DDS Delta-Sigma Interpolation for Quantization Noise Shaping
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Solution Overview
Problem
Direct digital synthesis (DDS) systems face challenges in minimizing phase and amplitude quantization errors due to limited ROM size and DAC bit limitations, leading to spurious tones and reduced resolution.
Innovation Solution
The implementation of high-order delta-sigma interpolators in the DDS circuit to noise-shape quantization errors through a transfer function of 1−(1−z−1)k, allowing for finer resolution and reduced ROM size by filtering phase and amplitude truncation errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Volume of stationary object
If the phase word is truncated to reduce ROM size, then the ROM size is reduced, but quantization noise is introduced
Solution Approach 1:
A delta-sigma modulator is introduced as an intermediary component between the phase accumulator and the ROM. This modulator processes the truncated phase word and shapes the quantization noise spectrum, pushing noise to higher frequencies where it can be filtered out, thereby reducing in-band quantization noise while maintaining small ROM size
Solution Approach 2:
The system changes the temporal distribution of quantization error through noise shaping. By using a delta-sigma modulator with a specific transfer function, the quantization noise is redistributed in the frequency domain, concentrating noise at high frequencies and reducing noise in the signal band, effectively improving precision without increasing ROM size
2Measurement precision
If the accumulator size is increased to achieve fine resolution, then the resolution is improved, but the ROM size increases
Solution Approach 1:
The delta-sigma modulator serves as an intermediary that allows the system to use a smaller accumulator and ROM while achieving fine resolution through noise shaping. The modulator compensates for the reduced precision by redistributing quantization noise, enabling fine frequency resolution without proportionally increasing ROM size
Solution Approach 2:
The system transitions from spatial precision (more accumulator bits leading to larger ROM) to temporal precision (noise shaping in time/frequency domain). By operating in the frequency domain through noise shaping, the system achieves fine resolution without increasing the spatial dimensions of the ROM
3Manufacturing precision
If the DAC input bits are increased to reduce quantization error, then the quantization error is reduced, but the die size and power consumption increase
Solution Approach 1:
The delta-sigma modulator is placed before the DAC to pre-process the digital signal and shape the quantization noise. This allows the use of a lower-resolution DAC (fewer input bits) while maintaining high output precision through noise shaping, thereby reducing die size and power consumption associated with high-bit DACs
Solution Approach 2:
The system changes the precision requirements of the DAC by using noise shaping. The delta-sigma modulator ensures that the quantization noise from a lower-resolution DAC is pushed to frequencies outside the signal band, allowing the use of simpler, lower-bit DACs while maintaining high overall precision
Data Source
AI summary
A direct digital synthesis (DDS) circuit utilizes high order delta-sigma interpolators to remove frequency, phase and amplitude domain quantization errors. The DDS employs an n-bit accumulator operative for receiving an input frequency word (FCW) representing the desired frequency output and converts the frequency word to phase information based upon the clock frequency of the DDS. A high-order delta-sigma interpolator is configured in frequency, phase or amplitude domain to noise-shape the quantization errors through a unit defined by the transfer function of 1-(1−z−1)k in either a feedforward or feedback manner. The delta-sigma interpolator of any order can be implemented using a single-stage pipelined topology with noise transfer function of (1−z−1)k. The DDS circuit also includes digital-to-analog converters (DACs) that convert the outputted sine and cosine amplitude words to analog sinusoidal quardrature signals; and deglitch analog low-pass filters that remove the small glitches due to data conversion.