Slew rate

Slew rate#

TL;DR

  • check_max_slew() compares the largest per-axis slew rate within each block, on the physical axes after that block’s rotation, with max_slew from the system limits. A nonpositive max_slew disables the comparison.

  • For an arbitrary gradient, the slew rate is the difference between neighbouring waveform corners divided by their spacing on the gradient raster of the system limits, so the same samples on a finer raster imply a proportionally higher slew rate.

  • The report also states the largest simultaneous vector slew rate and the peak of each axis; only the per-axis quantity is compared with the limit. A step across a block boundary is evaluated with the same limit by the gradient continuity check.

  • For an area \(A\) (1/m) at slew rate \(S\) (Hz/m/s), the shortest waveform is a triangle of duration \(T_{\min} = 2\sqrt{A/S}\) while its peak \(\sqrt{AS}\) does not exceed max_grad. Halving the duration of a prewinder or phase-encode blip requires four times the slew rate.

  • apply_system_derates() and cap_system() return copies of the system limits with reduced max_grad and max_slew, and repeated derating does not compound. A sequence that fails under reduced limits must be redesigned at the lower limit, which lengthens its ramps.

The rate of change of a gradient amplifier’s output is bounded by the voltage available across the coil inductance. check_max_slew() compares the largest per-axis slew rate within blocks with max_slew from the system limits.

Quantity compared with the limit#

The slew rate is evaluated within each block, on the physical axes after that block’s rotation:

\[ \max_{t}\;\max_{a \in \{x,y,z\}} \left| \frac{\mathrm{d}G_a}{\mathrm{d}t} \right| \;\le\; \mathtt{max\_slew}. \]

For a trapezoid this is the amplitude divided by the rise or fall time. For an arbitrary gradient it is the difference between neighbouring waveform corners divided by their spacing on the gradient raster given by the system limits, so the same samples on a finer raster imply a proportionally higher slew rate.

As in Gradient amplitude, the report also states the largest simultaneous vector slew rate and the peak of each axis; only the per-axis quantity is compared with the limit. A nonpositive max_slew disables the comparison.

Within-block and boundary evaluation#

A gradient that ends one block at a nonzero amplitude, followed by a block that starts at a different amplitude, is a step over one raster period that neither block’s waveform contains. Gradient continuity evaluates that step with the same limit. Trapezoids begin and end at zero, so the boundary condition constrains mainly readouts that do not return to zero between blocks, such as zero-echo-time and joined spiral readouts.

Minimum-duration gradient lobe#

For an area \(A\) (1/m) at slew rate \(S\) (Hz/m/s), the shortest waveform is the triangle with peak amplitude \(\sqrt{AS}\) and duration

\[ T_{\min} = 2\sqrt{A/S}. \]

When \(\sqrt{AS}\) exceeds max_grad, the waveform acquires a flat top and is longer. Halving the duration of a prewinder or phase-encode blip requires four times the slew rate. make_trapezoid() raises for an area and duration that cannot be satisfied together under the system limits.

Derating#

apply_system_derates() returns a copy of the system limits with max_grad and max_slew scaled from their base values, which the copy retains, so repeated derating does not compound. cap_system() returns a copy with the limits lowered to stated ceilings. Passing either to the check evaluates the sequence against the reduced limits; a sequence that fails under them must be redesigned at the lower limit, which lengthens its ramps.

See also#