= Current-polarity dead-time compensation
<Current-polarity dead-time compensation> adjusts a switching command to oppose the <dead-time output-voltage error> predicted from the direction of load <electric current>. During <bridge switching dead time>, an inductive current can flow through a <MOSFET> body <diode>; the resulting rail clamp makes the cycle-average error depend on current direction. The manufacturer’s bridge-state diagrams establish that current-path mechanism.<Using power MOSFETs in DC motor control applications by Nexperia>[IAN50004, §4.1, Figures 5–6: nonoverlap and body-diode recirculation]{ref}
Consider an original ideal half-bridge model with rail separation $V_d$, switching period $T$, duty fraction $D$, and effective dead-time fraction $\delta=t_d/T$. Assume current has one nonzero sign throughout the affected interval and that device drops are negligible. Let positive current leave the midpoint, so that the adopted clamping model gives
$$
\overline v_{\rm actual}=V_d[D-\operatorname{sgn}(i)\delta].
$$
For a desired normalized average $D_*$, choose
$$
\boxed{D_{\rm cmd}=D_*+\operatorname{sgn}(i)\delta.}
$$
Substitution cancels the average error in this model. The correction changes the commanded pulse duration; it does not remove the nonoverlap needed to avoid <H-bridge shoot-through>. Different full-bridge switching patterns require applying the appropriate event model to each leg before subtracting the terminal averages.
For $V_d=48\,\mathrm V$, $T=50\,\mathrm{\mu s}$ and $t_d=0.5\,\mathrm{\mu s}$, $\delta=0.01$ and the uncompensated error magnitude is $0.48\,\mathrm V$. At $D_*=0.40$, use $D_{\rm cmd}=0.41$ for positive current and $0.39$ for negative current. Each gives the intended $19.2\,\mathrm V$ average under the stated assumptions.
Command limits matter. Suppose the allowed duty range ends at $0.98$ because a minimum off-time is required. With positive current and $D_*=0.975$, the formula asks for $0.985$. Clipping to $0.98$ leaves an actual normalized average of $0.97$, an error of $-0.24\,\mathrm V$ at this bus potential difference. Thus a compensation law can be correct locally while the requested average lies outside its achievable range. Minimum pulse durations impose further limits.
<Current-sign uncertainty in dead-time compensation> is particularly important near a zero crossing. If an estimated sign $\widehat\sigma$ is used while the actual sign is $\sigma$, the residual error, before command clipping, is
$$
\overline v_{\rm actual}-V_dD_*=V_d\delta(\widehat\sigma-\sigma).
$$
A wrong opposite sign doubles the uncompensated error magnitude: $0.96\,\mathrm V$ in the example. Current-sensor delay, noise and a sign reversal within the switching interval can all invalidate a sign held constant for the cycle. Using a zero correction in an uncertain interval avoids that particular wrong-sign doubling, but does not cancel the original error.
A proposed bench comparison records gate commands, midpoint <electric potential difference> and load <electric current> together, then integrates each switching cycle with and without compensation. Compare positive-current, negative-current and crossing intervals separately, and repeat near pulse limits. This separates the average-error cancellation being tested from preservation of nonoverlap, device voltage drops and imperfect knowledge of switching delay.
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