This paper derives the equations leading to the analytic expression of the frequency spectrum at the output of multi-bit delta-sigma modulators afflicted by component mismatch in the digital-to-analog converter used in the feedback path. The effect of the mismatch is modeled as an error signal added to an ideal digital-to-analog converter. The frequency content of this error signal is derived from the probability density functions of the input signal and the shaped quantization noise. The analysis is applied to band-limited Gaussian input signals. Several simulation results are reported, showing a 0.3 dB accuracy of the analytic expressions whenever the number of quantization bits is higher than two.