Current sense resistors: what makes a shunt different

A shunt is chosen for the 10–130 mV it drops, and fails for reasons the value hides: TCR once I²R heats it, and the solder a two-terminal connection adds.

Any resistor in series with a load drops a voltage proportional to the current; that is Ohm’s law and it needs no special part. What makes a current-sense resistor a different product is everything that happens to that proportionality once the resistor is carrying amperes on a board: it heats, its terminations are copper, and the solder joints around it are resistances of the same order as the part. The vendors’ own notes — TI’s SBOA197, Bourns’ N1702 and Vishay’s TCR white paper — are about those three things, and this article is what they say. The current sense resistor calculator puts numbers on each for a given shunt and connection.

What the value is chosen for

Bourns: “current sense resistors work by detecting and converting current to voltage. These devices feature very low resistance values, and therefore, cause only an insignificant voltage drop of 10 to 130 mV in the application.” The value follows from the amplifier reading it. SBOA197: “the value of the resistor is usually based on achieving a desired maximum differential voltage at the highest expected current. The value of the resistor may also be selected based on a power loss budget for the resistor.” 10 A into 100 mV is 10 mΩ and a watt; the same 10 A into 20 mV is 2 mΩ and 200 mW, and a harder job for the amplifier, whose offset is now a larger share of the signal. The op amp error budget calculator is that half of the trade.

Then, in SBOA197’s order: “once the value and wattage of the current sense resistor is determined the second parameter to consider is the resistor tolerance since this will directly impact the accuracy of the sensed voltage and current measurement. However, a more subtle parameter that is often overlooked is the resistor temperature coefficient.” The rest of the article is that subtle parameter, and the connection that makes it worse.

TCR, and why a shunt heats itself

Every resistance changes with temperature, and Vishay’s white paper puts the relation and the numbers together: R = R₀[1 + α(T − T₀)], with α “measured in ppm/°C, which widely varies among different materials. For example, manganese-copper alloy has a TCR of < 20 ppm/°C (for 20 °C to 60 °C), whereas copper used in terminations is approximately 3900 ppm/°C. Another way to represent ppm/°C that may be easier to consider is that 3900 ppm/°C is the same as 0.39 %/°C … the change in resistance due to a temperature rise of 100 °C. For copper that would cause a 39 % change in resistance.”

Plot of percentage resistance change against temperature rise from 0 to 100 degrees. Copper rises steeply to 39 percent at 100 degrees. Thick film reaches 1 percent, a metal strip resistor half a percent, and foil is flat at a hundredth of a percent. The vertical axis is logarithmic. — Fig 1 — Vishay's R = R₀[1 + α(T − T₀)] for the materials in a current-sense circuit. Copper, "used in terminations" and in every trace and solder joint, "is approximately 3900 ppm/°C … a temperature rise of 100 °C. For copper that would cause a 39 % change in resistance." The resistive alloys are two orders of magnitude flatter — Bourns' K-type "within the range of ±50 ppm/°C" — which is the whole reason a sense line must not include any copper the current flows through.

The resistor’s temperature is not the ambient. SBOA197: the coefficient “is important since the temperature of the resistor will rise due to the power dissipated as current flows through the component”. Vishay calls this the power coefficient of resistance, “driven by construction, which is based on thermal conduction through the part or internal thermal resistance”, and its point is that “a resistor that has a very low thermal resistance on a high thermal conductivity board will maintain a lower resistor temperature”. A watt through 40 °C/W is 40 °C; at 50 ppm/°C that is 0.2 % of the reading, and at a thick-film 200 ppm/°C it is 0.8 %, more than the 1 % tolerance was worth buying. SBOA197’s warning: “often lower cost resistors will specify a tolerance less than 1 %, but will suffer in the real application due to the resistor temperature drift.”

The copper is part of the resistor

At milliohm values the alloy is not the whole part. Vishay’s metal strip resistors weld “a solid copper terminal” to “a low TCR resistance alloy”, and “the copper terminal has a high TCR (3900 ppm/°C) compared to the resistance alloy (< 20 ppm/°C), which still plays a role in the overall TCR performance as lower resistance values are required. … For the lowest resistance values of a specific resistor construction, the copper becomes more significant in the TCR rating.” Its example: “the TCR rating of the WSLP2512 is 275 ppm/°C at 1 mΩ” — for an alloy under 20 — against 75 at 5 mΩ, and a Kelvin-terminated WSK2512 “250” at 1 mΩ because “the notched construction reduces the amount of in-circuit copper from the measurement”.

This is why comparing datasheets needs care. “Some manufacturers will list the element TCR, which is only part of the overall product performance as the termination effects are ignored. The parameter that is most important is the component TCR that includes the termination effects, which is how the resistor will perform in the application.” And the range matters: “the resistor that is specified for a limited temperature range will present better performance than the resistor specified over a wider range. TCR performance is typically non-linear and worse in the negative temperature range.”

Where the sense lines go

The third error is the board’s, and it is the largest. Bourns: “designs that use very low ohmic 2-terminal surface mount resistors can find that the contact resistance of the solder pad and the traces of the printed circuit board (R_lead) are uncertain and usually higher than the resistance of the current sense shunt itself (R_shunt) — R_lead + R_lead ≫ R_shunt. This can cause inaccuracies in the current measurement. Additionally, the TCR of copper trace of the printed circuit board (3900 ppm/°C) is also much higher than the TCR of the shunt resistive element (< 50 ppm/°C).” A tenth of a milliohm of solder on each end of a 2 mΩ shunt is 10 % of the reading, and 10 % that drifts at 0.39 %/°C.

The remedy is where the voltage is picked up. SBOA197: “to achieve accurate current measurements there must be 4 connections to the current sense resistor. Two connections should handle the current flow, while the other two sense the voltage drop across the resistor.”

Four small layouts of a two-pad current sense resistor between two wide current-carrying traces. In the first, marked wrong, the two sense traces branch off the wide traces some distance from the resistor. In the second, the sense traces leave the resistor pads at their outer sides. In the third, they leave from the inner edges of the pads, under the resistor body. In the fourth, a four-terminal resistor has separate small sense pads. — Fig 2 — SBOA197's figure 2: "one of the most common mistakes in laying out the current sense resistor is connecting the current sense amplifier inputs to the current carrying trace instead of directly to the current sense resistor" (a). The others are valid; which is best "depends greatly on the measurement location used when the resistor was manufactured" — inside the pads favours (c), the side favours (b) — and "independent four-wire (Kelvin) connections" (d) are for "below 0.5 mΩ", where the solder itself is a share of the shunt.

The wrong way is the common one: “connecting the current sense amplifier inputs to the current carrying trace instead of directly to the current sense resistor”. The right ways differ in detail — “if the resistor value was measured on the inside of the pads, then the layout shown in figure 2c would provide the best measurement result. If the resistor value was measured at the side, then the layout shown in figure 2b” — and the difficulty is that “many resistor datasheets do not provide a layout recommendation for best current sensing accuracy or do not mention the measurement point used in the manufacturing process”. The four-terminal part, with its own sense pads, is “most commonly used when the value of the shunt resistor is below 0.5 mΩ and the solder resistance in series with resistor connections appreciably add to the overall shunt resistance”. Bourns’ advice runs the same way: the 4-wire Kelvin pattern on a 2-terminal part “unless extreme precision is required”, and “if the design permits, it is recommended to utilize a 4-terminal current sense resistor”. Vishay adds the limit of the trace trick: a 4-terminal pad on a 2-terminal part “does offer better measurement repeatability” but “does not remove the effects of copper from the measurement circuit. The resistor will still perform to the same rated TCR.”

The budget, with numbers

Two stacked bar charts of measurement error in percent. Two-terminal: tolerance 1 percent, TCR 0.2 percent, lead copper 4 percent, lead copper drift 0.6 percent, total 5.8 percent. Kelvin: tolerance 1 percent, TCR 0.2 percent, total 1.2 percent. — Fig 3 — The calculator's default shunt — 10 mΩ, 1 %, 50 ppm/°C, 1 W at 40 °C/W, so 40 °C of self-heating — with 0.2 mΩ of solder and trace in each connection. Sensed from the current pads, the copper is 4.0 % of the reading and drifts another 0.62 %: 5.8 % worst case from a 1 % part. Sensed at the element, 1.2 %. SBOA197: "often lower cost resistors will specify a tolerance less than 1 %, but will suffer in the real application".

The two bars are the same 1 % resistor. What separates 5.8 % from 1.2 % is nothing on the part’s datasheet: it is 0.4 mΩ of solder and trace the sense lines were allowed to include, and that copper’s drift. Fix the connection first, then the TCR, then buy tolerance — the order in which the errors are large, which is the reverse of the order in which they are usually shopped for.

What a current-sense resistor is, then

A resistive alloy with a low, specified component TCR; copper terminals sized so the alloy dominates the value, or notched into Kelvin terminals so the measurement excludes them; a construction with a low thermal resistance so I²R does not become a temperature; a low inductance, because at switching frequencies L·di/dt across the shunt is a voltage the amplifier cannot tell from current; and a rated power that is honest about the board it assumes. An ordinary thick-film resistor has none of these — Vishay: “a thick film current sense resistor utilizes a material that is primarily silver, with terminals of silver and copper. Silver and copper have similarly large TCR performance values” — and a 1 % thick-film part on a hot board with the sense lines on the traces is a 10 % ammeter with a 1 % label.

Sources

TI, SBOA197 — Integrated-Resistor Current Sensors Simplify PCB Design, 2017. Value and wattage first, then tolerance, then TCR; the four connections; figure 2’s layouts and the 0.5 mΩ Kelvin threshold.
Bourns, N1702 — Using Current Sense Resistors for Accurate Current Measurement, 2022. The 10–130 mV drop, K-type ±50 ppm/°C, R_lead ≫ R_shunt and the copper trace’s 3900 ppm/°C, the 4-wire Kelvin principle on 2- and 4-terminal parts.
Vishay Dale, Temperature Coefficient of Resistance for Current Sensing, white paper 30405, 2020. The TCR relation, copper’s 39 % per 100 °C, the terminal’s share at low values, Kelvin against 2-terminal, PCR, and the datasheet comparison checklist.