PWM Heater Common-Mode Current: Model Both Terminal-to-Frame Capacitances

System boundary

A drawing-defined thick-film resistive heater driven by a switching stage, with capacitive coupling from its energized features to a conductive support. A compact two-terminal approximation is used only where it represents the relevant electric field.

Integration interfaces

Integration risks

Separate differential voltage from common-mode voltage

Define Va and Vb as the instantaneous heater-terminal voltages relative to one stated frame reference. The differential voltage is Vd = Va − Vb. Define Vcm = (Va + Vb)/2. These are mathematical components of the measured pair, not additional independent supply outputs.

For an approximately resistive heater at a fixed resistance, instantaneous useful electrical input is Vd²/R. Adding the same voltage movement to both terminals leaves Vd unchanged but changes their relationship to the frame. Conversely, opposite terminal movements can change Vd while keeping Vcm constant. The distinction is essential when interpreting heating and interference together.

Keep two capacitances in the frame-current equation

Represent the effective coupling from terminal A and its associated energized region to the frame by Ca, and the corresponding coupling from B by Cb. With a sufficiently stable frame reference, the summed displacement current is Ca dVa/dt + Cb dVb/dt. Signs matter because opposing voltage movements can inject opposing currents.

Substitution of the common-mode and differential components gives a common-mode term weighted by Ca + Cb and a differential term weighted by half their difference. Thus constant Vcm does not guarantee zero frame current when the physical coupling is asymmetric.

Calculate cancellation and its loss through asymmetry

Consider hypothetical simultaneous linear transitions: A rises by 24 V in 0.2 microsecond while B falls by 24 V in the same interval. Each slope magnitude is 120 million V/s. With Ca = Cb = 100 pF, the two contributions are +12 mA and −12 mA, giving zero summed current in this idealized model.

Now keep the waveforms unchanged but let Cb be 80 pF. Its opposing contribution is only −9.6 mA, leaving +2.4 mA. Common-mode voltage is still constant during the perfectly opposing transitions. The residual follows the capacitance imbalance, which can arise from real differences in mounting overlap, lead routing or nearby conductive structure.

Compare terminal transitions, not only PWM duty

The following cases use the assumed 100 pF and 80 pF capacitances. They are electrical screening cases, not instructions to alter bridge switching without a complete driver review.

Do not replace a waveform with net transferred charge

Equal positive and negative charge over a switching cycle can coexist with large individual current pulses. A sensor input can be disturbed by either pulse before the opposite event arrives. Driver timing skew, dead time and unequal edge shapes therefore matter even when a cycle-average current appears close to zero.

Capture the actual transitions, including intervals in which terminals float or clamp through other circuit elements. Do not reduce required dead time simply to improve apparent cancellation; cross-conduction prevention and driver protection remain mandatory design constraints. The practical question is what residual the permitted switching sequence creates, not what an ideal simultaneous switch would produce.

Check whether two effective regions represent the printed heater

Potential changes along a distributed resistive pattern. Its capacitance to a metal base may be distributed as well, so terminal-only capacitances are a screening representation rather than an exact material model. A long pattern, nonuniform overglaze or large conductive backing can require several electrical regions and measured frequency-dependent behavior.

Determine capacitances with the installation and connection conditions documented. Tying both heater terminals together measures a combined coupling under that condition; it does not independently identify Ca and Cb. Extra fixtures and probe capacitances can become part of the measured result. Avoid fitting two parameters to a single combined measurement and presenting them as separately confirmed quantities.

Trace where the residual current returns

The frame current must close a circuit through bonding, shields, supply capacitance or other return paths. Only the portion that affects the sensitive reference contributes through the mechanism being investigated. A current estimate alone is not a sensor-error estimate; the relevant impedance and receiving circuit response must also be known.

Use suitable differential or isolated probes within their actual common-mode and bandwidth limits. A protective earth connection must not be defeated to change the trace. Compare intended hardware changes while preserving the measurement arrangement, and check whether an added probe has changed the cancellation by loading one terminal more than the other.

Validate a change across the allowed operating states

A proposed improvement might reduce unnecessary overlap, improve symmetry, change a permitted edge rate or redirect the intended high-frequency return. Each can affect other functions, including insulation geometry, switching loss or heat transfer. Keep those reviews separate from the interference observation so a quieter sensor does not conceal a worse electrical or thermal condition.

Record both terminal waveforms, the estimated or measured coupling network, frame-current observations and actual sensor error before and after the change. Include startup, low duty and shutdown states where switching differs from steady operation. The completed result identifies the residual mechanism and its bounded improvement; it does not establish an insulation rating or electromagnetic compatibility certification.