Table Of ContentRESEARCH PERSPECTIVES ON
DYNAMIC TRANS LINEAR
AND
LOG-DOMAIN CIRCUITS
THE KLUWER INTERNATIONAL SERIES
IN ENGINEERING AND COMPUTER SCIENCE
ANALOG CIRCUITS AND SIGNAL PROCESSING
Consulting Editor: Mohammed Ismail. Ohio State University
Related Titles:
CMOS DATA CONVERTERS FOR COMMUNICATIONS
M. Gustavsson, J. Wikner, N. Tan
ISBN: 0-7923-7780-X
DESIGN AND ANALYSIS OF INTEGRATOR-BASED LOG -DOMAIN FILTER CIRCUITS
G.W. Roberts, V. W. Leung
ISBN: 0-7923-8699-X
VISION CHIP
A.Moini
ISBN: 0-7923-8664-7
COMPACT LOW-VOLTAGE AND HIGH-SPEED CMOS, BiCMOS AND BIPOLAR
OPERATIONAL AMPLIFIERS
K-J. de Langen, 1. Huijsing
ISBN: 0-7923-8623-X
CONTINUOUS-TIME DELTA-SIGMA MODULATORS FOR HIGH-SPEED AID
CONVERTERS: Theory, Practice and Fundamental Performance Limits
I.A. Cherry, W. M. Snelgrove
ISBN: 0-7923-8625-6
LEARNING ON SILICON: Adaptive VLSI Neural Systems
G. Cauwenberghs, M.A. Bayoumi
ISBN: 0=7923-8555-1
ANALOG LAYOUT GENERATION FOR PERFORMANCE AND MANUFACTURABILITY
K. Larnpaert, G. Gielen, W. Sansen
ISBN: 0-7923-8479-2
CMOS CURRENT AMPLIFIERS
G. Palmisano, G. Palumbo, S. Pennisi
ISBN: 0-7923-8469-5
HIGHLY LINEAR INTEGRA TED WIDEBAND AMPLIFIERS: Design and Analysis
Techniques for Frequencies from Audio to RF
H. Sjiiland
ISBN: 0-7923-8407-5
DESIGN OF LOW-VOLTAGE LOW-POWER CMOS DELTA-SIGMA AID CONVERTERS
V. Peluso, M. Steyaert. W. Sansen
ISBN: 0-7923-8417-2
THE DESIGN OF LOW-VOLTAGE, LOW-POWER SIGMA-DELTA
MODULATORS
S. Rabii, B.A. Wooley
ISBN: 0-7923-8361-3
TOP-DOWN DESIGN OF HIGH-PERFORMANCE SIGMA-DELTA
MODULATORS
F. Medeiro, A. Perez-Verdu, A. Rodriguez-Vazquez
ISBN: 0-7923-8352-4
DYNAMIC TRANSLINEAR AND LOG-DOMAIN CIRCUITS: Analysis and
Synthesis
J. Mulder, W. A. Serdijn, A.C. van der Woerd, A.H.M. van Roennund
ISBN: 0-7923-8355-9
RESEARCH PERSPECTIVES ON
DYNAMIC TRANSLINEAR
AND
LOG-DOMAIN CIRCUITS
edited by
Wouter A. Serdijn
Delft University of Technology
Jan Mulder
Philips Research Laboratories
Reprinted from
a Special Issue of
ANALOG INTEGRATED CIRCUITS AND SIGNAL PROCESSING
An International Journal
Volume 22, Numbers 2 & 3
March 2000
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
ft
Library of Congress Cataloging-in-Publication Data
Research perspectives on dynamic trans linear and log-domain circuits / edited by
Wouter A. Serdijn, Jan Mulder.
p. cm. --(The Kluwer international series in engineering and computer science; 550.
Analog circuits and signal processing)
"Reprinted from a special issue of Analog integrated circuits and signal processing, an
international journal, volume 22, numbers 2 & 3, March 2000."
ISBN 978-1-4419-4973-8 ISBN 978-1-4757-6414-7 (eBook)
DOI 10.1007/978-1-4757-6414-7
I. Log domain filters. I. Serdijn, Wouter. II. Mulder, Jan. III. Kluwer international
series in engineering and computer science; SECS 550. IV. Kluwer international series in
engineering and computer science. Analog circuits and signal processing.
TK7872.F5 R37 2000
621.3815'324--dc2l
00-022059
Copyright © 2000 by Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 2000
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system or transmitted in any form or by any means, mechanical, photo-copying, recording, or
otherwise, without the prior written permission of the publisher,
Springer Science+Business Media, LLC
Printed on acid~free paper.
ANALOG INTEGRATED
CIRCUITS AND
SIGNAL PROCESSING
An International Journal
Volume 22, Nos 2/3, March 2000
Special Issue: Dynamic Translinear and Log-Domain Circuits
Guest Editors: Wouter Serdijn and Jan Mulder
Guest Editorial ........................................... W. A. Serdijn and 1. Mulder
Overview
Dynamic Translinear Circuits-An Overview ......................................... .
• .................... .T. Mulder. W. A. Set'dijn, It C. van de,. Woad and A. H. M. van Roermund 5
Analysis/Bipolar
A Bernoulli Cell-Based Investigation of the Non-Linear Dynamics in Log-Domain Structures ....... .
· . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. E. M. Drakakis and A. 1. Payne 21
Analysis and Compensation of Log-Domain Biquadratic Filter Response Deviations due to Transistor
Nonidealities .......................................... v. W. Leung and G. W. Roherts 41
A Study of Different Class AB Log Domain First Order Filters ........... A. T. Tola and D. R. Frey 57
Synthesis/Bipolar
Synthesis of Log-Domain Filters from First-Order Building Blocks ......................... .
· ............................................... R. T. Edwards and C. Cauwenberghs 71
A Very High-Frequency Transistor-Only Linear Tunable Companding Current-Mode Integrator ...... .
· ...................................... A. Worapishet, J Mahattanakul and C. Toumazou 81
Weak-Inversion MOS
A Log-Domain CMOS Transcapacitor: Design, Analysis and Applications .................... .
· ........................................... E. Fragniire, E. Vittoz and A. van Schaik 89
Low Voltage Micropower Log-Domain Filters ....................... E.!. El-Masry and I. Wu 103
A New Current-Mode Synthesis Method for Dynamic Translinear Filters and its Applications in Hearing
Instruments ..... D. Masmoudi, W. A. Serdijn, J Mulder, A. C. van de Woad, J Tomas and J P. Dom 115
Strong-Inversion MOS
"Square Root Domain" Filter Design and Performance ....... , ....... A, Payne and M, Eskiyali 125
Special Issue
Call for Papers. , , . , .......... , ............. , .... , . , , . , , .. , ... , .. , ........ , . .. 139
... Analog Integrated Circuits and Signal Processing, 22, 107-109 (2000)
., ~) 2000 Kluwer Academic Publishers, Boston.
Guest Editorial
Nowadays, the area of analog integrated circuits is state-of-the-art results obtained for both linear and
facing some serious challenges due to the ongoing non-linear applications are treated.
trends to low supply voltages, low power consump The second paper, by Drakakis and Payne, presents
tion and high frequency operation. The situation is a low-level treatment of the non-linear dynamics
becoming even more complicated by the fact that encountered in log-domain structures, by means of a
many transfer functions have to be tunable or non-linear circuit element tenned a Bernoulli Cell.
controllable. This cell comprises an NPN BJT and an emitter
A promising approach to face these challenges is connected grounded capacitance, and its dynamic
given by the class of dynamic translinear circuits, behavior is detennined by a differential equation of
which are as a consequence receiving increasing the Bernoulli form. This results in a system of linear
interest. Several different names are used in literature: differential equations, which describe the dynamics of
log-domain, exponential state-space, current-mode the derived log-domain state variables. The approach
companding, instantaneous companding, tanh aids the analysis of log-domain circuits, and allows
domain, sinh-domain, polynomial state-space, the internal non-linear currents to be expressed in
square-root domain and translinear filters. In fact, all closed analytical fonn. A worked example for a
these groups are (overlapping) subclasses of the specific topology with continning simulation results is
overall class of dynamic translinear circuits. presented.
Dynamic translinear circuits are based on the The third paper, by Leung and Roberts, discusses
dynamic translinear principle, which is a general the analysis of log-domain integrators in the presence
ization of the conventional, i.e. static, translinear of major time-invariant bipolar transistor imperfec
principle, which was treated previously in Vol. 9, No. tions, being parasitic emitter and base resistances,
2 of Analog Integrated Circuits and SiRnal Processing finite beta, Early effect and area mismatches. These
and can be applied to the structured design of circuits results are subsequently used to predict the transfer
to implement both linear and non-linear differential function deviations of biquadratic tilters, for both
equations, such as, e.g. filters, oscillators, RMS-DC lowpass and bandpass filter responses. Electronic
converters, PLLs and chaotic circuits. In fact, the compensations schemes are proposed and their
dynamic translinear principle facilitates a direct effectiveness verified by computer simulations.
mapping of any function, described by a polynomial The fourth paper, by Tola and Frey, compares
differential equation, onto silicon. several different class AB trans linear filters, of which
To address this growing field, which is of both two are new, in tenns of their noise and distortion
practical and theoretical interest, this Special Issue of hehavior using analytical and simulation results. The
Analog InteRrated Circuits and Signal Processing on study, although approximate, suggests ways in which
Dynamic Translinear Circuits has been compiled. It hath noise and distortion perfonnance may be
comprises ten contributions, coming from recognized optimized by appropriate choice of circuit topology.
"dynamic-translinear" researchers in Europe and Other practical aspects of the designs, being transistor
North America. mismatch and delay, are also discussed.
The first paper, by Mulder, Serdijn, van der Woerd The fifth paper, by Edwards and Cauwenberghs,
and van Roermund, gives an overview of this young, describes the synthesis of single-ended, first-order
yet rapidly developing, circuit paradigm. Emphasis is filter circuits, starting from the static and dynamic
placed on methods for analysis and synthesis, rather circuit principle. It is shown how higher-order filters
than on specific circuit implementations. The static can be easily constructed from these first-order
and dynamic principles are reviewed and the building hlocks. Additional issues related to audio
theoretical relevance, or better, irrelevance, of a frequency filter design are addressed and measure
generalization of the dynamic translinear principle ment results of a IS-channel filter-bank system,
to strong inversion MaS, resulting in so-called fabricated in both a 2 f1 and a 1.2 f1 BiCMOS IC
square-root domain filters, is discussed. Finally, process, are presenLed.
108 W A. Serdijn and 1. Mulder
The sixth paper, by Worapishet, Mahattanakul and issues, such as mobility reduction, channel length
Toumazou, presents a transistor-only linear tunable modulation, velocity saturation and threshold voltage
companding integrator, utilizing the non-linear base mismatch, are addressed. Finally, simulation and
emitter diffusion capacitance of the BIT. A first-order measurement results are presented to validate the
approximation of the circuit characteristics is approach.
explained, followed by a bricf discussion on the Thc editors would like to thank all thc authors who
departure from ideal characteristics due to transistor submitted papers, all the reviewers who participated
non-idealities. Experimental results indicate that the in the final selection of the papers, and the Kluwer
circuit exhibits a low-distortion performance to Editorial Staff for their efforts in creating this special
frequencies approaching the transit frequency of the issue. We hope that this issue will provide you, the
transistor. The integrator time constant can be simply reader, new insights into the potential of dynamic
adjusted over an octave using a current source. translinear integrated circuits.
The seventh paper, by Fragniere and Vittoz,
presents a CMOS implementation of a log-domain Gucst Editor
transcapacitor. The circuit integrates a differential Wouter A Serdijn
input current into an output "pseudo-voltage" and is Delft University of Technology
thus compatible with "pseudo-conductances" imple Faculty of Information Technology and Systems,
mented with a single transistor. The circuit is analyzed Delft, The Netherlands
and a collection of log-domain reactive components
and small circuits using it is proposed. Guest Editor
Thc cighth paper, by Wu and El-Masry, presents a Jan Mulder
design technique for micro-power continuous-time Philips Research Laboratories,
filters, employing CMOS devices operating in weak Eindhoven, The Netherlands
inversion, starting from a CMOS log-domain inte
grator. The effects of the device non-idealities on the
integrator perfonnance are investigated and verified
by computer simulations. Its application in a fifth
order Chebyshev lowpass ladder filter indicates a
proper operation from a 1.5 V supply and a frequency
control range of three decades (from 100 Hz to
100 kHz). At 100 kHz, its power dissipation equals
1.27fJ-W.
The ninth paper, by Masmoudi, Serdijn, Mulder,
van der Woerd, Tomas and Dom, proposes a current
mode synthesis method for dynamic translinear filters.
A second-order audio filter for hearing instruments,
employing subthreshold MOS transistors, is pre
sented. It operates from a supply voltage down to
1 V and consumes 5fJ-A. The filter cut-off frequency
and its quality factor can be tuned [rom 600 Hz to
13 kHz and from 0.6 to 1.1, respectively. Mismatch
problems are investigated on the circuit level and an
on-chip compensation method is proposed.
Finally, thc tenth paper, by Payne and Eskiyerli,
discusses the implementation and perfonnance of
square-root domain filters that are based on the large Wouter Serdijn was born in Zoetenneer ("Sweet
signal square law characteristic of MOS transistors in Lake City' '), The Netherlands, in 1966. He started his
strong inversion. The design of two non-linear course at the Faculty of Electrical Engineering at
subcircuits, being a geometric mean circuit and a the Delft University of Technology in 1984, and
squarer/divider, is described and various perfonnance received his "ingenieurs" (M.Sc.) degree in 1989.
2
Gues Editorial 109
Subsequently, he joined the Electronics Research
Laboratory of the same university where he received
his Ph.D. in 1994.
His research interests include low-voltage, ultra
low-power, RF and dynamic-translinear analog inte
grated circuits along with circuits for wireless
communications, hearing instruments and pace
makers. Since 1997, he has been a project leader in
the multi-disciplinary Ubiquitous Communications
(Ubi Com) research program of the Delf l University of
Technology.
He is co-editor and co-author of the book Analof? Jan Mulder was born in Medemblik, The
IC Techniques for Low-Voltage Low-Power Netherlands, on July 7, 1971. He received an M.Sc.
Electronics (Delft University Press, Delft, 1995), degree in electrical engineering from the Delft
and of the book Low-Voltage Low-Power Analog University of Technology in 1994. From 1994 to
Integrated Circuits (Kluwer Academic Puhlishers, 1998, he worked towards his Ph.D. thesis on static and
Boston, 1995). He authored and co-authored more dynamic-trans linear analog integrated circuits at the
than 60 publications. He teaches Analog Electronics Electronics Research Lahoratory. He received his
for Industrial Designers, Analog IC Techniques and Ph.D. in October 1998. He is now with Philips
Structured Electronic Design. Research Lahoratories, Eindhoven, The Netherlands.
3
... Analog Integrated Circuits and Signal Processing, 22, 111-126 (2000)
" (C 2000 Kluwer Academic Publishers, Boston.
Dynamic Translinear Circuits-An Overview
JAN MULDER! WOUTER A. SERDIJN,2 ALBERT C. VAN DER WOERD2 AND
ARTHUR H. M. VAN ROERMUND2
'Philips Research Lahoratories. Building WAY 5.93. Prot: Holstlaan. 4. 5656, AA Eindhoven. The Netherlands
lEleetmnies Research Lahoratory. Department of' Electrical EnKineering. Delft University oj Tcchn%gy. Delft. The Netherlands
Accepted 31 August, 1998
Abstract. Dynamic translinear circuits and log-domain filters form a promising and challenging approach to meet
the dynamic range limitations that conventional analog implementation techniques are facing due to ever lower
supply voltages, low power consumption and high-frequency demands. This paper aims to give an overview of this
young, yet rapidly developing, circuit paradigm. Emphasis is placed on methods for analysis and synthesis and on
state-of-the-art results obtained for both linear and non-linear applications.
Key Words: translinear circuits, companding log-domain filters
1. Introduction recognize the TL nature of these circuits, he coined
the term "log-domain filters", based on the loga
Due to the ongoing trends to lower supply voltages rithmic relation between the voltages and currents. For
and low power operation, the area of analog many years, the idea of log-domain filtering was to
integrated .filters is facing serious challenges [I,2J. gather dust. In 1990, Seevinck independently rein
The maximal dynamic range achievable using vented the TL filter concept, which he denoted by the
conventional filter implementation techniques, such term "current-mode companding" [5]. The filters
as opamp-MOSFET-C, transconductance-C and presented by both Adams and Seevinck were first
switched-capacitor, becomes severely restricted by order. The expansive interest in TL filters really took
the supply voltage. In ultra-low-power environments, off in 1993, when Frey published a synthesis method
linear resistors become too large for on-chip enabling the design of higher-order log-domain filters
integration. Finally, the situation is complicated by [6]. Tn addition, Frey proposed a more general class of
high-frequency demands and the fact that the filter TL filters, which he termed "exponential state-space
transfer function has to be tunable to compensate for 11 Iters" [7].
process tolerances. From that time, many other researchers began to
In the area of continuous-time filters, a promising investigate these filters. Toumazou et al. published an
approach to meet these challenges is provided by the implementation in weak inversion MOS, showing the
class of "translinear filters". Due to the encouraging potential for low-power operation [8]. The first
expectations, research efforts have increased rapidly experimental results were published by Perry and
and TransLinear (TL) filter design has become a trend. Roberts [9]. In addition, they proposed an alternative
This is illustrated in Fig. I. In a general context, synthesis method based on the simulation of LC
translinear filters form a sub-class of an encompassing ladder filters. The first experimental results in
class of companding networks that exhibit a theore subthreshold MOS were presented by Ngarmnil et
tically linear frequency-dependent transfer [unction al. [10]. Punzenberger et al. demonstrated the
externally even though the internal signal path suitability for low-voltage applications [11] and the
contains non-linear elements. An excellent general favorable dynamic range specification resulting from
overview of companding filters can be found in [3]. class AB operation: 65 dB at l.2 V supply voltage
Translinear filters were originally introduced by fl2]. Different synthesis methods were proposed by
Adams in 1979 [4]. Since Adams at the time did not various researchers [13-18J. A general analysis
5
