Two Drift Pages, One Physics: TCR on the Resistor and on the Channel

Resistor temperature coefficient of resistance (TCR) describes how resistance changes with temperature. In a 4–20 mA receiver, that resistance change can also change the voltage used to infer current. The resistor calculation estimates one component’s drift; the channel calculation expresses its measurement impact and compares it with the available error budget. They are related calculations, not interchangeable accuracy assessments.

A resistor specified at ±50 ppm/°C can change by up to ±0.1% over a 20 °C temperature change under a constant-coefficient model. That does not automatically mean ±0.1% of the 4–20 mA span: the denominator matters.

Calculate the Resistor’s Temperature Drift

For a first-order, constant-TCR estimate:

[
d=\alpha\times10^{-6}\times(T-T_0)
]

[
\Delta R=R_0d,\qquad R(T)=R_0(1+d)
]

where:

• (d) is fractional resistance change, dimensionless.
• (\alpha) is signed TCR in ppm/°C.
• (T_0) is the reference temperature in °C.
• (T) is the resistor’s operating temperature in °C.
• (R_0) is resistance at (T_0), in Ω.
• (\Delta R) is resistance change, in Ω.

If the datasheet gives a limit of ±(A) ppm/°C rather than a known signed coefficient, use (A\times10^{-6}\times|T-T_0|) to estimate the magnitude bound. Do not assume resistance must increase.

Vishay’s Temperature Coefficient of Resistance for Current Sensing, document 30405, gives this resistance–temperature relationship and explains that TCR can be nonlinear and dependent on the specified temperature interval. Use the component’s applicable datasheet specification, not a generic value assigned to “thick film” or “metal film.”

Worked Example: A 250 Ω Sampling Resistor

Assume these illustrative inputs:

• Resistance at 25 °C: 250.000 Ω.
• Signed TCR: +50 ppm/°C, treated as constant from 25 °C to 45 °C.
• Resistor temperature: 45 °C.
• Initial resistance error excluded to isolate temperature drift.

Then:

[
d=50\times10^{-6}\times(45-25)=0.001=0.1%
]

[
\Delta R=250.000\times0.001=0.250\ \Omega
]

[
R(45,^\circ\mathrm C)=250.250\ \Omega
]

This is a resistance-change estimate, not a complete receiver accuracy result.

Use resistor temperature, not automatically cabinet air temperature. Applied power can raise the element temperature above ambient; Vishay discusses both ambient-temperature effects and self-heating in document 30405. A temperature estimate that already includes self-heating should not have the same temperature rise added again.

Convert Resistor Drift to Current-Equivalent Channel Error

For an ideal receiver that measures the voltage across the resistor and divides by its reference resistance:

[
V=I_{\mathrm{true}}R(T)
]

[
I_{\mathrm{ind}}=\frac{V}{R_0}
=I_{\mathrm{true}}(1+d)
]

Therefore:

[
\Delta I=I_{\mathrm{ind}}-I_{\mathrm{true}}
=I_{\mathrm{true}}d
]

Here, (V) is in volts, resistance is in ohms, and current is in amperes. The final relationship also works directly in mA when both current terms use mA.

This model assumes the loop maintains the commanded current, the voltage input does not materially load the resistor, and the receiver uses unchanged reference scaling. It excludes amplifier, ADC, reference, wiring, and other errors. Texas Instruments’ An Engineer’s Guide to Current Sensing, particularly “Integrating the Current Sensing Signal Path,” describes the shunt, analog front end, ADC, and reference as distinct parts of the measurement path.

Worked Example: The Same Resistor in a 4–20 mA Receiver

The reference 250 Ω resistor produces 1–5 V at 4–20 mA. With the +0.1% resistance change calculated above:

The table uses:

[
e_{\mathrm{span}}=
\frac{\Delta I}{20\ \mathrm{mA}-4\ \mathrm{mA}}\times100%
]

Current errors are displayed to 0.001 mA and span percentages to 0.001%; retain unrounded values when comparing a result with a limit.

At 20 mA, the error is 0.1% of reading but 0.125% of the 16 mA span. At 4 mA, it is still 0.1% of reading, although the ideal process indication is zero. Do not substitute (I-4\ \mathrm{mA}) for (I) in the resistor-drift calculation: the resistor carries the full loop current.

These are indicated-current errors. They do not mean that the transmitter’s actual output current changed.

Choose the Calculation That Matches the Decision

Use a resistor-only calculation when the question is “How much can this resistance change?” Use a channel-error calculation when the question is “How much indicated-current error does that change create, and how much budget remains?”

For a conservative additive budget:

[
E_{\mathrm{other}}+
I_{\max}A,10^{-6}|\Delta T|
\leq B
]

Equivalently:

[
A\leq
\frac{B-E_{\mathrm{other}}}
{I_{\max}|\Delta T|}
\times10^6
]

where:

• (B) is the allocated channel-error limit in mA.
• (E_{\mathrm{other}}) is the sum of other non-overlapping error bounds, referred to the input in mA.
• (I_{\max}) is the maximum current being assessed, in mA.
• (A) is the resistor TCR magnitude limit in ppm/°C.
• (|\Delta T|) is the maximum resistor-temperature departure from the reference condition, in °C.

The rearranged expression requires a positive temperature excursion and available budget. If (E_{\mathrm{other}}>B), changing TCR alone cannot satisfy this allocation.

Numerical Decision Rule

Suppose a planning exercise allocates:

• Total channel-error limit: 0.024 mA, equivalent to 0.15% of a 16 mA span.
• Other error bounds: 0.010 mA.
• Maximum assessed current: 20 mA.
• Maximum resistor-temperature departure: 20 °C.

The remaining resistor-drift allowance is 0.014 mA, giving:

[
A_{\max}=
\frac{0.024-0.010}{20\times20}\times10^6
=35\ \mathrm{ppm/^\circ C}
]

Under these assumptions:

• A ±50 ppm/°C resistor contributes up to 0.020 mA, giving a combined bound of 0.030 mA—above the allocation.
• A ±10 ppm/°C resistor contributes up to 0.004 mA, giving a combined bound of 0.014 mA—below the allocation.

These are illustrative allocations, not universal acceptance limits. The comparison establishes only whether the stated model fits the stated budget; it does not establish field calibration acceptance.

Avoid the Wrong Comparison

Comparing “0.1% resistor drift” directly with “0.15% channel allowance” would appear favorable in the example above. It is the wrong comparison: the first percentage uses resistance, while the second uses the 16 mA measurement span. It also omits the other channel errors.

Convert both quantities to the same basis before deciding. Here, resistor drift alone is 0.020 mA at 20 mA; adding the stated 0.010 mA of other errors produces 0.030 mA, exceeding the 0.024 mA allocation.

Also check what a channel specification already includes. Do not add a separate shunt term if the applicable complete-channel limit already includes that resistor under the same conditions. Conversely, an amplifier-only specification does not describe the complete channel.

Checklist Before Using the Result

• Confirm the resistor value, component TCR limit, applicable temperature interval, and reference condition.
• Include initial resistance tolerance unless an established adjustment or measured reference value accounts for it.
• Estimate element temperature, including relevant self-heating, without counting the same contribution twice.
• Confirm the receiver’s actual scaling and whether it uses nominal or calibrated resistance.
• Keep % of reading, % of span, and absolute mA errors distinct.
• Evaluate the required operating range; for the simple multiplicative model above, absolute drift error increases with current.
• Check voltage headroom, resistor power rating, and loop compliance separately. The drift model assumes current remains regulated.
• Follow the site’s prescribed error-budget and acceptance method. A sum of bounds is not a measurement-uncertainty evaluation, and an uncertainty-based decision requires the applicable uncertainty inputs and decision rule.