# A Highly Sensitive and Miniature Optical Fiber Sensor for Electromagnetic Pulse Fields

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Operational Principles

#### 2.1. Sensor Design

_{L}. Moreover, the LD U1 is connected in series with the FET Q1. Due to the fact that the FET is a voltage-controlled current element and has high input resistance, the electric field signal induced by the antenna directly controls the drain current of the FET and realizes the high resistance output of the antenna-received signal, which is the antenna’s high resistance coupling principle of the electric field sensor. According to the analysis theory of the antenna, when the antenna is coupled with high resistance, the operating bandwidth of the antenna is fully utilized, which provides a broadband foundation for a pulse electric field test. The LD is connected in series with the FET; thus, the drain current of the FET becomes the operating current of the semiconductor laser, which realizes the direct drive of the LD by the antenna receiving the electric field signal, and finally achieves a direct conversion between the electric field signal and the modulated optical signal, which widens the bandwidth of the test system from the source. Then, the transmitted optical signal is received by the receiver and converted into an electrical signal, which is displayed by the oscilloscope.

_{D}and drain-to-source voltage V

_{DS}under different grid-to-source voltage V

_{GS}; here, V

_{GS}represents the voltage of the input signal received by antenna, and I

_{D}is used to drive LD. According to the parameters of FET, LD is customized by Jiuzhou company, which is a high-performance uncooled distributed feedback semiconductor laser (DFB–LD) with the wavelength of 1310 nm, an output power of 7 mW and a cut-off frequency of 2.5 GHz; moreover, the physical diagram of the laser is shown in Figure 4a,b, and the figures show that the laser has a threshold current I

_{t}, which is 4.5 mA. When the driving current generated by FET is less than the threshold current, the laser basically does not emit light or only emits very weak spectral lines. Conversely, when the driving current is greater than FET, the laser starts to emit a laser, and the output light intensity increases linearly with the increase in driving current, which is the operating area of electro-optic modulation. The linear region consistency of the two components determines the performance of the sensor.

_{GG}= −1.24 V; V

_{DD}= 3.3 V; Rs = 11 Ω; R

_{1}= 68 MΩ; R

_{2}= 43 MΩ; R

_{d}= 3.3 Ω; I

_{DQ}= 28 mA; and U

_{GSQ}and U

_{DSQ}are calculated by Equations (1) and (2) and equal −1.07 V and 2.1 V, respectively. The static operating point can be observed in Figure 3b.

_{t}of LD and the saturated drain current I

_{DSS}of the FET. I

_{t}corresponds to the minimum electric field strength and determines that FET is always in the amplification region. Due to the fact that the output power of LD has a large transient allowable value, I

_{DSS}represents the maximum electric field strength. By taking the static operating point Q of the FET as a reference point, when the input voltage in the grid electrode of FET was changed from −0.635 V to +0.635 V (that is, the AC signal is superimposed on the basis of U

_{GSQ}), the maximum and minimum grid-to-source voltages are −0.81 V and −2.08 V, respectively; at the same time, the maximum and minimum drain currents are 4.5 mA and 120 mA, respectively. Hence, the corresponding output optical power range of LD is 0–7 mW. In this case, the sensor can measure negative and positive pulses in an undistorted manner. For the case of only negative pulse or positive pulse, U

_{GSQ}can be adjusted by R

_{1}, R

_{2,}Rs and V

_{GG}to increase or decrease, and the measurement range of 0–1.27 V can be achieved when U

_{GSQ}is assumed at −2.08 V. Similarly, when U

_{GSQ}is set at −0.81 V, the negative pulse with voltage varying from −1.27 V to 0 V could be measured. In addition, when the input voltage is greater than the above measurement range, the appropriate attenuation capacitor C

_{L}is needed, which can be further broaden the measurement range, and the factor depends on the equivalent capacitance of antenna C

_{ant}and its capacitance value.

#### 2.2. Analytic Model

_{ant}, R

_{ant}and L

_{ant}are the equivalent capacitance, resistance and inductance of antenna, respectively. R

_{L}and C

_{L}are the resistance and capacitance of loads.

_{L}is calculated in the S domain and expressed as transfer function G(s).

_{L}C

_{L}) (that is, s

^{2}L

_{ant}C

_{ant}<< 1, sR

_{ant}C

_{ant}<< 1), and Equation (3) can be simplified as follows.

_{L}can be written as follows.

_{0}= ((C

_{ant}+ C

_{L})/(C

_{L}C

_{ant}L

_{ant}))

^{1/2}is the undamped angular frequency of the second-order system, and ζ = R

_{ant}/(2L

_{ant}ω

_{0}) is the damping ratio. Suppose s = jw, u = w/w

_{0}; then, Equation (6) can be written as follows.

_{H}can be expanded, but the resonance spike in the curve will appear, and its peak value M

_{r}increases with a decrease in ζ. By setting d/du|G(u)| as 0, the resonant frequencies f

_{r}and M

_{r}can be derived as follows [28].

_{ant}/(C

_{ant}+ C

_{L}); then, its upper cut-off frequency f

_{H}can be described as follows.

_{H}equals f

_{0}according to Equation (11); thus, its upper cut-off frequency f

_{H}can be simplified into the following.

_{L}and f

_{H}, the time domain output of antenna V

_{L}(t) on the terminal load can be written as follows:

_{ant}= h/(60 × c × (2 × ln(2 × h/a) − 2 − ln4)), h is the length of antenna, a is the radius of antenna and c is the propagation velocity of electromagnetic wave.

#### 2.3. Simulation Nalysis

_{ant}of the antenna is expressed as follows:

_{0}= 120 × (ln(2 × h/a) − 1), which is the average characteristic impedance of the antenna; η = 73.1 × (Z

_{0}× h × (1 − sin(2 × h × k)/(2 × h × k))), which is the attenuation constant of the equivalent transmission line after considering radiation loss; and k = ω/c, which is the wave number.

_{L}and V

_{o}is written in the form of a transfer function, and its frequency domain expression is described as follows:

_{L}(ω) = R

_{L}/(1 + jω × R

_{L}× C

_{L}).

_{L}, i.e., 50 Ω, 1 kΩ and 1 MΩ, and C

_{L}, i.e., 1 pF, 10 pF and 50 pF. The frequency characteristics of the sensor were analyzed based on Equations (14) and (15), which can be observed from Figure 7a.

_{L}and C

_{L}can obviously affect the low-frequency characteristic of the sensor, but it has little influence on its high-frequency characteristic. By fixing R

_{L}at 1 MΩ and increasing C

_{L}from 1 pF to 50 pF by a certain step, the lower cut-off frequency moves towards the direction of low-frequency; this trend broadens the bandwidth of sensor, but the cost is a decrease in gain. Conversely, by fixing C

_{L}at 50 pF and increasing R

_{L}from 50 Ω to 1 MΩ by a certain step, in this case, the change trend of the lower cut-off frequency is similar to the above case, and the only difference is that the gain does not decrease but retains a fixed value, which agrees with the theoretical calculation of the sensor’s lower-frequency in Section 2.2. Furthermore, assuming that R

_{L}is 1 MΩ and C

_{L}is 10 pF, when the size of antenna is changed, the effect on the frequency characteristic of the sensor can be observed from Figure 7b, and the result shows that the change of the antenna’s length and radius generates a distinct influence on the upper cut-off frequency of the sensor but has little effect on its lower cut-off frequency. Furthermore, when the radius a of antenna is maintained at 50 mm, increasing the length h of antenna causes the gain of the sensor to also increase, but the upper cut-off frequency obviously decreases. On the other hand, when the length h of antenna is fixed at 1 mm, increasing the radius a of the antenna causes the gain of the sensor to also increase, but its lower and upper cut-off frequencies do not experience significant change. Meanwhile, compared with the resonance spike of these curves in Figure 7b, it can be observed that the resonance peak of the curve becomes more obvious with an increase in h; that is, the damping ratio ζ shows a decreasing trend. However, with an increase in a, the curve of the frequency response tends to be flat, and the damping ratio ζ has an increasing trend, which means that the physical size of antenna can affect damping ratio ζ. Therefore, by optimizing the design of antenna, the frequency response characteristic curves with maximum flatness can be obtained.

_{L}in parallel with C

_{L}. Considering that the square pulse with a sharp edge has rich low frequency and high frequency components (that is, its response can directly reflect the performance of the sensor), the square pulse with 1 kV of the voltage peak, 0.5 ns of rise time and 20 ns of the pulse width was selected as the excitation signal (see Figure 8b), which can form a plane wave environment with 1 kV/m of EMP field strength at the position where the sensor was placed. In this case, Figure 9 shows the pulse responses of loads under different load resistances when h is 30 mm and a is 3 mm and the different sizes of the antenna when R

_{L}is 1 MΩ and C

_{L}is 10 pF.

_{L}is 50 Ω and C

_{L}is 50 pF, which is similar to the differential waveform of square pulses. This case demonstrates that the sensor possesses bad responses characteristic of lower cut-off frequencies. With an increase in R

_{L}, the response waveform becomes better, and the excitation signal can be restored correctly, except for the attenuation on magnitude when R

_{L}is 1 MΩ. In this case, by increasing capacitance C

_{L,}its magnitude will decrease gradually. As a result, a greater R

_{L}can reduce the lower cut-off frequency of the sensor effectively, and a lower C

_{L}can improve its gain (see Figure 9b). Moreover, Figure 9c shows that the gain of the sensor will obviously increase with an increase in the antenna’s length h or radius a. Furthermore, when a is fixed to 1mm and the length h of antenna is increased, a larger vibration occurs at the positions of the rising and falling edge. However, as shown in Figure 9d, the vibration of the edge cannot be improved by changing radius a. Therefore, the degree of edge’s vibration, i.e., the higher upper cut-off frequency of sensor, mainly depends on length h of antenna.

#### 2.4. Selection of Key Parameters

_{L}can be reduced by increasing R

_{L}, C

_{L}and C

_{ant}. The increase in C

_{ant}results in a decrease in its resonant frequency, which limits the high-frequency response characteristics of the sensor. Generally, in order to expand f

_{H}, C

_{ant}was designed to be relatively small (several pF). The value of C

_{L}mainly depends on input capacitance and parasitic capacitance of the load circuit. It can be observed from simulation results that an increase in C

_{L}reduces the output gain and affects the high frequency performance of the sensor. Therefore, the method of increasing R

_{L}is used to reduce f

_{L}. If we need to satisfy the condition that f

_{L}is less than 100 kHz, where C

_{L}+ C

_{ant}equals to 100 pF approximately, then the value of R

_{L}must be greater than 10

^{6}Ω.

_{H}is greatly affected by C

_{ant}, L

_{ant}and C

_{L}. Reducing these parameters can improve f

_{H}. This shows that the physical characteristics of the antenna itself such as its length h and radius a have a great influence on the high-frequency response characteristics of the electric field sensor. According to the theory of the antenna, the maximum upper cut-off frequency f

_{hm}of the sensor can be satisfied as follows.

_{H}is required to reach 1 GHz, then h should be less than 60 mm. Moreover, in order to decrease the influence of the parasitic parameter, a miniature circuit design is adopted for the PCB layout of the electro-optic modulation circuit shown in Figure 10a. Figure 10b,c show the photographs of two sensors. For the weak field sensor, the right part of the shielding shell acts as an antenna (see Figure 10b). Its package size is Φ 13 mm × 70 mm, h is 35 mm, a is 6.5 mm and R

_{L}equals R1/R2, which is 26 MΩ. For the strong field sensor, the wire acts as an antenna (see Figure 10c). Its length can be easily adjusted. Here, the package size is Φ 13 mm × 60 mm, h is 3 mm, a is 0.5 mm, C

_{L}is 100 pF and R

_{L}is also 26 MΩ. The designed strong field sensor can measure higher fields and has a wider measurement range. Conversely, the designed weak field sensor tends to improve sensitivity at the cost of reducing the measurement range, which can be used to test the very low field strength by removing attenuation capacitance C

_{L}. Due to the fact that these circuits use less dissipative elements, a 3.7 V battery can be guaranteed for the normal operation of the circuit for several hours.

## 3. Experimental Results

#### 3.1. Frequency Domain

_{max}of the strong field sensor is −43.6 dBm at 800 MHz, and P

_{min}is −40.7 dBm at 900 MHz. ΔP equals 2.9 dB. For the weak field sensor, P

_{max}and P

_{min}are −22.8 dBm at 100 kHz and −25.1 dBm at 200 MHz, respectively, and ΔP equals 2.3 dB. Obviously, ΔPs of the two sensors are both less than 3 dB; thus, the frequency bandwidth from 100 kHz to 1 GHz of them can be determined.

#### 3.2. Time Domain

_{out}detected by the oscilloscope. As observed in Figure 15b, the measurable linear electric field ranges from 645 V/m to 83 kV/m for the strong field sensor. The converted coefficient k from the electric field-to-output voltage is approximately 94 by examining the linear fit curve, and the correlation coefficient of the sensor is 99.98%, which indicates that the sensor possesses good linearity. With regard to the measurable linear electric field range of sensor, it mainly depends on the linear range of FET adopted; the position of the linear area can be adjusted according to the polarity of the test waveform. In any case, once the output voltage exceeds the maximum value of the linear range, it will no longer increase linearly. Moreover, due to the fact that the relation between the output voltage and the electric field is related to many factors, such as antenna parameters, attenuation capacitor C

_{L}, magnification of FET, the receivers and so on, it is hard to obtain the electric field by calculation; it can only be obtained by conducting tests. As observed from Figure 15a, when the measured field is 83 kV/m, the corresponding voltage value is only 0.8 V, which does not reach the saturation voltage of 1.3 V of FET. Therefore, we can obtain a measurable field greater than 83 kV/m. In addition, the designed weak field sensor has low energy consumption and is powered by a battery; thus, the base noise of sensor system is only 3 mV, which is known by conducting the test. For the weak field sensor, the minimum detectable electric field in the time domain can be tested at approximately 13 V/m (see Figure 15a).

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**The physical diagram (

**a**) and its output characteristic curve (

**b**) of the semiconductor laser.

**Figure 7.**Frequency characteristic curve of the sensor under different load resistances (

**a**) and different sizes of antenna (

**b**).

**Figure 8.**The simulation model of optical-fiber EMP field measurement system (

**a**) and the input EMP field waveform (

**b**).

**Figure 9.**Time domain response waveform of the sensor under (

**a**) different resistances R

_{L}when C

_{L}is 50 pF (h = 30 mm, a = 3 mm); (

**b**) the different capacitance C

_{L}when R

_{L}is 1 MΩ (h = 30 mm, a = 3 mm); (

**c**) the different length h of antenna when a is 1 mm (R

_{L}= 1 MΩ, C

_{L}= 10 pF); and (

**d**) the different radius a of antenna when h is 50 mm (R

_{L}= 1 MΩ, C

_{L}= 10 pF).

**Figure 10.**Photographs of the electro-optic modulation circuit (

**a**), weak field sensor (

**b**) and strong field sensor (

**c**).

**Figure 11.**The test configuration diagram of low frequency (100 kHz–450 MHz) (

**a**) and high frequency (450 MHz–1 GHz) (

**b**) and the location photo of EMR200 and the sensor in GTEM cell (

**c**).

**Figure 13.**The time domain test configuration diagram of the weak field strength test (

**a**) and strong field strength test (

**b**).

**Figure 15.**The relationship between the electric field and output voltage of the weak field sensor (

**a**) and the strong field sensor (

**b**).

PART NUMBER | NE72218 | ||||
---|---|---|---|---|---|

SYMBOLS | PARAMETER AND CONDITIONS | UNITS | MIN | TYP | MAX |

G_{S} | Power Gain at V_{DS} = 3 V, I_{D} = 30 mA, f = 12 GHz | dB | 5 | ||

P_{1dB} | Output Power at 1 dB Gain Compression Point at V_{DS} = 3 V, I_{D} = 30 mA, f = 12 GHz | dBm | 15 | ||

PN | Phase Noise at V_{DS} = 3 V, I_{D} = 30 mA, f = 11 GHz, 100 kHz offset | dBC/Hz | −110 | ||

g_{m} | Transconductance at V_{DS} = 3 V, V_{GS} = 0 V | mS | 20 | 45 | |

I_{DSS} | Saturated Drain Current at V_{DS} = 3 V, V_{GS} = 0 V | mA | 30 | 60 | 120 |

V_{GS(OFF)} | Grid to Source Cut Off Voltage at V_{DS} = 3 V, I_{D} = 100 μA | V | −0.5 | −2 | −4 |

I_{GSO} | Grid to Source Leakage Current at V_{GS} = −5 V | μA | 1 | 10 |

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## Share and Cite

**MDPI and ACS Style**

Zhao, M.; Zhou, X.; Chen, Y.
A Highly Sensitive and Miniature Optical Fiber Sensor for Electromagnetic Pulse Fields. *Sensors* **2021**, *21*, 8137.
https://doi.org/10.3390/s21238137

**AMA Style**

Zhao M, Zhou X, Chen Y.
A Highly Sensitive and Miniature Optical Fiber Sensor for Electromagnetic Pulse Fields. *Sensors*. 2021; 21(23):8137.
https://doi.org/10.3390/s21238137

**Chicago/Turabian Style**

Zhao, Min, Xing Zhou, and Yazhou Chen.
2021. "A Highly Sensitive and Miniature Optical Fiber Sensor for Electromagnetic Pulse Fields" *Sensors* 21, no. 23: 8137.
https://doi.org/10.3390/s21238137