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A cold-to-hot heater comparison needs a trustworthy electrical input measurement. With pulse-width modulation, two individually plausible voltage and current traces can produce the wrong power when their measurement paths have different delays. The error can become a large fraction of average power at short duty cycles. Define the terminal boundary, correct the acquisition timing and retain the actual load dynamics before assigning a power change to heater resistance.
Key design decisions
- Specify the voltage and current boundaries so the calculated power belongs to the heater rather than its supply leads or switch.
- Allocate voltage-current timing mismatch from the shortest measured on-time, not only the PWM frequency.
- Calibrate measurement-path delay separately from the heater waveform so a real electrical phase difference is not erased.
Place both measurements around the same electrical load
Measure voltage between the nominated heater terminals and current entering that same two-terminal boundary. Measuring supply voltage upstream of a cable and current through the heater includes an additional voltage drop in the product. That difference matters when cable resistance changes with temperature or when connectors are part of the test fixture rather than the supplied heater.
Record the polarity conventions. Current entering the terminal assigned positive voltage gives positive absorbed power. A reversed current-probe orientation can invert the result without changing the displayed pulse shape. For a low-voltage development setup, verify the signs at a stable energized state before evaluating switching edges. Probe insulation, voltage category, common-mode capability and current limits must suit the actual circuit; a grounding shortcut is not a timing correction.
Calculate energy from corresponding instants
For a record of duration L, average terminal power is the integral of v(t)i(t) over that record divided by L. A sampled calculation approximates this integral using corresponding voltage and current values and their actual time spacing. The acquisition system therefore needs a common time reference in addition to calibrated amplitude channels.
Voltage and current probes can introduce unequal propagation delays. Correct that measurement-path mismatch using a compatible calibration arrangement and preserve its settings with the record. Nominal delay correction may leave residual mismatch. Filtering and acquisition configuration also matter, so changing them requires reconsidering the validity of the timing calibration. These are acquisition controls; they do not prescribe how quickly the heater's own current must follow voltage.
Use pulse overlap to expose the timing sensitivity
Consider an explicitly ideal resistive heater whose voltage and current are rectangular pulses with common on-time DT in each period T. Their on-state values are V and I, and both are zero in the off interval. The true average power is VID. Suppose the recorded current has an additional delay delta while the voltage record has no residual delay.
If the magnitude of delta is no greater than either the on interval or the off interval, the two recorded pulses overlap for DT minus the magnitude of delta. Their multiplied record therefore underestimates power. This simple model isolates the effect of acquisition timing. Rounded edges, off-state current, reactive behavior and longer offsets require integration of the actual waveforms instead of extending this expression beyond its assumptions.
Ptrue = VID; Pmeasured = VI(D − |delta|/T); (Pmeasured − Ptrue)/Ptrue = −|delta|/(DT)
- V and I are the assumed constant on-state terminal voltage and current.
- D is duty fraction and T is period in seconds.
- delta is residual relative measurement-path delay in seconds.
Ideal coincident rectangular voltage and current pulses, zero off-state values and |delta| ≤ min(DT, (1−D)T). The heater is treated as resistive within one period; this is not a switching-device loss model.
Compare the same skew at two duty cycles
Assume a 12 V, 2 A on-state condition with a period of 100 microseconds. At ten-percent duty, the true average power is 2.4 W. A residual delay of 0.5 microseconds reduces recorded overlap from 10 to 9.5 microseconds, producing 2.28 W. The power error is minus five percent even though the delay occupies only half a percent of the full period.
At fifty-percent duty with the same on-state values and delay, the true power is 12 W and the calculated result is 11.88 W: a one-percent error. If a controller changes duty as the heater warms, a fixed acquisition skew can therefore create a changing percentage error. It can distort a cold-to-hot comparison without any change in probe amplitude calibration.
| Duty and on-time | Residual delay | True average power | Calculated power |
|---|---|---|---|
| 10%; 10 microseconds | 0.5 microseconds | 2.4 W | 2.28 W; −5% |
| 50%; 50 microseconds | 0.5 microseconds | 12 W | 11.88 W; −1% |
| 10%; 10 microseconds | 0.1 microseconds | 2.4 W | 2.376 W; −1% |
Turn the power budget into a timing requirement
Within the overlap model, limiting the magnitude of timing-related fractional error to epsilon requires residual delay no greater than epsilon DT. For a one-percent allocation at the ten-microsecond on-time above, the limit is 0.1 microseconds, or 100 nanoseconds. This allocation applies to the remaining mismatch after correction, not to the difference between the probes' uncorrected catalog delays.
Reserve other parts of the power uncertainty budget for amplitude gain, offsets, integration and boundary errors. Meeting the timing allowance alone does not establish one-percent total accuracy. Also inspect the shortest pulses actually present during startup or low-demand control. A requirement based on nominal fifty-percent duty may not cover the low-duty condition used to compare hot resistance or maintenance power.
Do not deskew by forcing the heater traces to coincide
Actual heater wiring and connections can have inductance, capacitance and switching transients. Their voltage and current need not have identical shapes at every instant. Moving one live trace until its edges look like the other can remove a real load response and replace an acquisition correction with an assumed circuit behavior.
Establish the measurement-path correction independently, then apply that correction unchanged to the heater record under the qualified setup. Retain both uncorrected and corrected data, including the sign of the applied shift. If delay uncertainty remains significant, recompute power across its allowed interval and report the resulting sensitivity. This produces a defensible power range without selecting the time shift that gives the preferred thermal conclusion.
Separate timing error from zero-offset error
Let the remaining voltage offset be ev and current offset be ei. The measured product contains the true product plus ei times voltage, ev times current and the constant product ev ei. Averaging gives offset error ei times mean voltage plus ev times mean current plus ev ei. Changing delay cannot remove those terms.
Using the ten-percent-duty example, mean voltage is 1.2 V and mean current is 0.2 A. Assumed offsets of 0.02 V and 0.01 A contribute 0.012 W, 0.004 W and 0.0002 W respectively: 0.0162 W in total, or 0.675 percent of 2.4 W. Its sign can oppose the timing error. An apparently correct total power can thus conceal cancellation between two wrong acquisition settings.
Retain complete periods and the measurement state
For steady PWM operation, integrate complete periods and record how those periods were identified. A partial pulse at the start or end of a short acquisition can change the reported average independently of channel skew. During warm-up or changing duty, use a defined observation window and preserve the pulse history instead of labeling the record as a steady-state average.
The final comparison should include terminal locations, corrected time axes, acquisition interval, duty history, probe ranges, timing correction and residual uncertainty. Pair the electrical record with the temperature observation used to identify cold and hot states. If the measured power difference is comparable to the acquisition uncertainty, improve the measurement before changing the printed heater geometry or attributing the result to a material resistance shift.
Provide the heater power measurement boundary
Include synchronized electrical records when asking for a cold-to-hot resistance or PWM power review.
- Heater drawing, connection locations, actual drive circuit and the resistance states being compared.
- Uncorrected voltage and current records with common timestamps, polarity and actual observation windows.
- PWM period, minimum on-time, duty changes and whether off-state current is present.
- Probe and acquisition settings, independently established delay correction and estimated residual mismatch.
- Amplitude and offset uncertainty allocations, temperature records and the intended terminal-power acceptance criterion.
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