Detailed explanation of the basic principle of resistor current detection

Current sensing resistors, also known as shunts, have been known for decades. However, the application of resistors is no longer limited to the narrow range of the past. Resistors with extremely low resistance values ​​and almost no error and very accurate detection data acquisition systems have opened up application areas for developers that were unimaginable ten years ago.

The control and regulation of vehicle drive mostly requires an operating current between 1-100A. In special cases (for example, oxygen sensor preheating), a current of 2-300A is required for a short period of time, and the current can reach 1500A when the vehicle starts. In the battery and power management system, there are even more extreme cases: when the vehicle is running, the continuous current is 100-300A; while at rest, the current is only a few milliamperes, all of which must be accurately detected.

Achieving the best detection results in the smallest space is one of the most common requirements of the automotive industry for automotive electronic systems. This is exactly the advantage of shunt technology. However, since the structure of the resistor itself and the resistor material will cause the resistor to produce completely different effects in actual applications, it is not possible to find the right resistor just by comparing the datasheet. The following will describe some important parameters for achieving the best design through calculation examples.

Basic principles of current detection with resistors
According to Ohm's law, when detecting the current through a resistor, the potential difference is used as the direct detection value of the current detection. It is no surprise that hundreds of milliamperes can be detected with a resistor higher than 1Ohm. But if the current reaches 10-20 amperes, the situation is completely different, because the power consumption in the resistor (P=R*I2) cannot be ignored. Although you can try to limit the power consumption by reducing the resistance value, the detected voltage is also reduced accordingly, and the detected resistance value is often limited by the valuation resolution and accuracy.

Typically, the sense voltage across a resistor is given by the following formula:

U=R*I+Uth+Uind+Uiext+......
Uth=thermal electromotive forceUind
=induced voltageUiext
=port lead voltage drop

In the above situation, the error voltage caused by factors unrelated to the current will affect the detection results, so the designer must clearly understand this reason and should minimize the impact of the voltage error through reasonable wiring design, especially by selecting appropriate resistors.

Although any conductive material can be used to make resistors, such components are not suitable for current sampling at all because the resistance value is affected by many parameters such as temperature, time, voltage, and frequency.

R=R(T, t, P, Hz, U, A, μ, p, ....)

There is no ideal current sensing resistor that is completely unaffected by the above parameters. The actual resistor can be described by the characteristic parameters listed in the table below, such as resistance temperature coefficient, long-term stability, thermal electromotive force, power load, inductance, linearity, etc.

Some of these properties are inherently material dependent, others are influenced by component design, and still others are determined by the manufacturing process, as described in the following table.

xxx = large impact
xx = moderate impact
x = small impact, but noteworthy

More than a hundred years ago (1889), Isabellenhütte Heusler from Dillenburg, Germany (ISAB) developed a precision resistor manganese-nickel-copper alloy (Manganin). Since the advent of this alloy, its excellent properties have laid the foundation for precision testing technology, for example, it is also used in standard resistors. Other alloy materials Isaohm and Zeranin supplement and expand the resistivity range upward and downward with their resistivity coefficients of 132 and 29μOhm*cm respectively. All alloys largely meet the requirements of resistor materials and have been successfully used for many years, but among them, Manganin alloy plays a special role due to its wide global popularity.

In the past 25 years, in response to the development of magnetic field-based current sensing methods, Isabellenhütte has been committed to expanding the range of accurate current detection more widely through physical optimization of shunt resistors. With the gradual improvement of compensation, temperature coefficient and operational amplifier interference signals, the selected resistance value can be reduced to the milliohm range, which largely solves the problem of high power loss under high current conditions (P=R*I2). However, at the same time, due to the great increase in relative errors caused by fault voltages (including interference, thermal EMF, etc.), characteristics such as low inductance and low thermal EMF are extremely important.

In the following we will briefly discuss some of the most important technical parameters.

Temperature coefficient (TCR)

The diagram shows the typical parabolic temperature characteristic curve of a Manganin resistor. Since this characteristic is determined solely by the material composition, resistors can be produced with extremely high reproducibility and very low batch variations.

The temperature coefficient is in ppm/K and is defined as follows:

TCR=(R(T)-R(T0))/R(T0)*1/(T-T0)=dR/R(T0)*1/R(T0)

The reference temperature T0 is usually 20°C or 25°C. If the temperature curve is a curved curve similar to Manganin's curve, the upper temperature limit for the detection temperature coefficient must also be given, such as TCR (20-60). Thick film technology resistors with TCR values ​​of several hundred ppm/K are usually used in the low resistance range. The red curve in the figure shows the temperature characteristics of a resistor with a TCR of 200ppm/K. A temperature change of 50°C is sufficient to cause the resistance value to change by more than 1%. In this way, the resistor cannot perform accurate current detection. In an even more extreme case, etched copper wire is used as a current detection resistor on a PCB board. Since the TCR value of copper reaches 4000ppm/K (or 0.4%/K), a temperature change of only 10°C is sufficient to cause a 4% resistance drift.

Thermal electromotive force (Uth)

When the temperature rises or falls slightly, a so-called thermoelectric potential is generated at the interface of different materials. This effect is particularly noteworthy for low-resistance resistors, because the voltage usually detected here is very small, so the microvolt-level thermoelectric potential can seriously affect the detection results.

To this day, the resistor alloy Konstantan is still one of the main materials for wound and stamped shunts in many lectures and textbooks. Although it has a good TCR, its thermoelectric potential to copper is as high as 40μV/K. Since a temperature difference of 10℃ causes a voltage error of 400μV, the error of the detection result using a 1 milliohm shunt resistor to detect a current of 4A increases by 10%. More seriously, if the resistor size is taken into account, the often ignored Peltier effect can increase the temperature difference to more than 20℃ through mutual heating or cooling between the contact surfaces (a very extreme example is the melting of the soldering part at one end of the resistor). Even if the detection circuit is in a constant current state, the temperature difference and thermoelectric potential generated by the Peltier effect can cause a significant current fluctuation. After the power is cut off, before the temperature difference disappears, the current can still be clearly detected. Depending on the design specifications and resistance value, the current error can be several percentage points or up to several amperes. The precision resistor alloys mentioned above are perfectly matched to copper in terms of thermal EMF, and the above effects can be completely ignored. For example, a 0.3mOhm resistor will produce less than 1μV voltage after cutting off a current of 100A (corresponding to a current of 3mA).

Long-term stability

Long-term stability is extremely important for any sensor, because even after years of use, the user expects it to retain the accuracy of the initial calibration. This means that the resistor material must be corrosion-resistant and must not undergo any changes in the alloy composition during its service life. The dielectrically homogeneous composite alloys Manganin, Zeranin and Isaohm are carefully calcined and stabilized to their thermodynamically basic state. The stability of such alloys can be maintained in the ppm/year range, as Isabellenhütte has demonstrated and proved for more than a hundred years with its standard resistors for international testing and calibration.

The graph shows the stability curve of a chip resistor that has been operating for more than 1000 hours at 140°C. The slight drift of about -0.2% is caused by grid defects caused by slight deformation during the production process, and indicates that the component is further stabilizing, that is, the stability will become better. The speed of resistance drift depends greatly on temperature, so at a temperature of +100°C, this drift is actually undetectable. [page]

Four-terminal connection technology

In the case of low-value resistors, the influence of the terminals and leads cannot be ignored, so additional terminals must be connected directly across the resistor material for voltage detection.

The example shows that defective resistor structure and improper wiring design can cause very large errors. For a 10mOhm two-terminal wirewound resistor, the resistance of the copper lead accounts for 20% of the total resistance, and only a small section of 4mm copper lead can cause a 100% deviation in resistance.

Although the redundant resistance of the terminals and leads can be eliminated by compensation calibration, it has a great influence on the temperature coefficient of the total resistance. (As shown in the figure below)

Even though the proportion of copper in this example is extremely small, only 2% (in stark contrast to 24% in the previous example), the TCR increases from nearly zero to about +80ppm/K. This means that it is absolutely worthless to give a TCR value for the resistor material used in the product data sheet.

Resistors made of electron beam welded synthetic material Cu-Manganin-Cu actually have very low terminal resistance, and through appropriate wiring design, two-terminal structure resistors can be reused to achieve four-terminal connection performance through reasonable layout design, welding, etc. However, during the design layout process, it is important to pay attention to the current path in the resistor not touching the voltage connection line (voltage sensing line). If possible, the sensing line should be connected to the terminal in the form of a microstrip line from the inside of the resistor.

High power load

Since the thermal conductivity of resistor materials is relatively weak compared to copper, and most resistors use alloy foils with etched structures with a thickness between 20-150μm, it is impossible to conduct the heat converted from power consumption to the terminals through the resistor material. Therefore, the Isa-Plan series resistors use a very thin, highly thermally conductive adhesive to stick the resistor alloy foil to a substrate (copper or aluminum) that also has good thermal conductivity. In this way, heat can be very effectively dissipated to the outside through the substrate and terminals, ultimately achieving a relatively low thermal internal resistance (usually 10-30K/W).

Conversely, resistors with this structure can operate at full load at very high terminal temperatures, which means that the power reduction point only appears at very high temperatures; at the same time, the maximum temperature of the resistor material can be maintained at a low level, which can effectively improve the long-term stability of the resistor and the resistance change caused by temperature.

The Manganin cross-sectional area and mechanical strength of the composite material are so large that no substrate is needed, which means that the resistor material has very good thermal conductivity and relatively low thermal resistance. For example, for a 1 milliohm resistor, the thermal resistance is about 10K/W, and for a 100 microohm resistor, the thermal resistance is even only 1K/W.

Low inductance

Many current applications require the detection and control of switch modulation currents, so the parasitic inductance parameters of the shunt are very important. Surface mount resistors are produced using special low inductance planar designs and with or without closely adjacent corrugated structures. The anti-magnetic properties of the precision alloys mentioned above, the metal base plate structure, and the four-terminal connection further achieve low inductance.

However, since the voltage sampling connection line and the resistor form a ring antenna structure, in order to avoid the induced voltage formed by the magnetic field generated by the current and the external magnetic field, it is necessary to emphasize that the area surrounded by the voltage sampling signal line should be as small as possible, and the most ideal is a strip line design. The two sampling signal lines connected to the amplifier should be designed to be as close as possible or preferably parallelly wired between different layers of the PCB. The consequence of an inappropriate layout (shown by the red line) is that this antenna effect will greatly increase the actual inductance of the resistor.

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Low resistance

Although the four-terminal design is used for high current and low resistance, the resistors directly stamped from Manganin alloy strips (Figure a) that are often used in practice are not the best solution, because although the four-terminal resistor has better TCR and thermal electromotive force, the total resistance value is 2-3 times higher than the actual measured resistance value.

This results in higher power consumption and temperature rise for resistors. In addition, resistor materials are difficult to connect to copper simply by screws and welding, resulting in increased resistance at the contact surface, which further increases power consumption.

These errors are largely reduced by stamping resistors from composite materials. The overall resistance is increased by less than 10%, and customers can still use proven copper-copper connection technology.

Dimensions and Applications

For cost and miniaturization reasons, surface mount (SMD) resistors with resistance values ​​starting from 200μOhm are increasingly used in the automotive electronics industry to detect currents up to 100A. The following will introduce some resistor dimensions, characteristics and application examples. All examples are two-terminal designs, and absolutely accurate detection with four-terminal technology can be achieved through optimized physical structure and appropriate PCB board wiring.