Design of hardware system

To capture the weak current signal emitted from the neutron ionization chamber, a preamplifier circuit utilizing ADA4530-1 was devised [34]. This circuit comprises IVC preamplifier-, second-order low-pass filter-, and inverse amplifier circuits, among others. The schematic diagram of the IVC method can be observed in Fig. 2.

Fig. 2Full-screen View

Schematic diagram of the IVC method

The output voltage of the IVC preamplifier circuit in the ideal state is: $V_0=-R_{\text{f}}{I}_{\text{i}}{}_{\text{n}}$ (1) where V₀ represents an output voltage, R_f represents a feedback resistance value, and Iin represents an input current of the IVC amplification circuit.

As shown in Eq. (1), the feedback resistance value determines the amplification factor of weak currents. It is imperative to carefully select this resistance value, avoiding either too high or too low values. The rationale is that the feedback resistance value must match the input range of the backend ADC to achieve higher resolution. In practice, choosing the feedback resistance value depends on the magnitude of the current being measured. Low currents require a large resistance, while higher currents require a smaller resistance. This study accomplished this goal by utilizing resistance values of 500 MΩand 50 KΩ. The currents are divided into two gears based on these feedback resistance values, namely 10 nA gear (500 MΩ) and 0.1 mA gear (50 KΩ). A gear-switching circuit was designed to achieve automatic resistance switching. This circuit enabled the microcontroller to control the on/off state of the optocoupler TLP521 by manipulating the corresponding pin’s high and low-level outputs, thereby realizing the on/off of the relay for switching gears.

Furthermore, the performance of operational amplifiers can be significantly influenced by various manufacturing processes and material characteristics. These factors can introduce deviations in the output voltage of the IVC amplification circuits. The actual output voltage of this circuit should be: $V_0=-R_{\text{f}}{I}_{\text{i}}{}_{\text{n}}+R_{\text{f}}{I}_{\text{B}}+\left(V_0{}_{\text{s}}-V_0/A\right)，$ (2) where A represents the open-loop gain of operational amplifiers, IB represents the input bias current, and V_0s represents the input offset voltage.

According to Eq. (1) and Eq. (2), if the input bias current and input offset voltage are small and the open-loop gain is large, then the error between the actual output voltage and the ideal situation is relatively small. Therefore, to enhance the accuracy of the measurement system, the operational amplifier ADA4530-1 is employed as a trans-impedance amplifier within the preamplifier circuit, owing to its distinct advantages. These include its ultra-low input bias current, which is much smaller than the measured current, its lower offset voltage, and its high open-loop gain and CMRR, which can minimize the influence of error caused by input voltage drop. Furthermore, the ADA4530-1 also incorporates a built-in guard ring buffer that isolates the input pins, thus preventing interference due to current noise leakage from the PCB board.

The IVC preamplifier circuit, as illustrated in Fig. 3(a), converts weak current signals into voltage signals and subsequently amplifies them. The second-order low-pass filter circuit is employed to mitigate the detrimental effects of high-frequency noise on the measurement system, as depicted in Fig. 3(b). This filter circuit effectively eliminates high-frequency noise from the amplified voltage signal outputted by the amplifier circuit. The inverse amplifier circuit ensures that the voltage value transmitted to the ADC circuit is positive, and its design is shown in Fig. 3(c).

Fig. 3Full-screen View

Hardware circuit diagram. IVC preamplifier circuit (a), Second-order low-pass filter circuit (b), Inverter amplifier circuit (c), and ADC circuit (d)

The ADC circuit converts the output voltage signal from the inverter amplifier circuit into a digital signal representation. The stability and linearity performance of the ADC directly impact the accuracy of the overall measurement system. In this circuit, AD7172-2 with 24-bit high-precision manufactured by Analog Devices, Inc. (ADI) is employed. It can sample the output voltage at a high sampling rate of 100MHz and convert an analog voltage signal into a digital signal, as shown in Fig. 3(d).

When measuring weak current signals, various minor interferences can introduce errors. Consequently, this study implements several measures for the hardware circuit to improve the anti-interference performance of the measurement system during the measurement of weak current signals. Firstly, high-quality PCB with excellent insulation properties is employed to minimize the impact of leakage current. Secondly, a metallic aluminum conductor is utilized to enclose the entire measurement system, creating a Faraday cage that effectively shields electromagnetic interference. Lastly, a triaxial cable with strong anti-interference capabilities is used as the signal input line, with an added insulation layer and shielding braid outside the cable to reduce electromagnetic interference on the weak current signal further.

Design of host computer software system

The host computer software in this system was developed utilizing the integrated development environment (IDE) of Visual Studio and Qt, serving as the pivotal controller for the entire system. Firstly, the main operation page configures the serial port parameters to initiate intercommunication between the host computer and the hardware system. Upon establishing a successful connection, the hardware system executes corresponding operations based on the parsed command packet sent by the host computer. Finally, the hardware system transmits the measured data to the host computer via the serial port. The host computer software analyzes and processes the data packets and displays a 2D weak current signal waveform diagram.

During the weak current measurement process, the presence of interferences arising from experimental environments and leakage currents can introduce noise bursts into the measured signals. These interferences result in fluctuations in the measurement outcomes. The Kalman filtering algorithm can estimate the state of a dynamic system from a series of data with measurement noise when the measurement variance is known [35, 36]. The Kalman filtering algorithm was incorporated into the host computer software program to further enhance the accuracy of the measurement results. This facilitated the filtration of the measured data, thereby effectively enhancing the overall stability of the system.

Test in normal temperature

During the testing process, the weak current measurement system was placed inside the Giant Force constant temperature and low humidity test chamber, with the relative humidity set at 10% and the temperature set at 25 ℃, as illustrated in Fig. 4. The Keithley 6430 source meter was used to generate standard weak currents [37]. The output current waveforms (250 measurement points) of the measurement system are depicted in Fig. 5. It can be observed from Fig. 5 that the waveform data exhibited slight fluctuations around their respective average measurement currents (presented in Table 1) for both the 10 nA and 0.1 mA gears. Moreover, these average values closely approximated the respective standard input currents.

Fig. 4Full-screen View

(Color online) Measurement system in the constant temperature and humidity test chamber

Fig. 5Full-screen View

(Color online) Measurement waveforms in 10 nA and 0.1 mA gears at normal temperature

To further illustrate the above conclusion, the relative errors and relative standard deviations (RSDs) were used to quantitatively evaluate this waveform data [38, 39]. The relative errors between the input standard currents and average measurement currents were employed to represent the accuracy; the RSDs between sample point values and their average measurement currents were employed to represent the precision; and the relative errors and RSDs for the waveform data were obtained, which are also shown in Table 1.

Table 1 shows that the measurement system had very small relative errors and RSDs in both the 10 nA and 0.1 mA gears. For example, their relative errors were maintained less than or equal to 0.086% in 10 nA gear and 0.124% in 0.1 mA gear; when the standard input currents were 1 nA and 0.07 mA, their relative errors reached an astonishing 0.010% and 0.006%, and their RSDs were only 0.0106% and 0.0002%, respectively. These qualitative and quantitative results demonstrate that this system has high accuracy and precision at normal temperatures.

Test in different temperatures

In order to ascertain the performance of a current measurement system at various ambient temperatures, we meticulously conducted a series of temperature experiments within a controlled test chamber. Consistently maintaining each temperature, we meticulously recorded the continuous measurements of the system while subjecting it to distinct standard input currents. When the measurement system was in the 10 nA gear, these standard input current values included 0.5 nA, 1 nA, 4 nA, and 7 nA. Similarly, when the measurement system was in the 0.1mA gear, our chosen standard current values encompassed 0.01 mA, 0.04 mA, 0.07 mA, and 0.1 mA. Subsequently, we proceeded to alter the temperature and repeated these steps. Our experimental endeavors encompassed a broad spectrum of temperatures, encompassing -20 ℃, -10 ℃, 0 ℃, 15 ℃, 35 ℃, 45 ℃, 55 ℃, and 70 ℃.

We averaged some measurement results attained from the distinct input standard current values and presented the averaged results in Table 2 and Table 3. Notably, the data at 25 ℃ were acquired from a previous experiment conducted at normal temperature conditions, contributing valuable reference points for our analysis. Also, the relative errors between the averaged measurement currents and standard input currents were computed, as shown in Table 2 and Table 3.

Table 2 and Table 3 show that the measured values gradually decrease as the temperatures increase under the same input currents. This indicates that temperature has an impact on the measurement system. In Table 3, when the standard input current is set to 0.1 mA, and the ambient temperature falls below 25 ℃, an intriguing phenomenon arises within the measurement system. The system’s output remains stable, unwavering at 0.1 mA. The following rationale can elucidate this occurrence: the value of 0.1 mA at the normal temperature corresponds to the maximum measurement capacity of the ADC. Consequently, when the ambient temperature descends below 25 ℃, the output value of the ADC corresponding to the 10 mA input has already reached the pinnacle of its full-scale measurement capability. As a result, the current value displayed on the host computer remains unaltered, in a state of resolute constancy.

Additionally, the relative errors are less than or equal to 0.484% in the Table 2 and 0.388% in the Table 3.

From Table 2 and Table 3, it can be seen that the influence of temperature on the 10 nA gear is greater than that on the 0.1 mA gear, so the measurement results in the 10 nA gear should be corrected more than in the 0.1 mA gear; in the same standard input currents, using 25 ℃ as the dividing point, the rate of change of the relative error differs on both sides. For example, in the 10 nA gear, the relative error gradually decreases with increasing temperatures, reaching its minimum at 25 ℃. Subsequently, as the temperature rises again, the relative error gradually increases. A similar situation also occurs in the 0.1 mA gear, except for 0.01 mA. This indicates that temperature significantly impacts the accuracy of our system, and it is necessary to correct the influence of temperature. Furthermore, under identical temperature conditions, in addition to normal temperature conditions, distinct input standard current values yield varying degrees of relative error when subjected to measurement. This revelation implies an intrinsic correlation between the input current and the resultant relative error.

In addition, the possible reasons for the absence of this phenomenon in 0.01 mA data are the comprehensive results of noise interference and temperature influence. The noise interference of the measurement system cannot be completely eliminated. In the same gear, the lower the input current, the higher the proportion of noise interference in the current. This implies that more gears can be adopted to reduce the proportion of noise interference by making the ADC a high-bit output. The output current is also affected by temperature, leading to unstable output results.

Temperature correction model

We have established a mathematical relationship to accurately depict the influence of temperatures on the output current, as illustrated in Eq. (3). Notably, we observed that the slopes on either side of the normal temperature (25 ℃) in Table 2 and Table 3 were different. Therefore, the data was divided into two categories for obtaining parameter values in Eq. (3): temperatures below and above 25 ℃.

In this study, we focused on analyzing the output current values of the 10 nA gear at temperatures below 25 ℃. Initially, we conducted a linear regression analysis, examining the values of standard input current (x) and output current (y) at various temperatures (T). The detailed outcomes of this regression analysis can be found in Table 4. $y=K_{\text{T}}\times x+C$ (3) where K_T represents the slope value at temperature T and C represents an intercept.

Based on the data presented in Table 4, it was observed that all five linear fittings exhibited an R² value of 1, indicating a commendable level of fitting accuracy. This implied that the linear equations could effectively describe the relationship between the input standard current value and the corresponding output current value at the same temperature.

On the other hand, the intercept values in the five fitting equations were very small at different temperatures, having a very small impact on the output current values. This intercept part was disregarded in our model. When discussing the relationship between the system output current value and temperature, we only considered the relationship between the slope values of the linear equations and temperatures. Hence, the relationship between the two can be described by the following linear equation: $y=K_{\text{T}}\times x.$ (4) According to Eq. (4), we can use the relationship between K_T and y to correct measurement errors caused by temperatures. The corrected output currents can be represented by the slope values and output current values as follows: $Y=1/K_{\text{T}}\times y,$ (5) where Y represents the corrected output current value.

When the same current value is input, the measurement system operates at different ambient temperatures and generates different K_T values. In order to correct the measurement error of the system at a certain temperature, it is necessary to find the relationship between the slope value and the temperature difference Δ T. The temperature difference Δ T and the five slope values in Table 4 were linearly fitted, where Δ T (Eq. (6)) represents the difference between the ambient temperature and 25 ℃. The linear fitting equation was shown in Eq. (7). $\Delta T=T-25$ (6) $K_{\text{T}}=-0.0000868\times \Delta T+0.9999$ (7) Eq. (7) shows a high degree of goodness of fit, indicating a strong linear relationship between the temperature difference (Δ T) and the slope values. This suggests that the slope values also increase or decrease consistently as the temperature difference increases or decreases. This linear relationship allows us to accurately correct the measurement error based on the ambient temperature difference. Thus, the temperature correction equation for the 10 nA gear at ambient temperature below 25 ℃ is: $Y_1=y/(-0.0000868\times (T-25)+0.9999)\mathrm{.}$ (8) Upon further examination, we expanded our analysis to encompass additional scenarios and unveiled a consistent linear relationship. Subsequently, by leveraging the practical measurements of test current values, we have successfully constructed models for the 10 nA gear at temperatures above 25 ℃ and for the 0.1 mA gear across both temperatures below and above 25 ℃.

The temperature correction equation for the 10nA gear at ambient temperature above 25 ℃ is $Y_2=y/(-0.000051\times (T-25)+1.0000)\mathrm{.}$ (9) The temperature correction equation for the 0.1 mA gear at ambient temperature below 25℃ is $Y_3=y/(-0.0000456\times (T-25)+1.0000)\mathrm{.}$ (10) The temperature correction equation for the 0.1 mA gear at ambient temperature above 25℃ is $Y_4=y/(-0.0000080\times (T-25)+0.9997),$ (11) where Y₁, Y₂, Y₃, and Y₄ represent the corrected output current value.

Verification of correction model

Some standard weak currents ranging between -5 ℃ and 40 ℃ were measured to verify the temperature correction model. The relative errors of the measured data and corrected data are shown in Fig. 6.

Fig. 6Full-screen View

(Color online) Relative error curves of the measured and corrected data. The results in the -5 ℃ and 40 ℃ range are shown in the first and second columns. The results for the 10 nA and 0.1 mA gears are shown in the first and second lines

We can intuitively deduce from Fig. 6a and 6c that at an ambient temperature of -5 ℃, the relative error of the measured data remained remarkably below 0.25% in the 10nA gear and below 0.15% in the 0.1mA gear. Following the implementation of temperature correction, except for 0.1mA (it is at full scale with an error of 0 and does not need to be corrected in actual situations), as illustrated in Fig. 6c, the relative error was consistently maintained below 0.03% in the 10nA gear and below 0.066% in the 0.1mA gear. Consequently, through the utilization of the temperature correction model, the accuracy of the system’s output has been greatly enhanced.

On the other hand, drawing from the valuable insights presented in Fig. 6b and 6d, we observe that at an ambient temperature of 40 ℃, the relative error of the measured data remained consistently below 0.2% in the 10nA gear and below 0.1% in the 0.1 mA gear. Following the temperature correction procedure, the relative error was effectively maintained below 0.1% in the 10 nA gear and below 0.05% in the 0.1 mA gear.

In conclusion, the implementation of the temperature correction model can improve measurement accuracy by mitigating the influence of temperature fluctuations on the measurement system.