When a quantizer input signal is the sum of the desired signal and input white noise, the quantization error is a function of total input signal. Our new equivalent model splits the quantization error into two components: a non-linear distortion (NLD) that is a function of only the desired part of input signal (without noise), and an equivalent out-put white noise. This separation is important because these two terms affect MIMO system performance differently. This paper introduces our model, and applies it to determine the minimal Analog-to-Digital Converter (ADC) resolution necessary to operate a conventional MIMO receiver with negligible performance degradation. We also provide numerical simulations to confirm the theory. Broad ramifications of our model are further demonstrated in two companion papers presenting low-complexity suppression of the NLD arising from insufficient ADC resolution, and a digital dithering that significantly reduces the MIMO transmitter Digital-to-Analog Converters (DAC) resolution requirement.