Don’t Ignore Current Sense Resistor TCR

It’s not easy being a current sense resistor. So much is expected of this basic function of determining current flow by the simple measurement of voltage across a known resistance (i.e., I = V/R) then applying Ohm’s law (Figure 1). What could be simpler?

Figure 1: Current sense resistor schematic

Using a resistor (“R”) and associated voltage drop (“V” from B to C) for a measurement of current flow (“I” from A to D) is simple in principle but has subtleties that must be acknowledged. Four-wire, high-impedance Kelvin sensing is commonly used when currents are high, and resistance is in the 100mΩ and lower range.

Hence, it’s not as simple as it appears. First, there is the issue of deciding on a resistor value. On one side, a larger value increases the voltage drop across the resistor, so the reading scale becomes larger for an improved signal-to-noise ratio (SNR) and resolution precision. However, a larger value wastes power, may affect loop stability as it places more idle resistance between the source and the load, and results in increased resistor self-heating. Therefore, a lower value would be better. In practice, many designers size the resistor for a maximum voltage drop of 100mV as a compromise point. Regardless of the resistance value chosen, it’s the self-heating that is an insidious, potential problem, especially when it is carrying several amps and above. Despite their low nominal value, typically on the order of mere milliohms, it’s unavoidable: When amps are flowing, you have watts of heat dissipation.

This is a reality that cannot be ignored. The first problem is that self-heating degrades the resistor’s reliability—those on/off thermal cycles are the worst. That’s a legitimate but long-term concern. Second, and of immediate concern, is that such self-heating will shift the nominal value of the sense resistor itself, thus corrupting the perceived current-value reading.

What to do? Unless you are in the milliamp or microamp current range, where any self-heating is acceptably small, a responsible designer must perform an analysis of resistance change using the vendor-supplied data for the temperature coefficient of resistance (TCR). Note that this may be an iterative process, considering resistance change may affect current flow (depending on what is driving the current into the load), which may (in turn) affect self-heating, which may affect resistance, which may … (it can go on and on!).

TCR is not a small number that can be ignored. It’s typically specified in parts per million per degree Celsius (ppm/°C). An ordinary one-percent resistor has TCR on the order of several thousand parts per million per degree Celsius. Overall resistance change is a function of the materials used in the resistor element as well as the power rating and actual physical size of the component. Fortunately, vendors offer specialized, precision metal-foil resistors that have very low TCR.

They achieve this by using various alloys composed of copper, manganese and other elements to manage TCR. For example, the Bourns® Model CRL2010-FW-R050ELF is a 50mΩ, one-percent device with a TCR of ±200ppm/°C; however, devices with lower TCR are available. For the ultimate precision measurements in instrumentation applications, the lowest TCR resistors also come with fully characterized curves of their resistance versus temperature, which have a parabolic shape and are dependent on an alloy mix. It’s a tricky alloy formulation. For example, somewhat counterintuitively, copper is added to the mix despite its extremely high TCR of 4,000ppm/°C; yet, this is done to improve overall thermal dissipation and reduces self-heating of the element. The TCR of the resistor leads must also be factored into a high-precision analysis.

Of course, some applications don’t need high accuracy but, rather, are okay with a rough gauge. For these cases, a standard resistor may work. But many situations do need reasonable consistency and accuracy, and resistor self-heating plus TCR can easily make the presumed current value surprisingly incorrect.

Hence, a low-TCR device should be specified on the bill of materials (BOM), but a lower-cost, higher-TCR unit should be accepted only after analysis and approval from the Design team is complete. The consequences of using a wrong current value in a system—such as an electric vehicle (EV) or hybrid electric vehicle (HEV) with a large battery pack, a photovoltaic (PV) array, or a motor driver—can range from inexplicable behavior (at first) to substandard performance and efficiency to simply dangerous.