Analysis of the measurement method of load current

Current measurement can be used to monitor many different parameters, input power is one of them. There are many sampling components that can be used to measure load current, but no component can cover all applications. Each sampling element has its advantages and disadvantages. For example, the power consumption of the shunt resistor will lead to a decrease in system efficiency, and the voltage drop generated by the current flowing through the shunt resistor is too large for applications with low output voltage. The advantage of the DCR (inductance direct current impedance) current detection circuit is that it can remotely measure the current in the switching power supply without loss, but the sampling accuracy of the DCR sampling circuit depends on the matching accuracy of the peripheral parameters (R, C) and the inductor. The advantage of the Hall sensor is that it can measure large currents remotely without damage. The disadvantage is that it is easily affected by environmental noise and is not easy to design.

In short, for specific applications, only by understanding the advantages and disadvantages of each method can we make full use of the technology in the field of current detection to improve measurement accuracy.

shunt resistor

As long as you pay more attention to the layout and selection of the detection resistor, you can use the shunt resistor to measure the current simply and directly. The rated power and temperature coefficient of the sense resistor are critical to the design of a high-precision current measurement system. According to Ohm's law, it is not difficult to use sense resistors in system design. The disadvantage is that the detection resistor will produce a voltage drop, consume power, and reduce the efficiency of the application.

When selecting the resistance value of the sensing resistor, it is necessary to know the voltage drop and current measurement value on the sensing resistor.

First of all, the voltage drop on the detection resistor should be as small as possible to reduce the power consumption of the detection element and reduce heat generation. The less the detection resistance heats up, the smaller the temperature change, and the smaller the resistance value changes with temperature. The full range of current The accuracy and stability of detection will be better.

Since the sum current is known in most current detection applications, the design engineer needs to select the voltage drop of the shunt resistor. For example, suppose the measured current is bidirectional, the voltage drop of the shunt is set to ±80mV, and the measured current is ±100A. The resistance of the shunt resistor can be calculated using Equation 1.



Formula 1, using Ohm's law to calculate the resistance of the shunt resistor.

For this example, the calculated value of the shunt resistor Rsense is 0.8mΩ. Table 1 is a list of the resistance values of the shunt resistors under other full-scale current conditions.

Table 1 corresponds to the full-scale current value, the resistance value of the shunt resistor and the rated power.



The rated power of the detection resistor is calculated by formula 2.



Formula 2, calculate the rated power of the sensing resistor.

If the rated power of the detection resistor is calculated as 8W. The general experience is to select 2 times the rated power calculated by formula 2. In this way, even if the current flowing through the shunt resistor is occasionally greater than its current, the sensing resistor will not malfunction. In fact, the larger the ratio of the rated power of the selected detection resistor to the calculated result, the smaller the temperature rise of the resistor in high-current applications.

The temperature coefficient (TC) of the detection resistor will directly affect the accuracy of current measurement. The environmental temperature change of the detection resistor and the temperature change caused by the power consumption of the resistor will cause the resistance value of the detection resistor to change. The temperature change of the resistor under different currents is inversely proportional to the rated power of the resistor. The change of the resistance value caused by the temperature change of the detection resistor will affect the change of the measurement accuracy of the system. The resistance change of the resistor caused by the temperature rise can be calculated by Equation 3.



Formula 3, calculate the change in resistance when the temperature changes. ΔTemperature is the temperature change value (unit: degrees Celsius). RsenseTC is the temperature coefficient of the sense resistor. Rsense is the resistance value of the sensing resistor at the initial temperature.

The change in the resistance of the detection element is proportional to the current flowing through the resistor. The package size of the sense resistor can also affect its temperature rise. The thermal resistance Θja, which is an important parameter of the sensing element package, should also be considered when selecting the sensing resistor. Θja refers to the thermal resistance between the resistor and the external environment of the resistor. Table 2 lists the thermal resistance of common surface mount packages.

Table 2, Thermal resistance of surface mount resistors, quoted from Vishay Application Note 28844 and 60122



It can be seen from Table 2 that the smaller the package, the greater the thermal resistance.

For example, a detection resistor with a resistance of 0.8mΩ will produce 2W power consumption when the current flowing through it is 50A, and its temperature change can be calculated by formula 4.



Formula 4, the relationship between the current flowing through the sensing resistor and the temperature change of the resistor.

In Equation 4, I2*Rsense is the power dissipated by the shunt resistor. Θja is the thermal resistance of the selected sensing resistor. Assuming that the package size of the detection resistor is 2512, the calculated value of the temperature change of the resistor is 50°C. Assuming that RsenseTC is 100ppm/℃, the resistance change calculated using formula 3 is 4μΩ. 4μΩ does not seem to be a big change, but the ratio of the resistance change to the total resistance can be compared. When a 50A current flows through the resistor, the rated The resistance value changes by 0.5%, resulting in 0.5% current measurement error.

As can be seen from Figure 1, the current measurement error caused by the heating of the resistor. The smaller the package, the easier it is to generate heat, and the smaller the package, the lower the allowable heating power. If you want to increase the power rating of the resistor while keeping a smaller package, you can choose a wider package. For example, the thermal resistance of the 0406 package is approximately equal to the thermal resistance of the 1206 package.



Figure 1. Current measurement error curve caused by the self-heating of the resistor

In practical applications, it is often difficult for us to buy shunt resistors with appropriate parameters. Often, either the resistance of the shunt resistor does not exist, or the rated power of the shunt resistor is too low. In order to solve this problem, you can use two or More shunt resistor methods to measure current.

Inductance DC resistance (DCR)

DCR current sampling circuit is a lossless sampling circuit, and its circuit board space is also small. However, this kind of circuit needs to be debugged to accurately sample, and it needs to take extra steps during production to ensure the accurate operation of the circuit. In addition, the tolerance of passive components will also cause differences in test accuracy between circuits. For example, the temperature coefficient of inductance and the tolerance of capacitance will increase the inaccuracy of current sampling. In general, the DCR sampling circuit is suitable for rough measurement of current, which can meet the purpose of lossless current sampling in the switching power supply. DCR sampling circuits are often used in low output voltage applications (in such applications, if resistors are used for sampling, the voltage drop will account for a large percentage of the output voltage). Low output voltage usually refers to an output voltage lower than 1.5V.



Figure 2. Simple schematic diagram of DCR circuit

DCR current detection circuit can also achieve the purpose of resistor detection current. The DCR current detection circuit uses the parasitic resistance of the inductor to measure the load current. It can remotely measure the current flowing through the inductor in the switching regulator circuit. Because no additional components are used in series with the load, it is called a lossless current sampling circuit.

Using a suitable DCR matching circuit can make it to the ADC, the value of the sampling resistance is equal to the internal resistance of the inductor. Figure 2 is a simple schematic diagram of a DCR sampling circuit. Before deriving the transfer function between the inductance current and the ADC input voltage, let's review the definition of reactance of inductance and capacitance in the Laplace domain.



Formula 5, the capacitive reactance formula of the capacitor and the inductive reactance formula of the inductor. Xc is the capacitive impedance related to frequency, and XL is the inductive impedance related to frequency. ω is equal to 2πf. f is the switching frequency of the regulator. According to Ohm's law, the voltage flowing through the inductor (in the DCR sampling circuit) is defined by Equation 6.



Formula 6, the voltage formula of the inductor in the DCR circuit. In Equation 6, Rdcr is the parasitic resistance of the inductor. The voltage drop of inductance (L) and parasitic resistance (Rdcr) is the same as the voltage drop of resistance (Rsen) and capacitance (Csen) (parallel relationship). Equation 7 is the voltage of the capacitor (Vcsen) defined by the inductor current (IL).



Formula 7, which represents the voltage of the capacitor (Csen).

If Equation 8 holds, the relationship between the inductive load current (IL) and the capacitor (Csen) voltage can be simplified.



Formula 8, the mathematical relationship that enables the DCR sampling circuit to work accurately.

If the condition of formula 8 is established, the numerator and denominator of the fraction in formula 7 can be canceled, so that the voltage of the detection capacitor (Csen) is simplified to the equation of formula 9.



The voltage on the capacitor (Csen) when the conditions of formula 9 and formula 8 are satisfied.

Most inductor specifications will give the average value of the inductor's internal resistance Rdcr. The Rdcr value is usually less than 1mΩ, and the average tolerance is 10%. The average tolerance of ordinary ceramic capacitors is also 10%.

In addition, the inductor is made of metal wire. Due to the high temperature coefficient of the metal, the value of the parasitic resistance (Rdcr) of the inductor will drift with temperature, causing the DCR matching circuit (Equation 8) to lose balance. The change of the parasitic resistance of the inductor may be caused by the temperature rise caused by the heating of the current flowing through the inductor or the environmental temperature rise. The resistance change rate of copper is 3.9 mΩ/C. The change of inductor wire temperature directly affects the value of Rdcr. To eliminate the influence of temperature changes, a temperature sensor can be used to monitor the temperature of the inductor. Thereby temperature compensation can be performed on the change of the resistance of the inductor.

In Figure 3, there is a resistor in series with the negative terminal of the 16-bit ADC (eg: ISL28023, digital power monitor), the resistance value is Rsen + Rdcr, the purpose of this resistor is to offset the vanishing bias current at the input of the ADC Of the generated bias voltage.

If the circuit in Figure 4 is an ISL85415 buck converter with a switching frequency of 900kHz, the inductance value is 22μH and the tolerance is ±20%. The inductance and output capacitor ensure normal operation of the buck converter and stable voltage. Rdcr is the parasitic resistance of the inductor. In this example, the typical value of Rdcr is 0.185Ω (the value is 0.213Ω). The parasitic resistance value varies by about ±13% due to the difference in inductance. The selected value of the DCR circuit Rsen is 11.8kΩ. Use formula 8 to calculate the matching capacitance Csen of the DCR circuit to be equal to 10nF. Assume that the tolerance of the capacitor is ±10%.

Inductance value and capacitance value cannot be strictly controlled. If the DCR current sampling circuit in the system does not have an additional adjustment circuit, what impact will the tolerance of the detection capacitance and inductance have on the current measurement error?



Figure 3. The curve in the figure shows the effect of capacitance tolerance on current measurement

Designing a DCR sampling circuit without adjustment function will cause up to 35% current measurement error, which is caused by the tolerance of the inductance and capacitance in the DCR sampling circuit. The curve in Figure 3 shows the measurement error caused by different capacitor tolerance values. If the change in Rdcr is taken into account, the measurement error will increase to about 50%.

A simple trimming circuit using a non-volatile digital potentiometer (DCP) can significantly improve current measurement accuracy.



Figure 4. The current measurement accuracy can be significantly improved by using DCP to adjust the circuit

Hall effect sensor

Hall-effect sensor technology has made significant progress recently, and the accuracy and noise immunity have been significantly improved, making the design easier. Despite these advances, the advantages of this technology are still limited to high-current applications. In high-current applications, the power consumption of Hall-effect sensors is much lower than that of shunt resistors.

Hall-effect sensor calculates the current magnitude through the strength of the magnetic field around the conductor. It can achieve the purpose of non-destructive measurement of current. The Hall-effect sensor measures the current flowing through the inductor by measuring the strength of the magnetic field generated by the current. It is very suitable for the case where the current is higher than 200A, because for high current applications, the power consumption of the sense resistor is very large. Figure 5 shows the basic concept of Hall effect current measurement.



Figure 5. Hall effect sensor example

Formula 10 expresses the relationship between the current size of the wire and the strength of the magnetic field. The expression of the ribbon trace will be slightly different. For simplicity, we use this formula to discuss the relationship between current and magnetic field.



Formula 10, the relationship between the current of the wire and the magnetic field. μ0 is the permeability of the magnetic field. The permeability of free space μo is equal to 4π*10-7 H/m. The value r is the distance (meters) between the inductance and the linear Hall effect sensor. The variable I is the current of the conductor. B is the magnetic induction intensity (unit: Gauss).



The side profile of the circuit in Figure 6, Figure 5

It can be seen from Equation 10 that the magnetic field strength decreases as the distance between the conductor and the sensor increases. The linear Hall effect sensor converts the measured magnetic field strength into current or voltage output. The gain of the sensor is expressed in mV/G or mA/G. Some measurements express this gain in Tesla. 1 Tesla is equal to 10,000 Gauss.

Suppose that the current flowing through a trace (the distance between the center of the line and the center of the Hall-effect chip is 0.03m) is 200A. So what is the magnetic field strength measured by the Hall-effect chip? If the gain of the sensor is 5mV/G, what is the output voltage of the sensor?

Using the relationship in the formula, we can see that the magnetic field strength is 13.33G. The calculated result of the inductor output is equal to 66.67mV.

Linear Hall-effect sensor is an active device with a working current of 3mA-10mA. The average noise level of the sensor is about 25mV or 5G. Therefore, linear Hall-effect sensors are not a good choice for low currents or large distances between traces and sensors.

The environment where the current trace and the sensor are located has an important influence on the measurement of weak magnetic fields. The linear Hall sensor measures the total magnetic field strength at the test location. Other current traces near the sensor will change the magnetic field at the location of the sensor and ultimately affect the accuracy of the measurement. In addition, the sensor will also measure changes in the environmental magnetic field. Switch-type motors or any equipment that radiates energy may cause changes in the environmental magnetic field.

One of the ways to reduce the influence of the environment on the sensor measurement is to use a magnetic shield to seal the current trace and the Hall effect sensor. Figure 7 shows the metal casing that wraps the trace and the magnetic field strength sensor. This metal shell is called a "Faraday cage".



Figure 7. Shielding conductors and sensors can improve the measurement of weak magnetic fields

The shield in Figure 7 should be grounded with as little impedance as possible, because the ground is a stable reference, so connection can improve the shielding effect.

Recently, a new Hall-effect sensor that integrates current path, temperature compensation, and shielded housing has been released. The integration of the current path can fix the distance between the current trace and the sensor chip, which simplifies the gain calculation between the current flowing through the conductor and the sensor output voltage. The integrated solution can simplify the layout and design of Hall-effect sensors in actual measurement applications, because users do not need to worry about the distance between the conductor and the sensor and the environment in which the sensor is located. Figure 8 is a simplified circuit diagram of this integrated solution.



Figure 8. Simplified circuit diagram of Hall-effect sensor with integrated current path

concluding remarks

Although each sampled electricity
None of the flow solutions are perfect, but knowing the advantages and disadvantages of various methods will help design engineers choose a solution that suits their system.