Accurate stability prediction of one-bit higher-order delta–sigma modulators for multiple-sinusoidal inputs
Accurate stability prediction of one-bit higher-order delta–sigma modulators for multiple-sinusoidal inputs
- Author(s): J. Lota ; M. Al-Janabi ; I. Kale
- DOI: 10.1049/iet-cds.2011.0194
For access to this article, please select a purchase option:
Buy article PDF
Buy Knowledge Pack
IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.
Thank you
Your recommendation has been sent to your librarian.
- Author(s): J. Lota 1 ; M. Al-Janabi 2 ; I. Kale 2
-
-
View affiliations
-
Affiliations:
1: School of Computing, IT and Engineering, University of East London, London, UK
2: Department of Electronic, Communication and Software Engineering, University of Westminster, London, UK
-
Affiliations:
1: School of Computing, IT and Engineering, University of East London, London, UK
- Source:
Volume 6, Issue 2,
March 2012,
p.
71 – 78
DOI: 10.1049/iet-cds.2011.0194 , Print ISSN 1751-858X, Online ISSN 1751-8598
- « Previous Article
- Table of contents
- Next Article »
The present approaches on predicting stability of delta–sigma (Δ–Σ) modulators are mostly confined to DC inputs. This poses limitations as practical applications of Δ–Σ modulators involve a wide range of signals other than DC such as multiple-sinusoidal inputs for speech modelling. In this study, a quasi-linear model for Δ–Σ modulators with non-linear feedback control analysis is presented that accurately predicts stability of single-loop one-bit higher-order Δ–Σ modulators for multiple sinusoids. Theoretical values are shown to match closely with the simulation results. The results of this study would significantly speed up the design and evaluation of higher-order single-loop Δ–Σ modulators with increased dynamic ranges for various applications that require multiple-sinusoidal inputs or any general input composed of a finite number of sinusoidal components.
Inspec keywords: delta-sigma modulation; feedback; circuit stability; nonlinear control systems
Other keywords:
Subjects: A/D and D/A convertors; Nonlinear control systems; A/D and D/A convertors
References
-
-
1)
- J. Lota , M. Al-Janabi , I. Kale . Nonlinear stability analyses of higher-order sigma–delta modulators for DC and sinusoidal inputs. IEEE Trans. Instrum. Meas. , 3 , 530 - 542
-
2)
- J. Reiss . (2003) Stability analysis of limit cycles of higher-order sigma–delta modulators.
-
3)
- J. Reiss . (2005) Towards a procedure for stability analysis of higher-order sigma–delta modulators.
-
4)
- Ritoniemi, T., Karema, T., Tenhunen, H.: `The design of stable high order 1-bit sigma–delta modulators', Proc. IEEE Int. Symp. on Circuits and Systems-ISCAS-90, 1990, 4, p. 3267–3270.
-
5)
- Kuei-Chih, L., Chuan-His, L.: `On the design and analysis of the 4th-order leapfrog sigma–delta modulator', Proc. Int. Conf. on Communication Circuits and Systems, ICCCAS-2006, June 2006, 4, p. 2304–2308.
-
6)
- Lota, J., Al-Janabi, M., Kale, I.: `Stability analyses of higher-order delta-sigma modulators for dual-sinusoidal inputs', Proc. IEEE Instrumentation and Measurements Technology Conf.-IMTC 2007, Warsaw, Poland, p. 1–5.
-
7)
- S. Hein , A. Zakhor . On the stability of sigma–delta modulators. IEEE Trans. Signal Process. , 7 , 2322 - 2348
-
8)
- Brigati, S., Francesconi, F., Malcovati, P., Maloberti, F.: `A fourth-order single-bit switched-capacitor sigma–delta modulator for distributed sensor applications', Proc. 19th IEEE Instrumentation and Measurement Technology Conf., 2002, IMTC/2002, August 2002, 1, p. 253–256.
-
9)
- Chih-Yuan, C., Rong-Guey, C., Jia-Hua, H., Shuenn-Yuh, L.: `Stability analysis and system design of sigma–delta-modulators', Proc. Int. Symp. on Integrated Circuits, ISIC’09, December 2009, p. 9–12.
-
10)
- J. Roh , S. Byun , Y. Choi , H. Roh , Yi-G. Kim , J.-L. Kwon . A 0.9-V 60-µW 1-bit fourth-order delta-sigma modulator with 83-dB dynamic range. IEEE J. Solid-State Circuits , 2 , 361 - 370
-
11)
- Zhang, J., Brennan, P.V., Juang, D., Vinogradova, E., Smith, P.D.: `Stable boundaries of a 2nd-order sigma–delta modulator', Proc. South. Symp. on Mixed Signal Design, February 2003.
-
12)
- C. Youngkil , R. Jeongjin , R. Hyungdong , N. Hyunseok , L. Songjun . A 99-dB DR fourth-order delta–sigma modulator for 20-kHz bandwidth sensor applications. IEEE Trans. Instrum. Meas. , 7 , 2264 - 2274
-
13)
- Liyuan, L., Run, C., Dongmei, L.: `A 20-Bit sigma–delta D/A for audio applications in 0.13 µm CMOS', Proc. IEEE Int. Symp. on Circuits and Systems, ISCAS 2007, May 2007, p. 3622–3625.
-
14)
- P. Steiner , W. Yang . A framework for analysis of high-order sigma–delta modulators. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. , 1 - 10
-
15)
- N. Wong , N.G. Tung-Sang . DC stability analysis of higher-order, lowpass sigma–delta modulators with distinct unit circle NTF zeroes. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. , 1 , 12 - 30
-
16)
- Steiner, P., Yang, W.: `Stability analysis of the second-order sigma–delta modulator', Proc. IEEE Int. Sym. on Circuits and Systems-ISCAS 94, 1994, 5, p. 365–368.
-
17)
- Fang, W., Toth, M.: `Using the digital microphone function on TLV320AIC33 with AIC33EVM/USB-MODEVM system', Texas Instruments Application Report SLAA275, November 2005, http://www.ti.com/lit/an/slaa275/slaa275.pdf, accessed on October 2011.
-
18)
- S.H. Ardalan , J.J. Paulos . An analysis of non-linear behaviour in Σ-Δ modulators. IEEE Trans. Circuits Syst. , 6 , 1157 - 1162
-
19)
- Fraser, N.A., Nowrouzian, B.: `A novel technique to estimate the statistical properties of sigma–delta A/D converters for the investigation of DC stability', Proc. IEEE Int. on Symp. Circuits and Systems-ISCAS 02, May 2002, 3, p. 111-289–111-292.
-
20)
- Eid, E.-S., Gaber, W.M.: `Design of a 0.9 V 5 MHz sampling frequency 120 µW 1-bit fourth-order feedforward sigma–delta modulator', Proc. IEEE TENCON 2009, January 2009, p. 1–4.
-
21)
- R.T. Baird , T.S. Fiez . Stability analysis of high-order delta–sigma modulation for ADC's. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. , 59 - 62
-
22)
- A. Gelb , W.E.V. Velde . Multiple-input describing functions and nonlinear system design, Appendix E: table of random-input describing functions (RIDFs).
-
23)
- Lota, J., Al-Janabi, M., Kale, I.: `Stability analyses of higher-order delta-sigma modulators using the describing function method', Proc. IEEE Int. Symp. on Circuits and Systems-ISCAS 2006, May 2006, p. 593–596.
-
24)
- F.J. Massey . The Kolmogorov–Smirnov test for goodness of fit. J. Am. Stat. Assoc. , 253 , 68 - 78
-
25)
- Yang, Z., Yao, L., Lian, Y.: `A 0.7-V 100-µW audio delta–sigma modulator with 92-dB DR in 0.13 µm CMOS', Proc. IEEE Int. Symp. Circuits and Systems, ISCAS 2011, May 2011, p. 2011–2014.
-
26)
- Youngkil, C., Hyungdong, R., Hyunseok, N., Jeongjin, R.: `99 dB high-performance delta–sigma modulator for 20-kHz bandwidth', Proc. Fourth IEEE Int. Symp. on Electronic Design, Test and Applications, January 2008, p. 75–78, DELTA 2008.
-
27)
- D.G. Altinok , M. Al-Janabi , I. Kale . Stability analysis of bandpass sigma–delta modulators for single- and dual-tone sinusoidal input. IEEE Trans. Instrum. Meas. , 99 , 1546 - 1554
-
28)
- Zhang, J., Brennan, P.V., Juang, D., Vinogradova, E., Smith, P.D.: `Stable analysis of a sigma–delta modulator', Proc. IEEE Int. Symp. on Circuits and Systems-ISCAS 03, May 2003, 1, p. 1-961–1-964.
-
29)
- Risbo, L.: `Stability predictions of higher-order delta-sigma modulators based on quasi-linear modeling', Proc. IEEE Int. Symp. on Circuits and Systems-ISCAS 94, 30 May–02 June 1994, 5, p. 361–364.
-
30)
- Rebai, C., Ghazel, A., Farhat, F.: `High order 1-bit sigma–delta ADC for multistandard GSM/UMTS radio receiver', Proc. 16th Int. Conf. on Microelectronics, ICM 2004, December 2004, p. 128–131.
-
31)
- Analog Devices: ‘Omni-directional microphone with bottom port and digital output’, Data Sheet for ADMP 421, http://www.analog.com/static/imported-files/data_sheets/ADMP421.pdf, accessed on October 2011.
-
1)