© The Institution of Engineering and Technology
This study addresses a new digital calibration filter design for cascaded ΣΔ modulators with finite amplifier gain. A recent approach based on the H-infinity loop shaping method to this problem has the merit of obviating the use of an estimation or adaptive digital correction scheme, which thus reduces the complexity of circuit implementation. For the approach to be successful, it is critical to find an appropriate weighting function so as to make the gain responses of the uncertain noise transfer function (NTF) in a proper shape for improving signal-to-noise ratio (SNR). However, the search of such a weighting function is difficult in general. Moreover, the introduced weighting function increases filter order and hence circuit complexity. To circumvent this difficulty and the inherited drawbacks, this study presents a new noise shaping method for the problem. Considering that it is hard to decide the optimal shape of the uncertain NTF a priori, the authors propose a dual-band design to achieve the shape adjustment task. In particular, the range of lower frequency band is determined by SNR performance evaluation rather than being arbitrarily given a priori. This step is crucial and increases the chance of finding a better filter.
References
-
-
1)
-
Chang, T.H., Dung, L.R., Guo, J.Y.: `On reducing leakage quantization noise of multistage ΣΔ modulator using nonlinear oscillation', Proc. Circuits and Systems, 2005, p. 2555–2558.
-
2)
-
T. Iwasaki ,
S. Hara
.
Generalized KYP Lemma: unified frequency domain inequalities with design applications.
IEEE Trans. Autom. Control
,
1 ,
41 -
59
-
3)
-
D.B. Ribner
.
A comparison of modulator networks for high-order oversampled ΣΔ analog-to-digital converters.
IEEE Trans. Circuits Syst.
,
2 ,
145 -
159
-
4)
-
K. Zhou ,
J.C. Doyle
.
(1997)
Essentials of robust control.
-
5)
-
M. Nagahara ,
Y. Yamamoto
.
Optimal design of ΔΣ modulators via generalized KYP lemma.
ICCAS-SICE
,
4376 -
4379
-
6)
-
G. Leger ,
A. Rueda
.
Cascade ΣΔ modulator with digital correction for finite amplifier gain effects.
Electron. Lett.
,
21 ,
1322 -
1323
-
7)
-
M.C. de Oliveria ,
J.C. Geromel ,
J. Bernussou
.
Extended H2 and H∞ norm characterizations and controller parameterizations for discrete-time systems.
Int. J. Contr.
,
666 -
679
-
8)
-
K. Martin ,
A. Sedra
.
Effects of the op-amp finite gain and bandwidth on the performance of switched-cap filters.
IEEE Trans. Circuits Syst.
,
8 ,
822 -
829
-
9)
-
M.R. Gani
.
Robust digital correction of analog errors in cascaded sigma delta converters.
Measurement
,
310 -
319
-
10)
-
P. Kiss
.
Adaptive digital correction of analog errors in MASH ADC's—Part II: Correction using test signal injection.
IEEE Trans. Circuits Syst. II
,
7 ,
629 -
638
-
11)
-
A.J. Davis ,
G. Fischer ,
H.-H. Albrechtc ,
J. Hess
.
Digital compensation of analog circuit imperfections in a 2-stage sixth-order ΣΔ modulator.
Measurement
,
2 ,
93 -
104
-
12)
-
Schreier R.: ‘The delta-sigma toolbox’ (Version 7), available at http://www.mathworks.com/matlabcentral/fileexchange, accessed 2004.
-
13)
-
J. McKernan ,
M. Gani ,
D. Henrion ,
F.W. Yang
.
Robust filter design for uncertain 2–1 sigma-delta modulators via the central polynomial method.
IEEE Signal Process. Lett.
,
737 -
740
-
14)
-
G. Fischer ,
A.J. Davis
.
Alternative topologies for sigma-delta modulators–a comparative study.
IEEE Trans. Circuits Syst. II
,
10 ,
789 -
797
-
15)
-
S.R. Norsworthy ,
R. Schreier ,
G.C. Temes
.
(1997)
Delta-sigma data converters: theory, design and simulation.
-
16)
-
J. McKernan ,
M. Gani ,
F.W. Yang ,
D. Henrion
.
Optimal low-frequency filter design for uncertain 2–1 sigma-delta modulators.
IEEE Signal Process. Lett.
,
362 -
365
-
17)
-
F.W. Yang ,
M. Gani
.
An H-infinity approach for robust calibration of cascaded sigma-delta modulators.
IEEE Trans. Circuits Syst. I
,
2 ,
625 -
634
-
18)
-
P. Gahinet ,
A. Nemirovski ,
A. Laub ,
M. Chilali
.
(1995)
LMI control toolbox.
-
19)
-
D.A. Johns ,
K. Martin
.
(1997)
Analog integrated circuit design.
-
20)
-
S. Boyd ,
L.E. Ghaoui ,
E. Feron ,
V. Balakrishnan
.
(1994)
Linear matrix inequalities in system and control theory.
-
21)
-
Chou, Y.S., Lin, C.C.: `Digital solution for improving the resolution of cascaded sigma-delta modulators', Proc. 20th VLSI Design/CAD Symp., 4–7 August 2009.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cds.2011.0177
Related content
content/journals/10.1049/iet-cds.2011.0177
pub_keyword,iet_inspecKeyword,pub_concept
6
6