Delta-Sigma Modulator NTF Shaping for Fractional-N Spur Mitigation
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Solution Overview
Problem
Fractional-N frequency synthesizers suffer from nonlinearity-induced spurs and noise due to interactions between the phase error signal and nonlinearities in the synthesizer, which degrade the overall system performance.
Innovation Solution
A digital delta-sigma modulator (DDSM) with a specific noise transfer function (NTF) is used to mitigate spurs and noise. The NTF is designed to minimize the impact of memoryless polynomial nonlinearities, implemented with a cascaded or nested cascaded structure comprising error feedback modulator stages and an error cancellation network.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a conventional digital delta-sigma modulator is used in the fractional-N frequency synthesizer, then the synthesizer can generate programmable carrier frequencies, but nonlinearity-induced spurs and noise are generated that degrade system performance
Solution Approach 1:
The patent modifies the noise transfer function parameters of the digital delta-sigma modulator by designing specific zero locations in the z-plane. The NTF is configured with zeros at particular angular positions to create notches that cancel the spectral components at frequencies where spurs and noise occur, thereby eliminating the harmful effects while maintaining frequency synthesis capability
Solution Approach 2:
The patent converts the harmful nonlinearity-induced spurs and noise into beneficial spectral nulls by strategically placing zeros in the noise transfer function. The harmful spectral components are transformed into cancelled frequencies, where the notches in the NTF magnitude response precisely align with the spur and noise frequencies, effectively eliminating them
2Reliability
If the noise transfer function is designed to eliminate spurs and noise, then spur immunity and noise performance are improved, but the complexity of the modulator structure increases
Solution Approach 1:
The patent segments the noise transfer function into multiple factors, each contributing specific zero locations. The NTF is decomposed into first-order or second-order sections that can be independently designed and implemented, making the complex function manageable and suitable for digital implementation in the frequency synthesizer
Solution Approach 2:
The patent introduces an intermediary error cancellation network that processes the quantization error from multiple modulator stages. This network combines the error signals with appropriate weighting coefficients to achieve the desired noise transfer function, acting as a mediator that simplifies the overall structure while achieving the complex spectral shaping goal
Data Source
AI summary
A digital delta-sigma modulator (DDSM) is disclosed with an input signal x[n], an output signal y[n], a quantization error signal e[n] and a dither signal d[n], having an equation described in the z-domain byY(z)=STF(z)X(z)+DTF(z)D(z)−NTF(z)E(z),wherein Y(z), X(z), D(z) and E(z) are z-transforms of the output signal, the input signal, the dither signal, and the quantization error signal, and wherein STF(z), DTF(z) and NTF(z) correspond to a transfer function of the input signal, a transfer function of the dither signal, and a transfer function of the quantization error signal, and wherein the transfer function of the quantization error signal is of the form:NTF(z)=Az-Q(1-z-1)(1+∑i=1Kciz-i),A, Q and K are constants, coefficients ci are real valued and cK≠0 and wherein at least one of the zeroes zj of(1+∑i=1Kciz-i)satisfies zj≠+1 for j=1, 2, . . . , K.