Higher-Order Modulator Noise Transfer Synthesis for Stable SQNR
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Solution Overview
Problem
Higher-order continuous-time delta-sigma modulators (CTDSMs) face limitations in stability and signal-to-noise ratio (SNR) due to their feedback loop design, particularly when shaping in-band quantization noise, which restricts their maximum achievable bandwidth.
Innovation Solution
The synthesis of a noise transfer function with a first-order roll-off at high frequencies is achieved by employing a cascade of integrators with a feed-forward (CIFF) loop filter, combined with a noise-shaping circuit, to enhance the signal-to-quantization-noise ratio (SQNR) and reduce sampling frequency requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If higher-order loop filters are used to shape in-band quantization noise, then signal-to-noise ratio is improved, but stability of the feedback loop deteriorates
Solution Approach 1:
The patent segments the feedback loop into multiple integrators (first, second, third, and fourth integrators) with distinct transfer functions. Each integrator handles a portion of the noise shaping task, allowing the system to achieve higher-order noise shaping while maintaining individual integrator stability. The segmented architecture distributes the complexity across multiple stable stages rather than relying on a single high-order filter.
Solution Approach 2:
The patent changes the parameters of the loop filter by using a specific transfer function configuration where each integrator has a pole at a different location in the s-plane. The first and second integrators have poles at -ω1 and -ω2 respectively, while the third and fourth integrators have poles at -ω3 and -ω4. This parameter distribution allows the system to achieve high-order noise shaping while maintaining stability through carefully selected pole locations.
2Speed
If gigahertz sampling frequencies are used to achieve greater bandwidth, then bandwidth is improved, but device complexity increases
Solution Approach 1:
The patent replaces the mechanical approach of increasing sampling frequency to achieve bandwidth with an electrical/filtering approach. Instead of relying on gigahertz sampling rates, the system uses a continuous-time delta-sigma modulator with a carefully designed loop filter that achieves the desired bandwidth through its transfer function characteristics. The noise transfer function is shaped to provide attenuation at specific frequencies, achieving bandwidth control through filtering rather than sampling rate.
3Measurement precision
If higher-order modulators are used to achieve high linearity, then measurement precision is improved, but stability deteriorates
Solution Approach 1:
The patent divides the higher-order modulator into multiple lower-order integrator stages. Each integrator (first through fourth) has a simple transfer function with a single pole, ensuring individual stability. The cumulative effect of these segmented stages achieves the desired high-order linearity and noise shaping performance without compromising the stability of any individual stage.
Solution Approach 2:
The patent changes the parameters of the modulator by distributing the order across multiple integrators with specifically chosen pole locations. The first integrator has pole at -ω1, second at -ω2, third at -ω3, and fourth at -ω4. This parameter distribution allows the system to achieve high-order linearity through the cumulative transfer function while each individual integrator remains stable with its own controlled pole location.
Data Source
AI summary
Embodiments of circuits and methods are described below that may provide a modulator that has an enhanced signal-to-quantization-noise ratio (SQNR) for a given sampling frequency and bandwidth or that may enable a reduced sampling frequency for a target SQNR and bandwidth. In one or more embodiments, a modulator circuit may include a first modulator including an input and a first output, and including one or more feed-forward components; an output circuit including an input coupled to the first output and including an output, the output circuit including one of a noise-shaping circuit, a noise-shaped quantizer circuit, or an integrator and feed-forward component; and coefficients of the one or more feed-forward components of the first modulator and a transfer function of the output circuit provide a higher-order modulator with a first-order roll-off at high out-of-band frequencies.