Current sense resistor calculator

A current-sense resistor is chosen for the voltage it drops at full current — 10 to 130 mV, Bourns says — and then judged on three errors the value does not show: its tolerance, its temperature coefficient once I²R has heated it, and, for a two-terminal connection, the solder and trace copper the sense lines pick up, which is uncertain, often larger than a milliohm shunt, and drifts at copper's 3900 ppm/°C. Enter the current, the sense voltage or the part, its tolerance, TCR and thermal resistance, and the connection, to get the value, the power, the element temperature, and each error as a share of the reading.

Fig 1 — The error budget of the reading at full current: the resistor's tolerance, its TCR at the 65 °C the element reaches, and the copper of the solder and traces that a two-terminal connection includes in the measurement, which SBOA197, Bourns and Vishay all point at as the error a Kelvin connection removes. Worst-case sum 5.82 %.

Maximum current (A)

Sense voltage at I_max (mV)

Resistor chosen (0 = derive) (mΩ)

Tolerance (%)

Component TCR (ppm/°C)

Thermal resistance, mounted (°C/W)

Ambient (°C)

Solder + trace per connection (mΩ)

Sense connection

Rated power (W)

Resistor · drop at 10.0 A · power: 10.0 mΩ · 100 mV · 1.00 W (50 % of rating)
Self-heating rise · element temperature · resistance there: 40.0 °C · 65 °C · 10.0 mΩ
Error: tolerance · TCR · lead copper · lead TCR: 1.00 % · 0.20 % · 4.00 % · 0.62 %
Worst-case error of the reading at I_max: 5.82 %

With the sense lines on the current pads, 400 µΩ of solder and trace is 4.0 % of the 10.0 mΩ shunt and drifts at copper's 3900 ppm/°C — more than the resistor's own tolerance. SBOA197: "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." Switch to Kelvin to see the budget without it.

The sense voltage of 100 mV is inside Bourns' "10 to 130 mV" band. Lower is less loss and less self-heating; the limit is the amplifier's offset and its common-mode range, which is the op amp error budget calculator's subject.

How this is calculated

Standard: TI SBOA197; Bourns N1702; Vishay 30405

$R = \frac{V_{sense}}{I_{max}}, \qquad P = I_{max}^2 R$: SBOA197: value from the maximum differential voltage at the highest current, or from a power budget.
$T_{el} = T_{amb} + P\,R_{th}, \qquad R(T) = R_0\left[1 + \alpha (T - T_0)\right]$: Vishay 30405: self-heating through the mounted thermal resistance, and the TCR relation with α in ppm/°C.
$\epsilon_{lead} = \frac{2 R_{lead}}{R}, \qquad \epsilon_{lead,T} = \epsilon_{lead}\cdot 3900\,\text{ppm/°C}\cdot(T_{el} - T_0)$: Two-terminal sensing: the copper in each connection is in the reading (Bourns: R_lead + R_lead ≫ R_shunt at low values) and drifts at copper's TCR. Zero for a Kelvin connection.
$\epsilon_{total} = \epsilon_{tol} + |\epsilon_{TCR}| + \epsilon_{lead} + |\epsilon_{lead,T}|$: Worst-case sum at I_max, as a percentage of the reading.

Assumptions

The element temperature is ambient plus I²R times a single thermal resistance; no derating curve is applied.
TCR is linear from the 25 °C reference; Vishay notes real curves are non-linear and worse below 0 °C.
Lead resistance is the same on both connections and its temperature equals the element's.
A Kelvin connection removes the lead terms entirely; Vishay's point that a 2-terminal part's own copper terminals remain in a 4-pad layout is left to the component TCR entered.
The amplifier's offset, gain error and common-mode limits are not included.

What sets a current-sense resistor

A shunt is Ohm's law with the resistor chosen backwards. Bourns: "a shunt resistor is placed in series with the electrical load whereby all the current to be measured will flow through it … a voltage drop is generated across the resistor of known value, which is proportional to the current", and the resistor is small enough that the drop is "only an insignificant voltage drop of 10 to 130 mV". SBOA197's order of decisions is the calculator's: "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. Once the value and wattage of the current sense resistor is determined the second parameter to consider is the resistor tolerance … However, a more subtle parameter that is often overlooked is the resistor temperature coefficient."

The temperature coefficient matters because the part heats itself. Vishay: R = R₀[1 + α(T − T₀)], and "self-heating causes a resistance change due to TCR" — its power coefficient of resistance, "driven by construction, which is based on thermal conduction through the part or internal thermal resistance". The calculator takes I²R through the mounted thermal resistance to the element temperature and applies the TCR there. What "the TCR" is 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." At low values the copper terminals dominate — "the TCR rating of the WSLP2512 is 275 ppm/°C at 1 mΩ" for an alloy under 20 — and the specified range matters, since "TCR performance is typically non-linear and worse in the negative temperature range".

The third error is the board. Bourns: with a two-terminal part "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", and "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)". Vishay's number for that: 0.39 %/°C, "a temperature rise of 100 °C … for copper would cause a 39 % change in resistance". The fix is the Kelvin connection — SBOA197: "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" — on a 4-terminal part, or as a trace pattern on a 2-terminal one.

Current sense resistor chart

The shunt value and the power it dissipates at full scale, for the currents a design usually measures and the two sense voltages most current-sense amplifiers are set up around, computed by the calculator above. The power column is the one to read first: it decides the package, the self-heating, and therefore the TCR error the rest of the page is about.

I_max	R for 50 mV	Power	R for 100 mV	Power
0.5 A	100 mΩ	25 mW	200 mΩ	50 mW
1 A	50 mΩ	50 mW	100 mΩ	100 mW
2 A	25 mΩ	100 mW	50 mΩ	200 mW
5 A	10 mΩ	250 mW	20 mΩ	500 mW
10 A	5 mΩ	500 mW	10 mΩ	1 W
20 A	2.5 mΩ	1 W	5 mΩ	2 W
50 A	1 mΩ	2.5 W	2 mΩ	5 W

Halving the sense voltage halves the power but also halves the signal the amplifier has to resolve its offset against; the trade is between the resistor's heat and the amplifier's error, and below a few milliohms the copper of a two-terminal connection becomes a third party to it.

Worked example: 10 A, 100 mV, on a two-terminal 2512

The defaults: 10 A full scale into 100 mV, a 1 %, 50 ppm/°C part of 2 W at 40 °C/W mounted, 25 °C ambient, 0.2 mΩ of solder and trace in each connection, sense lines on the current pads.

resistor         100 mV / 10 A                        = 10 mΩ
power            10² × 10 mΩ                          = 1.0 W   (50 % of the 2 W rating)
self-heating     1.0 W × 40 °C/W                      = +40 °C → element at 65 °C
TCR error        50 ppm/°C × 40 °C                    = 0.20 %
lead copper      2 × 0.2 mΩ / 10 mΩ                   = 4.0 %   of the reading, in the measurement
lead TCR         4.0 % × 3900 ppm/°C × 40 °C          = 0.62 %  drift of that copper
worst case       1 + 0.20 + 4.0 + 0.62                = 5.8 %
Kelvin           1 + 0.20                             = 1.2 %

The resistor is a 1 % part and the reading is a 6 % reading, and almost none of the difference is the resistor: it is the 0.4 mΩ of solder and copper the sense lines picked up, and that copper's own drift. Moving the sense connections to the element — SBOA197's figures 2b to 2d, or a 4-terminal part — leaves 1.2 %, and a 0.1 % part is then worth buying. Bourns puts the threshold where the copper overtakes the part: "R_lead + R_lead ≫ R_shunt" at very low values, and SBOA197 draws the line at 0.5 mΩ for full four-wire Kelvin.

Where the current-sense model stops being valid

The errors are summed worst-case. Tolerance is a fixed offset a calibration removes; TCR and lead drift move with temperature and do not. A calibrated system's error is the drift terms alone.
TCR is a straight line here. Vishay: "TCR performance is typically non-linear and worse in the negative temperature range", and a datasheet's 20–60 °C figure flatters a part used at −40 °C.
The lead resistance is a guess. 0.2 mΩ per joint is an order of magnitude; SBOA197 notes that even the right layout "depends greatly on the measurement location used when the resistor was manufactured", which datasheets rarely give.
The amplifier is not included. Its offset over the sense voltage, its gain error and its common-mode range are the other half of the budget; theop amp error budget calculatoris that half.
Switching currents add inductance. Bourns' "low inductance" parts exist because L·di/dt across the shunt is a sense voltage at every edge; at hundreds of kilohertz a metal-strip part's nanohenry is not negligible against milliohms.

Common current-sense mistakes

Sensing from the current-carrying trace. SBOA197's figure 2a, "one of the most common mistakes": the solder and the copper are in the reading and drift at 3900 ppm/°C.
Buying tolerance and ignoring TCR. A 1 % part that heats 40 °C at 100 ppm/°C is a 1.4 % part; SBOA197's "lower cost resistors … will suffer in the real application due to the resistor temperature drift".
Comparing an element TCR with a component TCR. Only the component figure "includes the termination effects, which is how the resistor will perform in the application".
Running at the rated power. The rating is at a reference temperature on a reference board; 50 % is a working figure, and the self-heating row says what even that costs.
An ordinary resistor as a shunt. Thick film is ±100 ppm/°C or worse and its terminations are silver and copper; Vishay's table and Bourns' K-type ±50 ppm/°C are what the current-sense construction buys.