By Mücahit Kozak
The research of the quantization noise in delta-sigma modulators isn't a trivial job. cutting-edge research tools comprise modelling the quantization noise as a uniform disbursed white noise. besides the fact that, it is common to monitor restrict cycle oscillations and tones on the output of a delta-sigma modulator. In many of the purposes, those restrict cycles and tones are strictly objectionable. Such an software, for example, is a Fractional-N PLL frequency synthesizer, the place idle tones and restrict cycles generated from the delta-sigma modulator without delay seem within the synthesized RF waveform as spurious parts. The rather small conversion bandwidth is one other vital predicament of delta-sigma modulators. because of their oversampling nature, delta-sigma modulators were utilized in low frequency functions. Oversampled Delta-Sigma Modulators: research, purposes, and Novel Topologies provides theorems and their mathematical proofs for the precise research of the quantization noise in delta-sigma modulators. vast mathematical equations are incorporated during the publication to research either single-stage and multi-stage architectures. it's been proved that adequately set preliminary stipulations generate tone loose output, only if the modulator order is no less than 3. those effects are utilized to the layout of a Fractional-N PLL frequency synthesizer to provide spurious loose RF waveforms. additionally, the ebook additionally provides time-interleaved topologies to extend the conversion bandwidth of delta-sigma modulators. The topologies were generalized for any interleaving quantity and modulator order. Oversampled Delta-Sigma Modulators: research, purposes, and Novel Topologies is stuffed with layout and research recommendations. The ebook comprises adequate aspect that permits readers with little historical past within the topic to simply keep on with the fabric in it. Oversampled Delta-Sigma Modulators: research, functions, and Novel Topologies can be of curiosity to graduate scholars, researchers, and training circuit designers within the parts of delta-sigma established information converters and Fractional-N PLL frequency synthesizer layout.
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Extra resources for Oversampled Delta-Sigma Modulators: Analysis, Applications and Novel Topologies
ANALYSIS OF SINGLE-STAGE DELTA-SIGM MODULA TORS where A = 2b/(2 " - I ) is the quantizer bin width. The no-overload region of the quantizer is defined as the range of input amplitudes, for which the absolute value of the quantizer error e = J - 1. , lei 5 A12 ). 4 depict the quantizer error for a twobit and three-bit quantizer, respectively, as a function of the input amplitude. It is clear from these figures that for a two-bit and three-bit quantizer, the nooverload region is given by V E [ - 2 ~ , 2 ~and ] V E [ - 4 ~ , 4 ~ respectively.
13 shows the spectral density for an artificially generated white noise, which is shaped by the third-order noise shaping transfer function. The theoretical noise transfer function is also overlaid on the same plot. The white noise1\as uniformly distributed between -1 and 0, and has a mean value of-112 and a variance of 1/12. The NSQ calculation indeed shows that NSQ,,, =a' = 1 :12 for this case, as predicted. 14. 1 1). The quantization process is embedded in the overflow mechanism of the accumulators.
1). 9) could be summarized as v,[n]=v,[n-~]+n[n]-y[n]; n=0,1,2;.. 1,2,... , is the quantizer error sequence, and rn! k! 1 16)). Proof: The proof is by induction on L . Observe that for L = 2 where \,, _,, v,_, and lJ;,,, are the initial conditions on the first, second and third accumulators, respectively. The following theorem will now state a general description for an L"' -order AX modulator. ,, ,,-,+ v,, - r; Figzrre 4-6. 6 employing M-bit quantization having maximum output levels of k b . r[ti] is applied at n = O .