: The * means that the valid key parameters can’t been extracted because of the preamplifier saturation.

Figure 15. signals afterafter the preamplifier. (a) Signal by using by the using traditional Figure 15. Time-domain Time-domain signals the preamplifier. (a) sampled Signal sampled the system; (b) Enlarged saturation signal from 10 to 30 ms in Figure 15a; (c) Signal sampled by using the traditional system; (b) Enlarged saturation signal from 10 to 30 ms in Figure 15a; (c) Signal sampled by new system with the CSMN. using the new system with the CSMN.

When the noise amplitude is greater than a certain value, the preamplifier of the traditional When the noise amplitude is greater than a certain value, the preamplifier of the traditional system will saturate. This value is determined by the maximum output voltage of the preamplifier system will saturate. This value is determined by the maximum output voltage of the preamplifier U0 and the preamplifier gain A. The value can be calculated as Vmax = U0/A. The maximum output U0 and the preamplifier gain A. The value can be calculated as Vmax = U0 /A. The maximum output voltage of the preamplifier is 4.76 V, and the preamplifier gain is 30 times. Therefore, when the noise voltage of the preamplifier is 4.76 V, and the preamplifier gain is 30 times. Therefore, when the noise amplitude is greater than 158.7 mV, the traditional system cannot obtain the effective data with the amplitude is greater than 158.7 mV, the traditional system cannot obtain the effective data with the signal distortion, whereas the new system can obtain valid data because the CSMN can effectively signal distortion, whereas the new system can obtain valid data because the CSMN can effectively suppress the noise. suppress the noise. 5.2. Experiment Experiment for for the the Sensitivity Sensitivity of of the the CSMN CSMN 5.2. To verify verify the the sensitivity sensitivity performance performance of of the the CSMN CSMN system, system, another another experiment experiment on on the the CSMN CSMN To system was was conducted conducted in in the the shielding shielding room. room. In In this this experiment, experiment, we we used used the the same same technical technical indices indices system and schematic diagram (Figure 14) as those of the experiment described above. The programmable and schematic diagram (Figure 14) as those of the experiment described above. The programmable signal source source is is adjusted adjusted to to generate signal generate an an exponential exponential decay decay signal signal with withEE00==30 30mV, mV,TT2*2 *= =150 150ms msand andfL Hz. InIn addition, signal coil coil f=L 2330 = 2330 Hz. addition,a asimulated simulatedFID FIDsignal signalwith withaa33nV nVamplitude amplitude is is produced produced in in the the signal 77 times voltage attenuator. In this experiment, we did not use the signal generator. through the 1 × 10 through the 1 × 10 times voltage attenuator. In this experiment, we did not use the signal generator. Similarly, as these two coils have the same configuration, an FID signal with E0 = 3 nV, T2* = 150 ms, and fL = 2330 Hz can be induced by the pickup coil. The CSMN system was tested in the same manner as before, and the number of stacking is 90 times. The results obtained by the CSMN system after a digital bandpass filter and 90 stacks are shown as Figure 16. The relaxation FID signal allows the signal to be observed in both the time

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Similarly, as these two coils have the same configuration, an FID signal with E0 = 3 nV, T2 * = 150 ms, and fL = 2330 Hz can be induced by the pickup coil. The CSMN system was tested in the same manner as before, and the number of stacking is 90 times. The results obtained by the CSMN system after a digital bandpass filter and 90 stacks are shown as Figure 16. The relaxation FID signal allows the signal to be observed in both the time (Figure 16a) and frequency domains (Figure 16b) using the CSMN system. An envelope fitting curve with the Sensors 2017, 17, 2463 14 of 16 exponential decay is found (the red line in Figure 16a), and the fitting E0 is 3.5 nV. The agreement between the and calculated shows system can The experimental agreement between thetheoretically experimental and theoreticallyresults calculated results that showsthe thatCSMN the CSMN effectively detect the signal, detect provided its amplitude greater isthan 3 nV. system can the signal, provided itsis amplitude greater than 3 nV. Sensors 2017, 17,effectively 2463 14 of 16 The agreement between the experimental and theoretically calculated results shows that the CSMN system can effectively detect the signal, provided its amplitude is greater than 3 nV.

Figure 16. The results for the CSMN system. (a) Time domain signals (the blue curves) and envelope

Figure 16. The results for the CSMN system. (a) Time domain signals (the blue curves) and envelope fitting curve (the red one); (b) Frequency domain signals. fitting curve (the red one); (b) Frequency domain signals. 5.3. Field Experiment Figure 16. The results the CSMN system. (a) Timesystem, domainasignals (the blue curves) and envelope 5.3. Field Experiment To further verify thefor performance of the CSMN field experiment was conducted in a fitting (the redcity one); Frequency suburb ofcurve Changchun in(b) China. A 100 domain m × 100signals. m square receiving coil with one turn is laid at a

To further verify performance of the CSMN system, a field experiment conducted in a field site near athe brickyard that generates a variety of large amplitude noises. In addition,was a borehole 5.3. Field Experiment suburb of exists Changchun A pumping 100 m ×tests 100were m square receiving coil with oneranging turn is laid at a near the city field in site,China. on which conducted. Ten different q values from to 4.5.verify As were anda90 time stacks were used theexperiment experiment. field site near brickyard that generates variety of large amplitude noises. was In addition, Toa0.2 further theemployed, performance of the CSMN system, a in field conductedainborehole a The detailed drilling data shows three aquifers can receiving be observed atwith a depth of 13–25 m, at a suburb of Changchun city in China. A that 100 m × were 100 mconducted. square one turn is laid exists near the field site, on which pumping tests Ten coil different q values ranging from 37.5–39 m and 45–50 m. The water content of the three aquifers is 5.0%, and the water content of the field site near a brickyard that generates a variety of large amplitude noises. In addition, a borehole 0.2 to 4.5. As were employed, and 90 time were used indata, the10experiment. other underground media layers is 1%. stacks Based on this drilling values of E0 vs. q marked by exists near the field site, on which pumping tests were conducted. Ten different q values ranging The detailed drilling data shows that three cangiven be observed at calculation a depth of red stars and the corresponding fitting curve (the aquifers red curve) are by the forward in 13–25 m, from 0.2 to 4.5. As were employed, and 90 time stacks were used in the experiment. Figure 17. The values of E 0 extracted from the data sampled by the CSMN system are marked by a 37.5–39 m and 45–50 m. drilling The water of the three aquifers 5.0%, and water content The detailed datacontent shows that three aquifers can beisobserved at athe depth of 13–25 m, of the green circle and the corresponding fitting curve of E0 vs. q (the green one) in Figure 17. This fitting other underground media layers is 1%. Based on this drilling data, 10and values of Econtent marked by 0 vs. q of 37.5–39 m and 45–50 m. The water content of the three aquifers is 5.0%, the water the curve of E0 vs. q is in good agreement with that of the forward calculation. The results of the field red starsother and the corresponding fitting curve (the red curve) are given by the forward calculation in underground media layers is 1%. Based on this drilling data, 10 values of E 0 vs. q marked by experiment show the satisfactory performance of the designed CSMN in accurately measuring the red stars and the corresponding fitting curve (the red curve) are given by the forward calculation in Figure 17. FID Thesignals values ofMRS E0 extracted from the data sampled by the CSMN system are marked by a of an system. Figure 17.the Thecorresponding values of E0 extracted from the data by the CSMN system are marked by a green circle and fitting curve of Esampled 0 vs. q (the green one) in Figure 17. This fitting green circle and the corresponding fitting curve of E0 vs. q (the green one) in Figure 17. This fitting curve of E0 vs. q is in good agreement with that of the forward calculation. The results of the field curve of E0 vs. q is in good agreement with that of the forward calculation. The results of the field experiment show the satisfactory performance of the designed CSMN measuring experiment show the satisfactory performance of the designed CSMNininaccurately accurately measuring thethe FID signals ofFID ansignals MRS system. of an MRS system.

Figure 17. E0 vs. q curves extracted by the forward calculation and the CSMN system.

6. Conclusions and Prospects For MRS applications, the proposed CSMN was designed to improve the sensitivity of the system and prevent signal distortion by adding an LC filter with a matching capacitor between the pickup coil and the preamplifier. The CSMN integrates the advantages of the tuned and non-tuned Figure 17. E0 vs. q curves extracted by the forward calculation and the CSMN system. configuration The basic working principle andcalculation design method of CSMN this CSMN were Figure 17. Esensors. vs. q curves extracted by the forward and the system. 0

6. Conclusions and Prospects For MRS applications, the proposed CSMN was designed to improve the sensitivity of the system and prevent signal distortion by adding an LC filter with a matching capacitor between the pickup coil and the preamplifier. The CSMN integrates the advantages of the tuned and non-tuned configuration sensors. The basic working principle and design method of this CSMN were

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6. Conclusions and Prospects For MRS applications, the proposed CSMN was designed to improve the sensitivity of the system and prevent signal distortion by adding an LC filter with a matching capacitor between the pickup coil and the preamplifier. The CSMN integrates the advantages of the tuned and non-tuned configuration sensors. The basic working principle and design method of this CSMN were elaborated, and a generalized electrical model was introduced. The schematic diagrams of the CSMN with noise sources were analysed correspondingly. To minimize the noise floor and maximize the SNR, the operational amplifier of the preamplifier was designed and optimized. To unify the capability of the MRS system detecting the minimum signal, we provided a more rigorous definition of the sensitivity of the MRS instrument using the Allan variance. Compared with the traditional system, the results of the laboratory indicated that the proposed sensor can have a greater ability at suppressing the low frequency noise with a higher sensitivity. Finally, a field experiment was performed using a fabricated sensor to demonstrate the reliability of an MRS system based on the designed matching network. Accordingly, the CSMN not only improves sensitivities of the MRS instrument but also inhibits the signal distortion by suppressing power harmonic noises in the strong electromagnetic interference environment. Moreover, the specifications of the sensor can be changed in accordance with the requirements of the local MRS exploration on the basis of the described optimization procedures. In our future work, the noise sources of the sensor (e.g., coloured noise in the developed areas) and a denoising algorithm will be explored. Acknowledgments: This research was supported by the National Key R&D Program of China (2017YFC0804105), the National Foundation of China (Grant Nos. 41722405, 2011YQ03113, 20140204022GX, and 41374075) and the Fundamental Research Funds for the Central Universities. Author Contributions: T.L. and Y.Z. conceived and designed the experiments; Y.Z., F.T. and S.L. performed the experiments; T.L., Y.Z. and L.W. analyzed the data; T.L. and Y.Z. wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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