We investigate a variant of the d-scan technique, an intuitive pulse characterization method for retrieving the spectral phase of ultrashort laser pulses. In this variant a ramp of quadratic spectral phases is applied to the input pulses and the second harmonic spectra of the resulting pulses are measured for each chirp value. We demonstrate that a given field envelope produces a unique and unequivocal chirp-scan map and that, under some asymptotic assumptions, both the spectral amplitude and phase of the measured pulse can be retrieved analytically from only two measurements. An iterative algorithm can exploit the redundancy of the information contained in the chirp-scan map to discard experimental noise, artifacts, calibration errors and improve the reconstruction of both the spectral intensity and phase. This technique is compared to two reference characterization techniques (FROG and SRSI). Finally, we perform d-scan measurements with a simple grating-pair compressor.