On the stability of high order Sigma-Delta modulators

Mladenov, Valeri; Hegt, Hans; Roermund, Arthur van

doi:10.1109/icecs.2001.957472

Cited by 9 publications

(13 citation statements)

References 8 publications

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“…This means that the initial condition with respect to x k should be taken in accordance with (7) in order to ensure stability of the solution. This fits with the results in [11], [12] concerning the stability of high order modulators when only one pole of the loop filter is larger than 1.…”

Section: If |λ K |<1 For Every L That Is Large Enough (After Enough supporting

confidence: 80%

“…The corresponding block diagram of modulator model is given in Fig. 2 [10], [11]. Based on this presentation the state equations of the Sigma Delta modulator are…”

Section: Parallel Decomposition Of High Ordermentioning

confidence: 99%

“…Especially we focus our attention on constant input signals. The method is based on the decomposition of the general N-th order modulator presented in [10], [11], [12]. Using this presentation the modulator could be considered as made up of N first order modulators (generally complex modulators), which interact only through the quantizer function.…”

Section: Introductionmentioning

confidence: 99%

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A method for searching the limit cycles of high order sigma-delta modulators

Mladenov

2009

2009 European Conference on Circuit Theory and Design

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Link to publication Citation for published version (APA):Mladenov, V. M. (2009). A method for searching the limit cycles of high order Sigma-Delta modulators. In Proceedings of the 19th European Conference on Circuit Theory and Design, ECCTD 2009, August 23-27, 2009 Antalya, Turkey, (pp. 543-546 General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

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Section: If |λ K |<1 For Every L That Is Large Enough (After Enough supporting

confidence: 80%

“…The corresponding block diagram of modulator model is given in Fig. 2 [10], [11]. Based on this presentation the state equations of the Sigma Delta modulator are…”

Section: Parallel Decomposition Of High Ordermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A method for searching the limit cycles of high order sigma-delta modulators

Mladenov

2009

2009 European Conference on Circuit Theory and Design

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“…Due to the fact that Σ-Δ modulation is a non-linear process, its analysis is particularly difficult and is usually based on linear or quasi-linear models. Many empirical stability criteria and optimization techniques can be found in [3], while a stability analysis of high-order Σ-Δ modulators is presented in [4]. Stability problems relate to the input amplitude, the loop filter zeros and poles and the number of quantization levels.…”

Section: Introductionmentioning

confidence: 99%

Single-bit-output all-digital frequency synthesis using multi-step look-ahead bandpass Σ-Δ modulator-like quantization processing

Basetas

Sotiriadis

2015

2015 Joint Conference of the IEEE International Frequency Control Symposium &Amp; The European Frequency and Time Forum

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A configurable single-bit-output Σ-Δ modulator variant is presented, which improves upon stability and dynamic range. The derivation of the proposed modulation scheme from the Σ-Δ error-feedback structure and its mathematical description are analyzed, while its application in fractional-N frequency dividers and all-digital frequency synthesizers is investigated. It is shown that stable high-order noise shaping is possible even when using noise transfer functions that are unstable in a conventional Σ-Δ modulator loop. Furthermore, multipliers can be avoided if the noise transfer function coefficients are chosen appropriately, leading to a low complexity hardware implementation. In special cases the architecture is equivalent to another Σ-Δ modulator with a different, stable, NTF than the initial one. The effectiveness of the proposed modulation scheme is demonstrated by specific examples for each application.978-1-4799-8866-2/15/$31.00 ©2015 IEEE

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“…There is a theory [5] that allows us to have an approximate estimate on the modulator stability ranges and that is based on loopfilter parallel decomposition. In this paper we present a derivation of an arbitrary SDM high order loopfilters from Z to S domain with performance result validation with software simulations in MATLAB.…”

mentioning

confidence: 99%

Higher order sigma-delta modulator loopfilter paralel form representation in Z and S domain

Tsenov

Mladenov

2011

Proceedings of the Joint INDS'11 &Amp; ISTET'11

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In this paper we present the conversion of arbitrary high order sigma-delta modulator Z-domain loopfilter transfer function into parallel form low order subsections in both S and Z domains. The benefit of this type filter form representation is the existence of theory that can validate sigmadelta modulator's stability. The S domain filter representation is suitable for analog schematic element value calculation stage done according to the utilized transfer function when direct analogue parallel loopfilter implementation is performed.

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On the stability of high order Sigma-Delta modulators

Cited by 9 publications

References 8 publications

A method for searching the limit cycles of high order sigma-delta modulators

A method for searching the limit cycles of high order sigma-delta modulators

Single-bit-output all-digital frequency synthesis using multi-step look-ahead bandpass Σ-Δ modulator-like quantization processing

Higher order sigma-delta modulator loopfilter paralel form representation in Z and S domain

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On the stability of high order Sigma-Delta modulators

Cited by 9 publications

References 8 publications

A method for searching the limit cycles of high order sigma-delta modulators

A method for searching the limit cycles of high order sigma-delta modulators

Single-bit-output all-digital frequency synthesis using multi-step look-ahead bandpass &#x03A3;-&#x0394; modulator-like quantization processing

Higher order sigma-delta modulator loopfilter paralel form representation in Z and S domain

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Single-bit-output all-digital frequency synthesis using multi-step look-ahead bandpass Σ-Δ modulator-like quantization processing