The invention measures the X-parameters (or large-signal S and T scattering functions, sometimes called linearized scattering functions, which are the correct way to define “large-signal S-parameters”) with only two distinct phases for small-signals on a frequency grid established by intermodulation frequencies and harmonics of the large-tones, with guaranteed well-conditioned data from which the X-parameter functions can be solved explicitly, without the need for regression, and not limited by performance limits of the reference generator or phase-noise.