1. Introduction

In recent years, the use of power conversion has continued to increase. A typical converter and inverter system uses current sensors to measure system current^(1-15). Accurate current information detection is essential for power control such as various power supplies, chargers, converters, and inverters that are controlled at high frequency above several hundred [kHz]^(1-8). In addition, power electronics provides a more stable and responsive power supply through current control rather than voltage control^(1-5). If the amount of current is relatively small, hall sensors or magnetic sensors are used. In the related art, the magnetic saturation of hall sensors increases, making it is difficult to sense high DC current above several ten [A], with resistor current sensors exhibiting higher accuracy^(1,6). This article gives a current sensor of split resistor placement for high-power and high-frequency application. This paper compares previous resistor current sensors and the proposed current sensor. In the frequency range of 10[Hz] to 50[MHz], changes in resistance, inductance and phase-difference are analyzed. The previous current sensor is stable in the frequency range of 10[Hz] to 1[kHz]. However, the proposed split resistor current sensor is stable in the frequency range of 10[Hz] to 1[MHz]. This paper provides an electrical model for the resistor current sensor. The validity of the proposed split resistor sensor is analyzed through PSIM simulation and a prototype experiment.

2. The Previous Current Sensor

Fig. 1 shows a previous current sensor for detecting high currents above several ten [A]. Fig. 1(a) shows a 30[A] previous current sensor, and Fig. 1(b) shows a 50[A] previous current sensor. In the 30[A] current sensor, the resistor is designed to detect the current of 30[A] as 50[mΩ], and the 50[A] current sensor, the resistor is designed to detect the current of 50[A] as 50[mΩ]. Therefore the resistance value of each ideal current is given by the followingequations (1) and (2) according to Ohm's Law.

3. The Proposed Current Sensor

Fig. 2 shows the current sensor for the proposed split resistor placement. The proposed current sensor of the split resistor placement is composed of an octagon. Alternatively, it is designed to flow up to 50[A] using 100 small resistors.

Fig. 3 shows the equivalent circuit model of the current sensor for the detection of high current.

where

${Z}$ : Impedance of current sensor

${R}$ : Pure Resistance of current sensor

${L}$ : Inductance of current sensor

${C}$ : Capacitance of current sensor

In the case of the capacitor component C = 0 in Equation (4), it can be expressed as Equation (5).

In the case of the capacitor component L = 0 in Equation (4), it can be expressed as Equation (6).

4. The Analysis of Skin Effect at High Frequency

For the precision of the resistor current sensor, skin effect must be considered for frequency of several ten [kHz].

The skin effect is that the induced electromotive force is generated inside the conductor because of the direction of the current changes rapidly at high frequency. That means the high frequency current flows through the surface of the conductor. In general, the skin depth can be expressed as Equation (7)^(10-12).

where,

$μ$ : copper permeability $4\pi\times 10^{-7}$[H/m]

$σ$ : copper conductivity $5.8\pi\times 10^{7}$[S/m]

The length of the wavelength can be expressed as in Equation (8).

where

$\lambda$ : wavelength

$f$ : frequency

$c$ : velocity of light

Therefore, the length of the wavelength($\lambda$) and the skin depth($δ$) according to the frequency($f$) is as follows.

Fig. 4 shows the skin depth of metals with frequency^(9-10).

5. Simulation and Experiment Results

In this paper, Newtons4th Ltd's frequency response analyzer is compared to the current sensors of the previous 30[A] and 50[A] current sensors with the proposed 50[A] split resistor placement of high current detection. The PSM 3750, frequency response analyzer was used to measure the change in resistance(R), inductance(L), and phase-differences at frequencies of 10[Hz] to 50[MHz].

Fig. 5 shows the resistance(R) variation analysis of the proposed split resistance current sensor and the previous current sensor.

In the case of the previous 30[A] and 50[A] current sensors, the resistance(R) is generally stable when the frequency of the range is 10[Hz] to 500[Hz]. However, it was confirmed that when performed, the resistance(R) exponentially increased from 1[kHz]. This is unusual, when the resistance decreases instantaneously at a frequency of about 1[MHz], and rapidly rises in a higher frequency range. The proposed 50[A] split resistor current sensor, however, has a characteristic that the frequency is almost constant in the range of 10[Hz] to 1[MHz]. Therefore, it can be seen that the proposed current sensor is an accurate advantage for current above hundred [kHz]s. Also the proposed current sensor may include a characteristic that has the resistance decreasing instantaneously at 5[MHz] and the resistance rapidly increasing from the higher frequency range.

Table 2 shows the resistance variation analysis according to the frequency. Referring to Fig. 6 and Table 1, with the resistance of 10[Hz] set to 1 which is the reference resistance, the change of the resistance according to the frequency was examined. With resistance based on 10[kHz], the proposed 50[A] current sensor arrangement has a 1.7% resistance variation.

Also, when the resistance is based on 10[kHz], the previous 50[A] current sensor has a 75.9% resistance variation, and in the case of the previous 30[A] current sensor has a 95.4% resistance variation.

When the resistance is based on 100[kHz], the proposed 50[A] current sensor arrangement has a 6.1% resistance variation whereas the previous 50[A] current sensor has a 399.6% resistance variation. The previous 30[A] current sensor has a 429.5% resistance variation.

With resistance based on 1 [MHz], the proposed 50[A] current sensor arrangement has a 2.0% resistance variation. The previous 50[A] current sensor has a 435.1% resistance variation while the previous 30[A] current sensor has a 762.5% resistance variation.

Alternatively, the previous 50[A] and 30[A] current sensor has large margin of error at 100[kHz] and 1[MHz]. Therefore, the proposed 50[A] current sensor can have a higher current accuracy in the range of 10[Hz] to 1 [MHz] compared to the previous 50[A] and 30[A] current sensor.

Fig. 6 and Table 3 show the variation in inductance(L) of the proposed 50[A] current sensor and the previous 50[A] and 30[A] current sensor.

The inductance(L) of the proposed 50[A] current sensor and the previous 50[A] and 30[A] current sensor had similar characteristics. It can be seen that it has the highest inductance(L) of the frequency of 100[Hz], and thereby it is confirmed that it performs variation in 200[nH] to 430[nH].

In this study, the simulation was performed using PSIM based on the measured resistance, inductance, and phase-difference. Alternatively, the results were confirmed by experiments in the range of 10[Hz] to 50[MHz].

In particular, the simulation was performed based on the model shown in Fig. 3.

Fig. 7 shows the PSIM simulation circuit and Fig. 8 to Fig. 11 display the voltage/current experiment waveforms of the proposed 50[A] current sensor and the previous 50[A] and 30[A] current sensor. The proposed 50[A] current sensor is verified by simulation and experiment and has a phase-difference between voltage-current phase smaller the previous 50[A] and 30[A] current sensor.

(1) 100[kHz]

▷ The proposed 50[A] current sensor :

6.612[deg] voltage-current phase-difference

▷ The previous 50[A] current sensor :

21.057[deg] voltage-current phase-difference

▷ The previous 30[A] current sensor :

36.047[deg] voltage-current phase-difference

(2) 1[MHz]

▷ The proposed 50[A] current sensor :

85.751[deg] voltage-current phase-difference

▷ The previous current 50[A] sensor :

89.725[deg] voltage-current phase-difference

▷ The previous current 30[A] sensor :

89.513[deg] voltage-current phase-difference

(3) 10[MHz]

▷ The proposed 50[A] current sensor :

97.243[deg] voltage-current phase-difference

▷ The previous 50[A] current sensor :

99.062[deg] voltage-current phase-difference

▷ The previous 30[A] current sensor :

103.975[deg] voltage-current phase-difference

From Fig. 8 to Fig. 11, simulation and experiments show that the proposed 50[A] current sensor has a smaller voltage-current phase difference than that of the previous 50[A] and 30[A] current sensor.

6. Conclusion

This paper presents a split resistor current sensor for stable resistance up to 1[MHz]. Where previous current sensors consist of a single resistor, the proposed split resistor current sensor is divided into 100 detailed resistors. The current sensor can be flexibly selected according to the current level. In the proposed current sensor of the split resistor arrangement, there is stable resistance(R), and the voltage-current phase- difference shows a relatively small technical characteristic compared with the previous current sensor. Therefore, experimental results show that the proposed split resistor current sensor is reliable over a wide range of frequencies and achievement is more exact than previous current sensors.