Delta modulation quantizing noise analytical and computer. Understanding deltasigma modulators electronic design. Design of an error output feedback digital delta sigma. Furthermore, signal is clearly not a bandlimited signal, but, as mentioned above, the sigmadelta modulator is capable of processing such a discontinuous signal. An exact discretetime analysis of the moments and spectra of the quantization noise of a discretetime singleloop sigma delta modulator with a dc input is presented. Quantization noise power distributed uniformly across nyquist. Quantization noise conditioning techniques for digital delta.
The sigma delta modulator was first introduced in 1962. Again the total quantization noise of the converter is the same. In this paper, the ntfenhancement technique is developed for ct 6 modulators. Delta modulation uses 1bit per sampling period t s it is a 1bit adc 3. The subdac can be as simple as a multiplexer that switches between two. Jan 19, 2011 deltasigma modulator with nonuniform quantization abstract. Elliott, in handbook of digital signal processing, 1987. Delta modulation dm is the simplest method for analogtodigital conversion adc. If we now combine the oversampled 1bit sigmadelta modulator with a digital decimation filter rate reduction filter we obtain a basic sigmadelta adc see figure 2. Based on these two techniques, the paper designs a high performance sigma delta adc modulator. The noise shaping oversampling adcs are also known as delta sigma adcs. This is used with an earlier result for the granular noise to give overall signalto. This technique is known generally as quantization noise shaping, but in the context of data conversion is usually referred to as modulation for historical reasons 1.
Reduced baseband quantization noise power utilizes low cost, low power digital filtering. Staircase curve of a linear n bit adc converter assume that the input in busy, moderate signal level. Roundoff noise is a function of the hardware utilized and the algorithm. Delta modulation is also viewed as a 1bit dpcm scheme. Thus, third and higher order modulators based on the use of a single twolevel quantizer. Sigma delta modulator is the core part of sigma delta adc, and it is composed of the difference summation unit, integrator, quantizer and a dac. When the sn ratio is not too small, the noise power from these two sources is additive. Following are some of the features of delta modulation. The type of modulation, where the sampling rate is much higher and in which the stepsize after quantization is of a smaller value. A deltasigma modulator using a nonuniform quantizer. The sigmadelta modulator was first introduced in 1962. With respect to the quantizer on its own, lloyd proposed a nonuniform. The main parameters that were simulated are signalto noise ratio snr, effective number of bits enob, bandwidth and power consumption. The signalto noise ratio snr is one of the most significant measures of performance of the sigma delta modulators.
Quantization and quantization noise correspond to the mathematical process of rounding and roundoff noise. Noise in delta modulation utas eprints university of tasmania. Galton, ian 1992 an analysis of quantization noise in delta sigma modulation and its application to parallel delta sigma modulation. Slewrate limitation of the input signal if exceeds the range, additional quantization noise is generated. Quantization noise analysis sigmadelta modulators are. Figure 7c illustrates the noise shaping of the oversampled sigma delta modulator. The proposed delta sigma modulator has less quantization noise compared to the one that uses a uniform quantizer with the same number of output values.
Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set often a continuous set to output values in a countable smaller set, often with a finite number of elements. Alan mantooth, in modelbased engineering for complex electronic systems, 20. The delta modulator has now become a sigmadelta modulator. Device noise simulation of modulators introduction 2 of 23 the designers guide community 1 introduction deltasigma data converters are widely used, particularly in applications where high precision is required and the signal band is relatively small, such as in the processing of audio and sensor signals. The output of a delta modulator is a bit stream of samples, at a. Suppose the message signal is the sinusoidal signal a m cos2 f m t, then where f m noise occurs when the slope of the input signal is greater than the delta modulator is capable of reproducing. The in creased quantization noise is amplified by the analog filter, leading to instability in the form of large, uncontrollable, lowfrequency oscillations. Delta modulation utilities, wideband true rms meter preparation principle of operation delta modulation was introduced in the 1940s as a simplified form of pulse code modulation pcm, which required a difficulttoimplement analogtodigital ad converter. Continuoustime delta sigma modulators with noisetransfer. Spectral analysis of quantization noise in a singleloop. Nov 27, 2017 oversampling adc, delta modulator and delta sigma modulator, quantization noise, reduction of quantization noise by oversampling in delta modulator, reductio. The design of a multibit quantization sigmadelta modulator. Slope overload noise occurs when the slope of the input signal is greater than the delta modulator is capable of reproducing.
Our approach for signalto noise ratio computation does not require modulator modeling and simulation. Sigmadelta modulation is the most popular form of analogtodigital conversion used. This is used with an earlier result for the granular noise to give over. In this paper, a novel deltasigma modulator which has a nonuniform quantizer is proposed. The total quantization noise is still the same but the quantization noise in the bandwidth of interest is greatly reduced. A novel delta sigma modulator that employs a nonuniform quantizer whose spacing is adjusted by reference to the statistical properties of the input signal is proposed. In this method, the dpwm dutycycle command is preprocessed by a multibit digital sigma delta modulator, so that the dpwm quantization noise is shaped in frequency. Approximation formula for easy calculation of signaltonoise.
Quantization noise conditioning techniques for digital deltasigma modulators sudhakar pamarti abstractthis paper presents an overview of outstanding theoretical problems in deltasigma modulator based electronic digitaltoanalog circuits and outlines quantization noise conditioning techniques that are being employed to address these problems. As a leadin to the following sections which deal with sigma delta modulation, consider that the inband quantization noise power can also be given as a function of the noise transfer function and the power spectral density of the unshaped quantization noise. They turn an analog signal into a bit stream corresponding to the input with the oversampling used to partly shift the noise from the baseband into a higher end of the spectrum more details. Low pass filtering the adc output will reduce the noise power and yield more effective bits. Since there is no noise shaping, just oversampling, we have that.
We will only consider the delta sigma type oversampling adcs. Green curve is a scaled version of vin without any quantization. As the sampling interval is reduced, the signal correlation will be higher. This type of modulator firstorder provides a 9db improvement in snr for every doubling of the sampling rate. The differences between sigma delta adc and general nyquist converter are that the former adopts the oversampling and noise shaping technique. Therefore, sqnrmax maximum signal power inband quantization noise power. A formula for the slope overload noise power for gaussian input signals is derived. The quantization noise power is the area obtained from integrating the power spectral. A firstorder delta sigma modulator comprises an integrator, a comparator that acts as a subadc, and a subdac fig. Quantization noise shaping in digital pwm converters. Secondorder sigmadelta modulation for digitalaudio signal. Quantization noise quantization is the mapping of a range of analog voltage to a single value. Delta sigma modulation is one of the most effective forms of conversion in the data converter world.
Pdf modeling and analysis of quantization noise and power. The design of n bit quantization sigmadelta analog to. The ddsm and mash structure is modified and efficient dithering schemes are implemented to reduce quantization noise and achieve the spectral purity. An exact difference equation for the discretetime nonlinear system is used to evaluate the first and secondorder moments and power spectrum of the binary quantizer. As an example of the effect of the hardware, a microprocessor may have a recoverable overflow bit so that scaling by 12 can be accomplished after addition of two numbers rather than before, but this overflow bit recovery also. Derived forms of delta modulation are continuously variable slope delta modulation, delta sigma modulation, and differential modulation. Understanding sigmadelta modulation semantic scholar. Deltasigma modulator with nonuniform quantization ieee. As the input signal increases,k decreases and the suppression of quantization noise degrades sqnr increases less quickly than the signal power, and eventually the. If we apply a digital filter to the noise shaped delta sigma modulator, it removes more noise than does simple oversampling figure 6.
Quantization is the mapping of a range of analog voltage to a single value. Power consumption is also optimized for the sigma delta modulators adc presented based on the modeling of every constraint such as thermal noise, clock jitter noise, quantization noise deciding. The delta modulator comprises of a 1bit quantizer and a delay circuit along with two summer circuits. Delta modulation is a simplified form of dpcm technique, also viewed as 1bit dpcm scheme. Granular noise exists because the decoded output signal can assume only a specified number of levels in the range of interest. For higher orders of quantization, we can achieve noise shaping by including more than one stage. Rounding and truncation are typical examples of quantization processes. Delta modulation was introduced in the 1940s as a simplified form of pulse code modulation pcm, which required a difficulttoimplement analogtodigital ad converter. This is achieved by using passive ct filters, which have the potential for low power design. An oversampled input is taken to make full use of the signal correlation. Quantization noise conditioning techniques for digital delta sigma modulators sudhakar pamarti abstractthis paper presents an overview of outstanding theoretical problems in delta sigma modulator based electronic digitaltoanalog circuits and outlines quantization noise conditioning techniques that are being employed to address these problems. The quantization noise power is the area obtained from integrating the power spectral density function in the range from. Again the total quantization noise of the converter is the same as in figure 7a, but the in band quantization noise is greatly reduced. An approximate formula for calculation of signalto noise ratio of an arbitrary sigma delta modulator sdm has been proposed.
The name is derived from the summation point sigma followed by the delta modulator. How sigma delta modulators achieve high performance and. Quantization noise power an overview sciencedirect topics. The sigmadelta modulator was first introduced in 1962, but until recent. An analysis of quantization noise in delta sigma modulation. Quantization noise conditioning techniques for digital. These simulations were performed using a combination of ltspice, and matlab. Following is the block diagram of a delta modulator. Delta modulation requires a sampling rate much greater than the nyquist rate commonly four or five times the nyquist rate. Sigma delta modulators are also called, collectively, oversampled converters. Pdf of the quantization noise is shown in figure 5. Slopeoverload distortion and granular noise slope delta modulation transmits the derivative of signal mt. The paper designs a sigma delta modulator with 24 significant digits, uses simulink toolbox fully in matlab to model the multibit quantization sigma delta modulator, gets its topological. The step sizes of a nonuniform quantizer are, in general, uniquely determined by the probability density function pdf of an input signal amplitude, while deltasigma modulators usually.
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