Analytical evaluation of VCO-ADC quantization noise spectrum using pulse frequency modulation

Abstract

Oversampled ADCs based on voltage-controlled oscillators have been analyzed using statistical models inherited from sigma-delta modulation. This letter shows that the discrete Fourier transform of a VCO-ADC output sequence can be calculated analytically for single tone inputs. The calculation is based on the transformation of the VCO output into a pulse frequency modulated signal that can be represented by a trigonometric series. Knowledge of the VCO-ADC output spectrum allows accurate evaluation of the SNDR dependence with the VCO oscillation frequency and gain constant. The SNDR predictions of the proposed model have been compared to behavioral simulations displaying only a deviation of 0.7 dB.