Tiny Quantizers, Big Impact: Pseudo Multi-Bit Delta sigma modulation

Pseudo multi-bit Delta-Sigma Modulation (DSM) is a technique used in digital audio processing to improve the performance of digital-to-analog and analog-to-digital converters. It involves using multiple 1-bit quantizers to mimic the behavior of a single multi-bit quantizer, combining their outputs to achieve better signal quality and noise shaping.


Key Concepts

1. Delta-Sigma Modulation (DSM):
   • A method used to convert analog signals to digital (and vice versa) by oversampling and shaping quantization noise to higher frequencies where it can be easily filtered out.
2. Pseudo Multi-Bit DSM:
   • Utilizes multiple 1-bit quantizers to approximate the performance of a single multi-bit quantizer.
   • Combines the outputs of these 1-bit quantizers to create an effective multi-bit output.
3. Selective Feedback:
   • Involves selectively feeding back certain 1-bit quantizer outputs or combinations to optimize noise shaping and linearity.
4. Unary (Thermometer) Code:
   • A unary code represents each quantization level with a specific number of 'on' elements in a sequence, ensuring monotonicity and improving linearity.
   • Conversion to a thermometer code helps in effectively managing and processing the quantizer outputs.
5. Dynamic Element Matching (DEM):
   • A technique used to average out mismatches in the digital-to-analog conversion process by dynamically reordering the active elements.
   • Helps in reducing distortion and improving the overall linearity and performance of the modulator.

How It Works
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1. Input Signal Processing:
   • The analog input signal is oversampled, increasing its resolution.
   • Noise shaping filters process the oversampled signal to spread quantization noise across a wider frequency range.
2. Multiple 1-Bit Quantization:
   • The processed signal is fed into several 1-bit quantizers operating in parallel.
   • Each quantizer produces a single-bit output based on the input signal.
3. Combining Quantizer Outputs:
   • The 1-bit outputs are combined using digital logic to form a pseudo multi-bit output.
   • This can involve a binary weighted sum or conversion to a thermometer code (unary representation) for further processing.
4. Selective Feedback Path:
   • Instead of feeding back the combined output directly, specific 1-bit outputs or their combinations are selectively fed back into the noise shaping loop.
   • This selective feedback can be dynamically controlled to optimize performance under varying signal conditions.
5. Dynamic Element Matching (DEM):
   • The combined outputs, if not already in unary/thermometer code, are converted to such by digital logic in the DEM circuitry.
   • DEM dynamically reorders the active elements to average out mismatches and reduce distortion, ensuring better linearity.  

Benefits of Pseudo Multi-Bit DSM

1. Improved Signal-to-Noise Ratio (SNR):
   • By using multiple quantizers, the system reduces quantization noise, resulting in a cleaner signal.
2. Enhanced Linearity:
   • Selective feedback and dynamic element matching (DEM) techniques help maintain linearity and reduce distortion.
3. Adaptive Performance:
   • The ability to dynamically adjust the feedback path allows the system to adapt to different signal conditions, maintaining high performance across various scenarios.
4. Cost-Effective:
   • Provides many benefits of true multi-bit systems without the higher complexity and cost associated with precise multi-bit DACs and ADCs.

Applications

Pseudo multi-bit DSM is widely used in high-fidelity audio systems, professional audio equipment, and precision measurement instruments where maintaining high signal quality is crucial.


Conclusion

Pseudo multi-bit DSM is a sophisticated technique that enhances digital audio processing by using multiple 1-bit quantizers to achieve the benefits of multi-bit systems. Through various possible options such as selective feedback, dynamic element matching (DEM), and the use of unary (thermometer) codes, the choice and uses of which depend on if the DSM is pure digital, or involves conversion to and from analog, it provides improved signal quality, reduced noise, and better linearity. This makes it ideal for high-performance audio applications. By understanding these principles, audio enthusiasts can appreciate the advanced technology behind modern digital audio converters.

However as effective as such techniques may be in linearizing Delta Sigma Conversion, it is 'pseudo' for a reason.  For even better performance, there is actual multi-bit Delta Sigma, which can somewhat blur the lines between Delta Sigma and PCM, but Multi-Bit DSM retains certain distinctions, especially if it makes use of unary/thermometer coding as opposed to binary coding.  The most advanced of Multi-Bit Delta Sigma converters these days, that use 64, 128 or possibly even more levels, simply must use binary (often two's complement)  for the sake of practicality.  This DOES introduce PCM 'weaknesses' if you will, into the Delta Sigma system, however, the system as a whole as judged by the incredible resolution and linearity of the latest chips from ESS and AKM, speaks for itself.  However, it is worth noting that, ironically, for the final stage of conversion, even these systems convert back into an unary coded system and use dynamic element matching to overcome the inherent linearity issues of PCM.  (See ESS 'revolver' technology and DCS 'Ring DAC' technology)