US 20050270201 A1 Abstract A method for reducing the resolution of a digital-to-analog converter in a multi-bit sigma-delta ADC is described. With the addition of digital sigma-delta modulators in the feedback path of a sigma-delta ADC, the truncation errors between the digital word output of the multi-bit sigma-delta ADC to the DAC input can be shaped to higher order than that of the quantization error. Thus, the DAC resolution can be reduced and the implementation of DEM for multi-bit DAC can be avoided. A preferred embodiment comprises selecting an outermost feedback loop in a sigma-delta ADC that has not been replaced and replacing it with a circuit with an equivalent transfer function. The circuit can be further enhanced with an additional term if the order of the noise shaping of the circuit is less than the order of the noise shaping of the sigma-delta ADC.
Claims(19) 1. A method for reducing resolution in a digital-to-analog converter (DAC) in a sigma-delta analog-to-digital converter (ADC), the method comprising:
selecting an outermost feedback loop in the sigma-delta ADC; replacing the selected outermost feedback loop with a circuit with an equivalent transfer function; adding an additional term to the circuit if order of noise shaping performed by the circuit is less than the order of noise shaping performed by the sigma-delta ADC; and repeating the selecting, replacing, and adding for remaining feedback loops in the sigma-delta ADC. 2. The method of 3. The method of 4. The method of 5. The method of 6. The method of 7. The method of 8. The method of 9. The method of 10. The method of 11. The method of 12. The method of 13. The method of 14. A method for converting a sub-net of sampled-data networks, the method comprising:
verifying that the sub-net can be converted; selecting an outermost feedback loop; replacing the selected outermost feedback loop with a circuit with equivalent transfer function; and repeating the selecting and replacing for remaining feedback loops in the sub-net. 15. The method of determining if the sub-net has a single signal input; determining if the sub-net has multiple noise inputs; and determining if the sub-net has no feed-forward and feedback loops crossing domains. 16. The method of 17. The method of 18. The method of 19. The method of Description The present invention relates generally to a method for signal processing, and more particularly to a method for reducing the resolution of a DAC in a multi-bit sigma-delta ADC. Sigma-delta analog-to-digital modulators, which can be used in a sigma-delta analog-to-digital converter (ADC) or a sigma-delta digital-to-analog converter (DAC), can provide a degree of shaping (filtering) of quantization noise that can be present. The higher the order of the sigma-delta modulator, the further the quantization noise is pushed into the frequency band, away from the signal being converted and the quantization noise. As such, sigma-delta ADCs and DACs (and their attendant modulators) have become popular in high frequency and high precision applications. However, sigma-delta modulators do not offer noise shaping for noise that is due to a mismatch between the unity elements used in a DAC (referred to as a feedback DAC) that is a part of a feedback loop in the sigma-delta modulator and a quantizer. The mismatch can therefore be a problem in the sigma-delta modulator if it is of significant magnitude. The mismatch can result in an overall reduction in the signal-to-noise ratio (SNR) of the sigma-delta modulator. One solution that can be used to reduce the mismatch that is present in the feedback DAC is to use a feedback DAC with high linearity. Ideally, the feedback DAC should have a linearity corresponding to the final resolution of the quantizer. A useful technique used to improve the DAC linearity is commonly referred to as dynamic element matching (DEM). Its use can reduce the mismatch in the sigma-delta modulator. One disadvantage of the prior art is that if the feedback DAC has high resolution, then it can potentially be difficult to achieve an effective DEM. A high resolution feedback DAC may require a large number of elements, and too many elements to average can lead to tones in the signal band for signals with low input levels. A second disadvantage of the prior art is that even if the mismatch can be transformed into noise, it can remain unshaped and become a component in the signal band, thus having an impact on the SNR of the sigma-delta modulator. These and other problems are generally solved or circumvented, and technical advantages are generally achieved, by preferred embodiments of the present invention, which provides a method for reducing DAC resolution in the feedback loop of a sigma-delta modulator. In accordance with a preferred embodiment of the present invention, a method for reducing resolution in a digital-to-analog converter (DAC) in a sigma-delta analog-to-digital converter (ADC) includes selecting an outermost feedback loop in the sigma-delta ADC that has not been replaced and replacing the selected outermost feedback loop with a circuit that has an equivalent transfer function. An additional term can be added to the circuit if the order of the noise shaping performed by the circuit is less than the order of the noise shaping performed by the sigma-delta ADC. The selecting, replacing, and adding can be repeated for all remaining feedback loops in the sigma-delta ADC. In accordance with another preferred embodiment of the present invention, a method for converting a sub-net of sampled-data networks includes verifying that the sub-net can indeed be converted. If the sub-net can be converted, then the outermost feedback loop that has not already been replaced is selected and then replaced with a circuit with an equivalent transfer function. The selecting and replacing can be repeated for all remaining feedback loops in the sub-net. An advantage of a preferred embodiment of the present invention is the multi-bit digital-to-analog converters (DACs) in the feedback loop of a sigma-delta modulator can be implemented with a lower number of bits (lower resolution). This means that the DAC can be simpler to implement and can operate without dynamic element matching (DEM). Therefore, this can help to alleviate issues that may exist with the multi-bit DAC. Another advantage of a preferred embodiment of the present invention is that the possible digital hardware required to dynamically match the unity elements of the DAC is replaced by less complex digital circuitry to, achieve digital noise shaping located in the feedback loop. The foregoing has outlined rather broadly the features and technical advantages of the present invention in order that the detailed description of the invention that follows may be better understood. Additional features and advantages of the invention will be described hereinafter which form the subject of the claims of the invention. It should be appreciated by those skilled in the art that the conception and specific embodiments disclosed may be readily utilized as a basis for modifying or designing other structures or processes for carrying out the same purposes of the present invention. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the invention as set forth in the appended claims. For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: The making and using of the presently preferred embodiments are discussed in detail below. It should be appreciated, however, that the present invention provides many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific ways to make and use the invention, and do not limit the scope of the invention. The present invention will be described with respect to preferred embodiments in a specific context, namely a second order sigma-delta ADC and its sigma-delta modulator. The invention may also be applied, however, to other sigma-delta ADCs and modulators of differing order (first order and higher). The present invention may also be applied to sampled-data networks in general. With reference now to The sigma-delta modulator The quantizer With reference now to Given a certain transfer function, there is likely to be several different circuit implementations, but they provide the same response at a functional level. For example, a circuit with a unity transfer function can be implemented as simply as a single wire or as complicated as a combination of integrators, adders, and delay units. Note that a circuit with a unity transfer function can also be referred to as a circuit with a no delay transfer function. The use of alternate circuit implementations can enable benefits that are exploited in the present invention. With reference now to With reference now to According to a preferred embodiment of the present invention, a sigma-delta generic network can be expanded by replacing a simple sub-network (like a wire or a delay) with an equivalent circuit (the replacement circuit having the same transfer function as the simple sub-network). An initial noise-shaping sigma-delta modulator can be transformed by expansion so that additional of inputs (possibly due to truncation errors) can be accommodated. The additional quantization inputs can be used to reduce the resolution of the DAC in the feedback loop of the sigma-delta modulator. The noise shaping provided by the inclusion of the generic sampled-data expansion networks can help to push the noise mismatch into frequency bands that are beyond the frequency band of interest. With reference now to The circuit With reference now to Meeting the two requirements discussed above may mean that the sampled-data network (sigma-delta modulator) can be a candidate for expansion to exploit noise shaping in order to reduce noise in the network. However, to further optimize the performance gained by the expansion, several design criterions should be considered and adhered to. In order to simplify the design, a first criterion states that the number of bits in the feedback signal at a first integrator (the integrator closest to the signal input) for a sigma-delta modulator should be at a minimum. However, the noise shaping achieved via the expansion for the feedback loop to the first integrator must be the highest degree of all feedback loops. Therefore, the greatest truncation noise shaping should be placed on the feedback loop for the first integrator. A second criterion states that the number of bits in the ADC of the sigma-delta modulator should be maximized, depending upon other constraints, such as data rates, operating frequencies, and so forth. A reason for this could be that the output quantization error can decrease (by −6 dB) for each bit used in the ADC. A third criterion states that the order of the noise shaping of the truncation noise should be higher than the order of the noise shaping of the ADC of the sigma-delta modulator. This criterion can help to ensure that noise truncation receives higher-order noise shaping. A fourth criterion states that internal points in the sigma-delta modulator (both analog and digital) should remain bounded. This criterion is a stability criterion and can imply that the design of the expanded sigma-delta modulator should still be stable. With reference now to A first operation in the conversion of the sub-net of generic sampled-data networks may be to verify that the sub-net of generic sampled-data networks is a candidate for conversion (block However, if the sub-net of generic sampled-data networks does meet both of the restrictions (block After replacing the outermost feedback loop with a circuit with equivalent transfer function (block With reference now to The algorithm Then, the first operation may be to replace the outermost feedback loop with a circuit having the same transfer function as the feedback loop being replaced (block If the order of the noise shaping in the replaced feedback loop exceeds the order of the noise shaping of the sigma-delta modulator (block With reference now to With reference now to The outermost feedback loop The third criterion states that the order of the noise shaping performed by the expanded feedback loops should be higher than the order of the noise shaping performed by the sigma-delta modulator (two in the second-order sigma-delta modulator With reference now to The inner feedback loop The output of the expanded inner feedback loop After expanding the feedback loops of a sigma-delta modulator, perhaps by using the algorithm With reference now to With reference now to With reference now to Although the present invention and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims. Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and steps described in the specification. As one of ordinary skill in the art will readily appreciate from the disclosure of the present invention, processes, machines, manufacture, compositions of matter, means, methods, or steps, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present invention. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps. Referenced by
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