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A current-sign certificate from sensor delay is a bound proving that load electric current keeps one specified sign throughout a future switching interval, despite measurement error and the age of the reading. It supplies a condition under which a direction-dependent correction in current-polarity dead-time compensation can use its assumed current path. Manufacturer switching diagrams show why current direction matters: inductive current can continue through body diodes during nonoverlap.^[ref]

Suppose a sensor reports $i_m$ for sampling time $t_s$, with $|i(t_s)-i_m|\le {ϵ}_i$. The command begins at $t_0\ge t_s$ and the affected interval ends at $t_e=t_0+t_d$. Assume $|di/dt|\le L_i$ throughout $[t_s,t_e]$. Integrating the derivative bound givesThus $i_m>b$ certifies positive current throughout the interval; $i_m<-b$ certifies negative current. The strict inequalities exclude a possible zero at the limiting time. A failed certificate does not prove a sign change; it means the stated information does not rule one out.

For an original numerical example, let ${ϵ}_i=0.020\mathrm{A}$, $L_i=5000A/s$, sample age $t_0-t_s=2\mu \mathrm{s}$ and $t_d=0.5\mu \mathrm{s}$. Then $b=0.0325\mathrm{A}$. A $0.040\mathrm{A}$ reading has a certified minimum of $0.0075\mathrm{A}$. If the sample could be another $0.5\mu \mathrm{s}$ older because of timestamp uncertainty, use that oldest possible time: the bound becomes $0.0350\mathrm{A}$. Ignoring acquisition-to-controller delay would overstate the available margin.

A current-sign certificate for an averaged sensor sample must model the averaging aperture too. Suppose the sensor returns the uniform average over $[t_b-T_a,t_b]$, plus error at most ${ϵ}_i$. For a future time $t\ge t_b$,The interval certificate therefore uses $b={ϵ}_i+L_i(t_e-t_b+T_a/2)$. With $T_a=4\mu \mathrm{s}$ and the preceding delay and switching interval measured from $t_b$, $b=0.0425\mathrm{A}$. The same $0.040\mathrm{A}$ reading is no longer sufficient. The half-aperture term is justified here by a uniform averaging model; a different filter needs its own response model.

The slew bound must apply during switching, not only to the slow visible current envelope. For an ideal inductor of inductance $\mathcal{L}$, $di/dt=v_L/\mathcal{L}$, so an independently justified bound on its terminal electric potential difference gives $L_i\le V_{L,\max }/\mathcal{L}$. A smaller slope measured in a quiet part of the cycle need not bound a subsequent rail-clamped interval.

Several consistent measurements can be combined. If each provides an enclosure of the current over the entire target interval, intersect those enclosures. For example, $[-0.01,0.07]\mathrm{A}$ and $[0.02,0.08]\mathrm{A}$ imply the tighter $[0.02,0.07]\mathrm{A}$, certifying positive current. An empty intersection flags inconsistent measurements or assumptions; it is not an especially strong certificate.

A proposed bench validation timestamps the sensing aperture, controller decision and actual gate transitions, while an independent current record checks the asserted error and derivative bounds. Repeat near current zeros and across the intended load range. This distinguishes a deterministic enclosure from a standard uncertainty or confidence interval and tests the complete timing chain needed by current-sign uncertainty in dead-time compensation.

Current-sign uncertainty in dead-time compensation occurs when the direction of measured load electric current does not reliably identify its direction during the switching interval being corrected. The recirculation path during bridge switching dead time depends on that direction. Manufacturer switching diagrams show how the body diodes provide paths when the controlled devices are off.^[ref]

Use the ideal half-bridge model in current-polarity dead-time compensation: bus separation $V_d$, period $T$, effective delay $t_d$, and an actual nonzero current sign $\sigma \in \{-1,1\}$ held constant throughout that interval. Let $a=V_d{t}_d/T$. A commanded additive correction $au$, where $-1\le u\le 1$, leaves average output errorA correct sign gives zero error with $u=\sigma$. An opposite sign gives magnitude $2a$, twice the uncompensated magnitude. For $V_d=48\mathrm{V}$, $t_d=0.5\mu \mathrm{s}$ and $T=50\mu \mathrm{s}$, $a=0.48\mathrm{V}$ and a wrong full-sign correction gives $0.96\mathrm{V}$ error. These conclusions assume unclipped commands and the stated rail-clamping model.

A current-sign certificate from sensor delay combines measurement and motion bounds. Suppose a reading $i_m$ refers to time $t_0-\tau$, has absolute error at most ${ϵ}_i$, and the true current satisfies $|di/dt|\le L_i$ from then through the end of $[t_0,t_0+t_d]$. For every time in that switching interval,This follows by adding the measurement error to the integrated derivative bound. A positive sign is certified if $i_m>b$; a negative sign if $i_m<-b$. Within the remaining band, neither sign is certified by those bounds. At equality, a zero can still occur, so strict sign certification requires a strict inequality.

For an original example, take ${ϵ}_i=0.020\mathrm{A}$, $L_i=5000A/s$, $\tau =2\mu \mathrm{s}$ and $t_d=0.5\mu \mathrm{s}$. Then $b=0.0325\mathrm{A}$. A $0.060\mathrm{A}$ reading certifies positive current, whereas $0.025\mathrm{A}$ permits currents from $-0.0075$ to $0.0575\mathrm{A}$. A sign selected solely from the latter reading can therefore be wrong. A bound covering only the sensing instant would miss the delay contribution.

Robust and probabilistic choices answer different questions. If both signs are possible and nothing else is known, the worst-case error is $a(1+|u|)$; its minimum occurs at $u=0$. If instead a validated conditional probability $p=\mathrm{Pr}(\sigma =1)$ is available and mean squared error is the objective, differentiation givesFor $p=0.75$, the optimal fractional correction is $u=0.5$ and the predicted RMS error is about $0.416\mathrm{V}$ for the bus example. That is a probability-model prediction, not a worst-case sign guarantee.

A proposed validation records sensor timestamps, actual load electric current, gate timing and midpoint electric potential difference on a common time base. Compare integrated cycle errors in certified and uncertified sign intervals, including crossings within the dead time. A dead band or Schmitt trigger can reduce noisy toggling, but holding a previous sign through a genuine crossing can prolong a wrong correction; the relevant test is whether the current-path assumptions and timing bounds hold.