This concept is called noise shaping Fig. Note that in Equation 9, as frequency approaches zero, Y approaches input component X. As the frequency increases, the first term with the input signal component approaches zero, and the output approaches Q n. In other words, at high frequencies, the output consists mostly of quantization noise.
Overall, it seems as if a low-pass filter is acting on the signal in the forward path and a high-pass filter is acting on noise in the feedback path. Noise shaping has been achieved!
After that, all that needs to be done is to filter out the noise at high frequencies Fig. The sub-DAC can be as simple as a multiplexer that switches between two reference voltages. Latch operation is usually embedded in the comparator. Oversampling improves signal-to-noise ratio SNR.
When noise power is reduced, an increase in SNR is expected. From a quantitative point of view, starting with the quantization noise for non-oversampled converters obtained by Equation 2, the theoretical SNR value for quantized noise is expressed by the ratio of input signal to noise signal:. Equation 6 expresses the noise power for an oversampled converter.
SNR improves by 3 dB, or 0. For example, a bit converter has a theoretical value for SNR of about 98 dB. Using higher-order modules, delta-sigma will further improve SNR. A second-order modulator improves SNR by 15 dB for each doubling of oversampling ratio. The improvement that is achieved for each doubling of oversampling ratio generally can be calculated from:.
The full scale in this example is 2. On a 5-V scale, because the lower reference is sitting at —2.
This is 0. This average value is close to the actual value of the input 0. If one continues the operation and obtains more bits for the table, the average value gets closer and closer to 0.
For input values that are closer to —V Ref , the modulator generates more lows. A typical sine-wave input generates a code that has more highs or lows at its two peaks. As the input gets closer to the mid-range, on average, the resulting number of ones and zeros becomes comparable Fig. The bit stream output by the model of a sixth-order modulator is followed by a decimation filter to form a bit delta-sigma ADC, resulting in this output. Again, as the input amplitude is increased, the modulator generates more ones and, moving toward the lowest voltage of the input, more zeros Fig. Norseworthy, R.
Temes, Wiley Interscience, CAS, July , pp. Blad, P. Lowenborg, H. Johansson, 14th European Signal Processing Conference, For more information on data converters, visit www. By adding extra feedback coeffi- cients a3 and a2 referring to Fig.
Oversampled A/D converters have become very popular in recent years. Some of their advantages include relaxed requirements for anti-alias filters, relaxed. Fundamentals of Oversampled A/D Converters. 2. Opamp Topologies for Oversampled Converters. 3. Optimal Design of Opamps for Oversampled Modulators.
To ous-time filter. The images and noises from 1. Here we use a two-stage interpolator shown in upper edge of signal band. As a guide, the transmit higher than before. If the input is a single-tone If we 1. For low power consumption, integrator word-length The noises after 2. The ated by the semi-digital FIR filter and analog filter word-length of each integrator can be obtained by simu- because the noises are generated by the digital modulator. The use of current-steering circuits allows the 4 5 6 7 10 10 10 10 10 Frequency semi-digital filter to be implemented in a standard digital CMOS technology.
The sampling frequency increases 2 times at first stage and increases 16 times at References second stage. Candy and G.
clublavoute.ca/warax-corbera-dating-site.php Since the continuous-time filters tion. IEEE Press, Karema, T. Ritoniemi and H. Su and B. The power dissipation of Circuits, pp. Ten- supply. Conclusions  T. Ritoniemi, T. Karema and H.
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IEEE Int. With a 5-th order modulator and an oversam- niques, Ph. D Dissertation No. The out-of-band quantization. Related Papers.
A b 1. By Pier Andrea Francese. By Mohammad Hossein Maghami. By J Jacob Wikner. By yogita Gajare. A multiplier-free structure for 1-bit high-order digital delta-sigma modulators.
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