Systems and methods for generating a gradient waveform for use by a low-field MRI system to generate a gradient magnetic field are provided herein. The gradient waveform can be determined using first information indicative of the gradient waveform and second information indicative of hardware constraints of the low-field MRI system including a maximum voltage of the gradient power amplifier, a maximum slew rate of the gradient coil, a resistance of the gradient coil, and an inductance of the gradient coil. In some embodiments, the gradient waveform can be a trapezoidal gradient waveform determined to have a non-linear ramp-up portion and/or a non-linear ramp-down portion.