How to Diagnose a Circuit That Drifts When It Heats Up

It often starts as a minor annoyance. A sensor board reads correctly at room temperature — dead-on, even — but after roughly twenty minutes of operation, the output creeps by several percent. The problem is easy to miss when a device is tested in a climate-controlled lab where equipment barely warms up before someone shuts it down. Field deployment tells a different story. Inside a metal enclosure sitting on a hot rooftop, that same drift can be enough to trigger false alarms.

This is a practical guide to thermal drift: what causes it, how to chase it down systematically, and — critically — how to calculate your way to a fix rather than guess your way there.

What Thermal Drift Actually Is (And Why It's Sneaky)

Resistors, capacitors, semiconductors, and even PCB traces change their electrical behavior as temperature rises. This isn't a defect — it's physics. The atoms in a conductor vibrate more energetically at higher temperatures, which increases collisions with charge carriers and raises resistance. In carbon-film resistors, the resistance change can be quite significant. In precision metal-film resistors, it's smaller but never zero.

The spec that matters here is the Temperature Coefficient of Resistance, or TCR, expressed in parts per million per degree Celsius (ppm/°C). A resistor rated 100 ppm/°C will change its resistance by 100 parts per million for every degree of temperature change. That sounds tiny. Over a 50°C rise, though, it becomes 0.5% — and in a bridge circuit or precision amplifier, errors compound.

Physical expansion plays a role too. A copper PCB trace gets slightly longer and wider as it heats, and the resistance changes accordingly. Trace resistance is given by:

R = ρ × L / A

Where ρ is resistivity (which itself increases with temperature), L is length, and A is cross-sectional area. Thermal expansion increases both L and A, but since resistivity dominates in copper, resistance still rises with temperature. For long, thin signal-path traces, this becomes measurable.

How to Reproduce and Read the Problem

The first step is to reproduce the problem in a controlled way. Set the board up on a bench, attach a thermocouple to the hottest component — often a linear regulator running without adequate heatsinking — and log both temperature and output voltage every thirty seconds. Within a few minutes you can usually see a clear thermal signature: if the output climbs roughly linearly as board temperature rises and then levels off as the board reaches equilibrium, you are almost certainly looking at thermal drift.

That linearity is a useful clue. Random component failures tend to produce step changes. Thermal drift produces smooth, monotonic curves. If the output climbs as the board heats, resistance somewhere in the signal path is likely increasing — reducing current or shifting a voltage divider ratio in a way that makes the output read high.

A good place to start is the voltage divider feeding the ADC input. Consider a typical circuit using two resistors — say 10 kΩ and 4.7 kΩ — to scale a 0–5V signal down to 0–3.3V for the microcontroller. Measure both resistors in-circuit (after powering down) at room temperature, then remeasure after running the board hot for fifteen minutes.

The output ratio of a voltage divider is:

V_out = V_in × R2 / (R1 + R2)

If, hypothetically, the 10 kΩ resistor climbs to about 10,043 Ω and the 4.7 kΩ climbs to about 4,724 Ω, the math works out like this:

At room temperature: V_out = 5 × 4700 / (10000 + 4700) = 1.599 V

After heating: V_out = 5 × 4724 / (10043 + 4724) = 1.601 V

That's only about 0.12% change from the divider itself — not nearly enough to explain a large drift. In a case like this the resistors aren't the main culprits, but the calculation confirms the methodology is sound and tells you to look elsewhere.

A Common Offender: The Op-Amp Gain Stage

Suppose the signal then feeds a non-inverting amplifier stage before the ADC, with gain set by another pair of resistors — both nominally 47 kΩ, giving a gain of 2. A frequent mistake is mixing resistor types here: one a garden-variety carbon-film part, the other a proper metal-film unit. Carbon film might be rated at 200 ppm/°C, while metal film could be 50 ppm/°C.

The gain of a non-inverting amplifier is:

G = 1 + R_f / R_in

At room temperature (25°C), with both resistors at exactly 47 kΩ:

G = 1 + 47000 / 47000 = 2.000

At 67°C (a rise of 42°C), the carbon-film feedback resistor changes by:

ΔR = R × TCR × ΔT = 47000 × 200×10⁻⁶ × 42 = 394.8 Ω

So R_f becomes approximately 47,395 Ω. The metal-film R_in changes by:

ΔR = 47000 × 50×10⁻⁶ × 42 = 98.7 Ω

So R_in becomes approximately 47,099 Ω. New gain at 67°C:

G = 1 + 47395 / 47099 = 2.00629

That's a gain increase of about 0.315% — still small, but the effect stacks with the sensor's own thermal characteristics and any offset drift in the op-amp itself. A typical op-amp input offset voltage drift of 5 µV/°C over a 42°C rise adds another 210 µV of offset error before gain — multiplied by the gain of 2, that's 420 µV at the output, which on a 3.3V full-scale signal is another 0.127%.

In many designs the bigger issue is the sensor itself. Always check the sensor datasheet first: a sensitivity drift of, say, 0.18% per °C over 42°C works out to 7.56% — easily enough to dominate an 8% total drift on its own.

Fixing It Properly

Sensor drift typically requires a software correction table or a hardware analog compensation circuit. The software route is often simplest: measure output at several temperature points, fit a linear correction function, and bake it into the firmware. The correction might look like:

V_corrected = V_raw × (1 - 0.0018 × (T - 25))

This usually means adding a cheap NTC thermistor near the sensor to feed temperature into a second ADC channel — roughly a dime in parts and a few lines of code.

For a resistor mismatch in the op-amp stage, the fix is straightforward: replace the carbon-film resistor with a matched metal-film part, and ideally use a resistor network where both elements sit on the same substrate and track each other thermally. Several manufacturers make dual-resistor packages specifically for this — the ratio stays constant even as absolute values drift, because both resistors drift together. That's exactly what you want in a gain-setting application.

For PCB traces, re-route signal paths that run close to a hot regulator. The regulator itself benefits from a small heatsink and a revised power budget; switching to a more efficient topology can drop its case temperature substantially and reduce thermal stress on every component nearby.

What to Check First on Your Next Thermal Drift Hunt

If you're staring at a system that drifts with temperature, here's a sequence worth following:

• Log temperature and output simultaneously. If the drift is smooth and monotonic, it's almost certainly thermal. If it's abrupt, look for intermittent connections or thermal expansion causing mechanical contact issues.
• Check your resistor types. Carbon film (brown-black body, gold band tolerance) has high TCR. Metal film (blue body, tighter tolerances) has low TCR. Never mix them in a ratio-dependent circuit.
• Calculate before you swap. Use the TCR formula — it tells you whether a given component can realistically explain the drift you're seeing, so you don't chase ghosts.
• Read the sensor datasheet for thermal specs. Sensitivity drift and offset drift are almost always specified. It's the first thing to calculate.
• Consider thermal layout. Components that generate significant heat should be placed to minimize thermal gradients across precision circuitry. A hot regulator and your precision resistors should not be neighbors.

Thermal drift is one of those problems that feels mysterious until you start calculating, and then it becomes very mechanical. Everything has a coefficient. Everything has a temperature delta. Multiply them, add them up, and the numbers either explain what you're seeing or tell you where to look next. That's the job.

Done methodically, a roughly dime-sized thermistor, one matched resistor pair, a small heatsink, and a short firmware correction can take a system's drift from several percent down to a small fraction of a percent across the full operating temperature range — and keep it stable in the field.