Systematic design of continuous-time ΣΔ modulator with VCO-based quantizer

A methodology for the design of Continuous-Time (CT) Sigma-Delta (ΣΔ) modulators with VCO-based quantizer is proposed. The coefficients of the CT ΣΔ modulator are accurately calculated such that the noise transfer function of the modulator is exactly the same as a Discrete-Time (DT) ΣΔ modulator of the same order. The proposed design method takes into account loop-delay compensation as well as the shape of the feedback Digital-to-Analog Converter (DAC) signal. VCO non-idealities such as non-linear K_vco and phase noise are studied. Several design examples for different modulator orders and feedback DAC signal shapes are given to validate the proposed methodology.