A Bibliography of the Work Done on Externally-Linear-Internally-Nonlinear Circuits during 1979-2014

Manoj Kumar Jain, V. K. Singh, Raj Senani

American Journal of Electrical and Electronic Engineering OPEN ACCESSPEER-REVIEWED

A Bibliography of the Work Done on Externally-Linear-Internally-Nonlinear Circuits during 1979-2014

Manoj Kumar Jain1, V. K. Singh1, Raj Senani2,

1Department of Electronics and Communication Engineering, Institute of Engineering and Technology, Lucknow, India

2Division of Electronics and Communication Engineering, Netaji Subhas Institute of Technology, Sector 4, Dwarka, New Delhi, India

Abstract

There is a continued demand of analog circuits which are capable of operating at low supply voltages and have low-power consumption and large dynamic range. There are several techniques of designing circuits satisfying such requirements a majority of which fall into the general category of externally-linear-internally-nonlinear (ELIN) circuits. In this paper, we present a bibliography of ELIN circuits which covers log-domain, exponential state-space domain, square root domain and other related circuits, based upon the work done during 1979 to 2014. It is hoped that this compilation (with a brief overview) should be useful to research scholars, educators, students, practicing engineers and anybody who is interested in knowing about the current state-of-the- art of log domain, translinear and square root domain circuits.

Cite this article:

  • Manoj Kumar Jain, V. K. Singh, Raj Senani. A Bibliography of the Work Done on Externally-Linear-Internally-Nonlinear Circuits during 1979-2014. American Journal of Electrical and Electronic Engineering. Vol. 3, No. 3, 2015, pp 64-71. http://pubs.sciepub.com/ajeee/3/3/1
  • Jain, Manoj Kumar, V. K. Singh, and Raj Senani. "A Bibliography of the Work Done on Externally-Linear-Internally-Nonlinear Circuits during 1979-2014." American Journal of Electrical and Electronic Engineering 3.3 (2015): 64-71.
  • Jain, M. K. , Singh, V. K. , & Senani, R. (2015). A Bibliography of the Work Done on Externally-Linear-Internally-Nonlinear Circuits during 1979-2014. American Journal of Electrical and Electronic Engineering, 3(3), 64-71.
  • Jain, Manoj Kumar, V. K. Singh, and Raj Senani. "A Bibliography of the Work Done on Externally-Linear-Internally-Nonlinear Circuits during 1979-2014." American Journal of Electrical and Electronic Engineering 3, no. 3 (2015): 64-71.

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1. A Brief Overview of ELIN Circuits

The log-domain circuits are based on natural logarithmic relation between the voltage and current of diodes and between base-emitter voltage and collector current of bipolar junction transistors. The first log-domain filter circuit was proposed by Adams in 1979 [1]. Adams conceived the first ever log-domain filter as a circuit, composed of both linear and non-linear elements, which, when placed between a log converter and an anti-log converter (in the ‘log-domain’), caused the system to act as a linear filter. Thus, Adams circuit was also the first externally linear and internally nonlinear (ELIN) circuit, demonstrating the compressing and expanding (companding) technique.

The log-domain filters are also recognized as translinear (TL) filters. The TL filters are essentially dynamic translinear circuits, which are based upon the dynamic translinear principle which is inherited from the conventional static translinear principle, formulated by Gilbert in 1977 [2].

The last few decades have witnessed considerable interest of researchers in realising linear analog signal processing employing ELIN circuits. A number of ELIN circuits are realized by using companding techniques. Tsividis [3] showed the advantages of syllabic companding in signal processing. The log-domain circuits, dynamic translinear circuits, square-root-domain circuits and syllabically companding filters all are the subsets of ELIN circuits.

The TL filter concept was reinvented in 1990 by Seevinck [4] who coined the term Current-mode companding and also introduced the first class-AB integrator. Both Adams [1] and Seevinck [4] however, proposed first-order filters and hence, these ideas unfortunately, did not attract the required attention of the researchers for many years. The idea of log-domain filtering actually took off in 1993, when Frey [5] demonstrated that higher-order log-domain filters can be systematically synthesized using state-space techniques, in which BJTs were directly used to realize the log-domain filters by mapping from state-space linear differential equations. Furthermore, Frey also proposed ‘Exponential State-space Filters’ in [6], and showed that this technique is also suitable for high frequency applications [9]. After that many researchers started taking interest in log-domain/translinear circuits. In 1994, Toumazou, Ngarmnil and Lande [7] proposed the first log-domain filters for implementation in MOS technology. However, the first experimental results of log-domain filters were published by Perry and Roberts in [12] in 1995 who also proposed an alternative synthesis method based on the simulation of LC ladder filters. The first experimental results of MOSFET-based circuit were presented by Ngarmnil, Toumazou and Lande [11] in 1995. On the other hand, the first application of the underlying design principle for the realization of an oscillator was proposed in 1995 by Pookaiyaudom and Mahattanakul [10].

In syllabic companding, the gains of the compressor and expander are adjusted according to slowly varying characteristic of the signal envelope or power [3, 14, 87].

Log-domain or dynamic translinear circuits are the examples of instantaneous companding circuits but the true instantaneous companding in log domain circuits is required to operate in class B or class AB [4, 8, 23, 31, 49, 67, 69, 72, 74, 77, 81, 84, 91, 92, 94, 125, 126, 40, 153, 171, 181, 187, 191]. Both the type of circuits are suitable to implement linear and nonlinear differential equations and several synthesis approaches have been advanced by the various researchers on their own preferences such as, the state-space methods as in [5, 8, 13, 19, 50, 51, 64, 66, 77, 156, 160, 171, 186, 181, 188], wave active filter concepts as in [131, 164, 173, 203], signal flow graph based approaches as in [12, 22, 52, 53, 110], leap frog designs as in [38, 158, 173], synthesis based on Bernoulli operator as in [33, 64, 68, 79], modular design approaches as in [35, 70], linear transformation based methods as in [21, 152, 175], approaches based upon simulation of LC ladders as in [22, 52, 97, 142, 154, 164, 166, 195], unified matrix method as in [96, 133], Taylor series based design as in [73], image parameter methods as in [44] and Impedance scaling based method as in [195].

Initially, log-domain circuits employed only BJTs and capacitors but subsequently it was recognized that such circuits may also be realized by using MOS transistors as well when they are operated in subthreshold region or weak inversion, as in [7, 47, 65, 69, 71, 74, 80, 86, 89, 94, 97, 118, 136, 137, 139], BiCMOS technology as in [11, 16, 31, 32, 44, 46, 69, 138, 177, 178], using lateral bipolar transistors as in [95], using floating gate MOS (FGMOS) transistors as in [125, 126, 129, 165, 191] and using multiple input translinear elements as in [99, 135]. Researchers have also found scope of using Darlington topology in log-domain circuits to improve gain [151].

Many different approximation techniques have so far been used to realize log domain/translinear filters such as Chebyshev [12, 16, 22, 31, 46, 53, 84, 86, 97, 154, 157], Elliptic [21, 22, 110, 181], Bessel [162, 179] and Butterworth [38, 58, 132]. These filters have been realized by using the cascaded-biquads approach, methods based upon simulation of LC ladders or using multiple-feedback topologies. Besides filters and oscillators, work has also been done on realizing integrators [15, 17, 26, 38, 43, 72, 194] and differentiators [15, 108] which are the basic building blocks of analog circuit synthesis.

Apart from normal filter realization techniques, researchers have also given attention on filters using common mode feedback topology [130], multiple feedback follow the leader feedback (FLF) topology [49, 168], inverse-follow-the leader-feedback approach [53] and wavelet based filter designs [113, 143, 170].

Other than conventional filters, such as those presented in [146, 187], the log-domain/dynamic translinear techniques have also been used in a number of other applications, such as realization of oscillators [10, 13, 27, 32, 56, 67, 92, 101, 119, 169, 189, 197, 205, 211], PLL [32, 60], RF applications [19], syllabic companding filters [36, 42, 58, 102], RMS detectors [18, 147], RMS-DC converters [24, 30, 41, 62, 177, 204], ΣΔ A/D convertors [122], pulse duration modulation (PDM) circuits [114] and adaptive filters [28, 111, 129, 140, 165, 201].

A number of researchers have also carried out noise analysis and the analysis of other second order effects/transistor non-idealities; for instance, see [34, 37, 45, 48, 50, 55, 59, 61, 75, 78, 81, 83, 106, 109, 116, 182, 199, 202].

The circuits containing MOS transistors operating in the quasi-quadratic law (or strong inversion) are called square-root domain circuits [25, 57, 124]. Exponential State-Space circuits [6, 9, 23], Sinh domain circuits [6, 23, 167], Tanh domain circuits [6, 23, 167], circuits with Piecewise-Linearization [63] and the circuits having voltage dependent capacitors [63] are few more examples of ELIN circuits.

In conclusion, the log-domain/translinear circuits have attracted a great deal of technological interest. Such circuits are useful for realizing high performance current mode linear and nonlinear signal processing and are highly suitable for VLSI implementation because of employing only transistors and capacitors and offering several of the following advantages such as electronic tunability of the parameters of the realized functions, use of low-voltage supply voltages, low-power consumption, extended dynamic range, low noise, low third order intermodulation distortion and low total harmonic distortion, etc.

It is hoped that the bibliography presented in this communication should be useful to research scholars, educators, students, practicing engineers and anybody who is interested in knowing about the current state of the art of log domain, translinear and square root domain circuits and their applications.

References

[1]  Adams, R.W., “Filtering in the Log-domain”, Preprint #1470 presented at the 63rd AES conference, New York, NY, 1979.
In article      
 
[2]  Gilbert, B., “Translinear circuits: A proposed classification”, Electronics Letters, 11 (1), 14-16, 1975.
In article      View Article
 
[3]  Tsividis, Y.P., Gopinathan, V. and Tόth, L., “Companding in signal processing”, Electronics Letters, 26 (17), 1331-1332, 1990.
In article      View Article
 
[4]  Seevinck, E., “Companding current-mode integrator: A new circuit principle for continuous-time monolithic filters”, Electronics Letters, 26 (24), 2046-2047, 1990.
In article      View Article
 
[5]  Frey, D.R., “Log-domain filtering: An approach to current-mode filtering”, IEE Proceedings G Circuits, Devices and Systems, 140 (6), 406-416, 1993.
In article      View Article
 
[6]  Frey, D.R., “A general class of current mode filters”, IEEE International Symposium on Circuits and Systems (ISCAS’93), 2, 1435-1438, 1993.
In article      
 
[7]  Toumazou, C., Ngarmnil, J. and Lande, T.S., “Micropower log-domain filter for electronic cochlea”, Electronics Letters, 30 (22), 1839-1841, Oct. 1994.
In article      
 
[8]  Frey, D., “Current-mode class AB second order filter”, Electronics Letters, 30 (3), 205-206, 1994.
In article      View Article
 
[9]  Frey, D., “A 3.3 volt electronically tunable active filter usable to beyond 1 GHz”, International Symposium on Circuits and Systems (ISCAS’94), 5, 493-496, 1994.
In article      View Article
 
[10]  Pookaiyaudom, S. and Mahattanakul, J., “A 3.3 volt high-frequency capacitor-less electronically-tunable log-domain oscillator”, International Symposium on Circuits and Systems (ISCAS’95), 2, 829-832, 1995.
In article      View Article
 
[11]  Ngarmnil, J., Toumazou, C. and Lande, T.S., “A fully tuneable micropower log-domain filter”, Twenty-first European Solid-State Circuit Conference (ESSCIRC’95), Lille, France, 86-89, 19-21 Sep., 1995.
In article      View Article
 
[12]  Perry, D. and Roberts, G.W., “Log-domain filters based on LC ladder synthesis”, Proceeding of the IEEE International Symposium on Circuits and Systems (ISCAS '95), Scattle, WA, 1, 311-314, 30 Apr.-3May, 1995.
In article      View Article
 
[13]  Thanachayanont, A., Pookaiyaudom, S. and Toumazou C., “State-space synthesis of log-domain oscillators”, IET Electronics Letters, 31 (21), 1797-1799, 1995.
In article      View Article
 
[14]  Tsividis, Y., “General approach to signal processors employing companding”, Electronics Letters, 31 (18), 1549-1550, 1995.
In article      View Article
 
[15]  Tsividis, Y., “On linear integrators and differentiators using instantaneous companding”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 42 (8), 561-564, 1995.
In article      View Article
 
[16]  Punzenberger, M. and Enz, C., “A new 1.2 V BiCMOS log-domain integrator for companding current-mode filters”, IEEE International Symposium on Circuits and Systems (ISCAS '96) Connecting the World, Atlanta, GA, 1, 125-128, 12-15 May, 1996.
In article      View Article
 
[17]  Fried, R., Python, D. and Enz, C.C., “Compact log-domain current mode integrator with high transconductance-to-bias current ratio”, Electronics Letters, 32 (11), 952-953, 1996.
In article      View Article
 
[18]  Frey, D.R., “Explicit log domain root-mean-square detector”, United States Patent, 1996.
In article      
 
[19]  Frey, D.R., “Log domain filtering for RF applications”, IEEE Journal Solid-State Circuits, 31 (10), 1468-1475, 1996.
In article      View Article
 
[20]  Ngarmnil, J. and Toumazou, C., “Micro power log-domain active inductor”, Electronics Letters, 32 (11), 953-955, 1996.
In article      View Article
 
[21]  Liu, S.I. and Liao, Y.H., “Table-based log-domain linear transformation filter”, Electronics Letters, 32 (19), 1771-1772, 1996.
In article      View Article
 
[22]  Perry, D. and Roberts, G.W., “The design of log-domain filters based on the operational simulation of LC ladders”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 43 (11), 763-774, 1996.
In article      View Article
 
[23]  Frey, D., “Exponential state space filters: A generic current mode design strategy”, IEEE Transaction on Circuits and Systems I: Fundamental Theory and Applications, 43 (1), 34-42, 1996.
In article      
 
[24]  Mulder, J., van der Woerd, A.C., Serdijn, W.A. and van Roermund, A.H.M., “An RMS-DC converter based on the dynamic translinear principle”, Proceeding of the 22nd European Solid-State Circuits Conference (ESSCIRC`96), Neuchatel, Switzerland, 17-19 Sept., 1996.
In article      
 
[25]  Mulder, J., van der Woerd, A.C., Serdijn, W.A. and van Roermund, A.H.M., “Current-mode companding √x-domain integrator”, Electronics Letters, 32 (3), 198-199, 1996.
In article      View Article
 
[26]  Mahattanakul, J., Toumazou, C. and Pookaiyaudom, S., “Low-distortion current-mode companding integrator operating at fT of BJT”, Electronics Letters, 32 (21), 2019-2021, 1996.
In article      View Article
 
[27]  van der Woerd, A.C., Mulder, J., Serdijn, W.A. and van Roermund, A.H.M., “Recent trends in translinear circuits”, in Proc. Electronics-ET’96, Sozopol, Bulgaria, 1, 14-21, 1996.
In article      
 
[28]  Frey, D.R. and Steigerwald, L., “An adaptive analog notch filter using log filtering”, IEEE International Symposium on Circuits and Systems (ISCAS’96) Connecting the World, Atlanta, GA, 1, 297-300, 12-15 May, 1996.
In article      View Article
 
[29]  Frey, D.R., “Log-filtering using gyrators”, Electronics Letters, 30 (1), 26-28, 1996.
In article      View Article
 
[30]  Mulder, J., Serdijn, W.A., van der Woerd, A.C., and van Roermund, A.H.M., “Dynamic translinear RMS-DC converter”, Electronics Letters, 32 (22), 2067-2068, 1996.
In article      View Article
 
[31]  Punzenberger, M. and Enz, C.C., “A 1.2-V low-power BiCMOS class AB log-domain filter”, IEEE Journal Solid-State Circuits, 32 (12), 1968-1978, 1997.
In article      View Article
 
[32]  Thanachayanont, A., Payne, A. and Pookaiyaudom, S., “A current-mode phase-locked loop using a log-domain oscillator”, Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS '97), 1, 277-280, 9-12 Jun., 1997.
In article      View Article
 
[33]  Drakakis, E.M., Payne, A.J. and Toumazou, C., “Bernoulli operator: a low-level approach to log-domain processing”, Electronics Letters, 33 (12), 1008-1009, 1997.
In article      View Article
 
[34]  Leung, V.W., El-Gamal M. and Roberts, G.W., “Effects of transistor non-idealities on log-domain filters”, Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '97), 1, 109-112, 9-12 Jun., 1997.
In article      PubMed
 
[35]  Mahattanakul, J. and Toumazou, C., “Modular log-domain filters”, Electronics Letters, 33 (13), 1130-1131, 1997.
In article      View Article
 
[36]  Frey, D.R. and Tsividis, Y.P., “Syllabically companding log domain filter using dynamic biasing”, Electronics Letters, 33 (18), 1506-1507, 1997.
In article      View Article
 
[37]  Mulder, J., van der Woerd, A.C., Serdijn, W.A. and van Roermund, A. H. M., “General current-mode analysis method for translinear filters”, IEEE Transaction on Circuits and Systems I: Fundamental Theory and Applications, 44 (3), 193-197, 1997.
In article      
 
[38]  Serdijn, W.A., Broest, M., Mulder, J., van der Woerd, A.C. and van Roermund, A.H.M., “A low-voltage ultra-low-power translinear integrator for audio filter applications”, IEEE Journal of Solid-State Circuits, 32 (4), 577-581, 1997.
In article      View Article
 
[39]  Payne, A. and Thanachayanont, A., “Translinear circuit for phase detection”, Electronics Letters, 33 (18), 1507-1509, 1997.
In article      View Article
 
[40]  Tsividis, Y., “Externally linear, time-invariant systems and their application to companding signal processors”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 44 (2), 65-85, 1997.
In article      View Article
 
[41]  Mulder, J., van der Woerd, A.C., Serdijn, W.A. and van Roermund, A.H.M., “An RMS-DC converter based on the dynamic translinear principle”, IEEE Journal of Solid-State Circuits, 32 (7), 1146-1150, 1997.
In article      View Article
 
[42]  Mulder, J., Serdijn, W.A., van der Woerd, A.C. and van Roermund, A. H. M., “A syllabic companding translinear filter”, Proceeding of IEEE International Symposium on Circuits and Systems (ISCAS’97), 1, 101-104, 9-12 Jun., 1997.
In article      View Article
 
[43]  Mahattanakul, J. and Toumazou, C., “Instantaneous companding and expressing: A dual approach to linear integrator synthesis”, Electronics Letters, 33 (1), 4-5, 1997.
In article      View Article
 
[44]  Ruymbeke, G. van, Enz, C., Krummenacher, F. and Declerq, M., “A BiCMOS programmable continuous-time filter using image-parameter method synthesis and voltage-companding technique”, IEEE Journal of Solid-State Circuits, 32 (3), 377-387, 1997.
In article      View Article
 
[45]  Mulder, J., Kouwenhoven, M.H.L. and van Roermund, A.H.M., “Signal x noise intermodulation in translinear filters”, Electronics Letters, 33 (14), 1205-1207, 1997.
In article      View Article
 
[46]  Punzenberger, M. and Enz, C.C., “A compact low-power BiCMOS log-domain filter”, IEEE Journal Solid-State Circuits, 33 (7), 1123-1129, 1998.
In article      View Article
 
[47]  Germanovix, W., O'Neill, G., Toumazou, C., Drakakis, E.M., Kitney, R.I. and Lande, T.S., “Analogue micro powered log-domain tone controller for auditory prostheses”, Electronics Letters, 34 (11), 1051 - 1052, 1998.
In article      View Article
 
[48]  Fox, R.M., “Design-oriented analysis of log-domain circuits”, IEEE Transactions Circuits and Systems II: Analog and Digital Signal Processing, 45 (7), 918-921, 1998.
In article      View Article
 
[49]  Punzenberger, M. and Enz, C., “Log-domain filters for low-voltage low-power applications”, IEEE International Conference on Electronics, Circuits and Systems, Lisboa, 1, 41-44, 1998.
In article      View Article
 
[50]  Frey, D.R., “State-space synthesis and analysis of log-domain filters”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 45 (9), 1205-1211, 1998.
In article      View Article
 
[51]  Frey, D.R., “Synthesis of distortion compensated log-domain filters using state space techniques”, Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS '98), Monterey, CA, 1, 321-324, 31 May-3 Jun.,1998.
In article      View Article
 
[52]  El-Gamal, M. and Roberts, G.W., “Very high-frequency log-domain band pass filters”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 45 (9), 1188-1198, 1998.
In article      View Article
 
[53]  Wu, J. and El-Masry, E.I., “Log-domain synthesis of an nth-order filter”, International Journal of Electronics, 84 (4), 359-369, 1998.
In article      View Article
 
[54]  Brandtner, T., Papathanasiou, K. and Hamilton, A., “Palmo cell using sampled data log-domain integrators”, Electronics Letters, 34 (8), 733-735, 1998.
In article      View Article
 
[55]  Mulder, J., Kouwenhoven, M.H.L., Serdijn, W.A., van der Woerd, A.C. and van Roermund, A.H.M., “Noise considerations for translinear filters”, IEEE Transaction on Circuits and Systems II: Analog and Digital Signal Processing, 45 (9), 1199-1204, 1998.
In article      View Article
 
[56]  Serdijn, W.A., Mulder, J., van der Woerd, A.C. and van Roermund, A.H.M., “A wide-tunable translinear second-order oscillator”, IEEE Journal of Solid-State Circuits, 33 (2), 195-201, 1998.
In article      View Article
 
[57]  Mulder, J., Serdijn, W.A., van der Woerd, A.C. and van Roermund, A.H.M., “A 3.3 V current-controlled √-domain oscillator”, Analog Integrated Circuits and Signal Processing, 16 (1), 17-28, 1998.
In article      View Article
 
[58]  Mulder, J., Serdijn, W.A., van der Woerd, A.C. and van Roermund, A.H.M., “An instantaneous and syllabic companding translinear filter”, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 45 (2), 150-154, 1998.
In article      View Article
 
[59]  Tόth, L., Tsividis, Y.P. and Krishnapura, N., “On the analysis of noise and interference in instantaneously companding signal processors”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 45 (9), 1242-1249, 1998.
In article      View Article
 
[60]  Payne, A., Thanachayanont, A. and Papavassilliou, C., “A 150-MHz translinear phase-locked loop”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 45 (9), 1220-1231, 1998.
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[61]  Kouwenhoven, M.H.L., Mulder, J. and van Roermund A.H.M., “Noise analysis of dynamically nonlinear translinear circuits”, Electronics Letters, 34 (8), 705-706, 1998.
In article      View Article
 
[62]  Surakampontorn, W. and Kumwachara, K., “A dual translinear based true RMS to DC convertor”, IEEE Transactions on Instrumentation and Measurement, 47 (2), 459-464, 1998.
In article      View Article
 
[63]  Tsividis, Y.P., “Externally linear integrators,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 45 (9), 1181-1187, 1998.
In article      View Article
 
[64]  Drakakis, E.M., Payne, A.J. and Toumazou, C., ““Log-domain state-space”: a systematic transistor-level approach for log-domain filtering”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 46 (3), 290-305, 1999.
In article      View Article
 
[65]  El-Masry, E.I. and Wu, J., “CMOS micropower universal log-domain biquad”, IEEE Transactions Circuits and Systems I: Fundamental Theory and Applications, 46 (3), 389-392, 1999.
In article      View Article
 
[66]  Frey, D., “Distortion compensation in log-domain filters using state-space techniques”, IEEE Transactions Circuits and Systems II: Analog and Digital Signal Processing, 46 (7), 860-869, 1999.
In article      View Article
 
[67]  Ferrer, E. and Fox, R.M., “Limit-cycle oscillations in a log-domain-based filter”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 46 (6), 832-836, 1999.
In article      View Article
 
[68]  Drakakis, E.M., Payne, A.J. and Toumazou, C., “Log-domain filtering and the Bernoulli cell”, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 46 (5), 559-571, 1999.
In article      View Article
 
[69]  Enz, C., Punzenberger, M. and Python, D., “Low-voltage log-domain signal processing in CMOS and BiCMOS”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 46 (3), 279-289, 1999.
In article      View Article
 
[70]  Mahattanakul, J. and Toumazou, C., “Modular log-domain filters based upon linear Gm-C filter synthesis”, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 46 (12), 1421-1430, 1999.
In article      View Article
 
[71]  Fox, R.M. and Nagarajan, M., “Multiple operating points in a CMOS log-domain filter”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 46 (6), 705-710, 1999.
In article      View Article
 
[72]  Poort, P.J., Serdijn, W.A., Mulder, J., van der Woerd, A.C. and van Roermund, A.H.M., “A 1-V Class-AB Translinear Integrator for Filter Applications”, Analog Integrated Circuits and Signal Processing, 21 (1), 79-90, 1999.
In article      View Article
 
[73]  Abuelmáatti, M.T. and Abed, S.M., “A translinear circuit for analogue function synthesis based on a Taylor series”, International Journal Electronics, 86 (11), 1341-1348, 1999.
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[74]  Serdijn, W.A., Kouwenhoven, M.H.L., Mulder, J. and van Roermund, A.H.M., “Design of high dynamic range fully integratable translinear filters”, Analog Integrated Circuits and Signal Processing, 19 (3), 223-239, 1999.
In article      View Article
 
[75]  Mulder, J., Kouwenhoven, M.H.L., Serdijn, W.A. and van der Woerd, A.C., “Nonlinear analysis of noise in static and dynamic translinear circuits”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 46 (3), 266-278, 1999.
In article      View Article
 
[76]  Seevinck, E., Vittoz, E.A., du Plessi, M. and Joubert, T.H., “CMOS translinear circuits for minimum supply voltage”, IEEE Transactions on Circuits and systems II: Analog and Digital Signal Processing, 47 (12), 1560-1564, 1999.
In article      View Article
 
[77]  Frey, D.R. and Tola, A.T., “A state-space formulation for externally linear class AB dynamical circuits,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 46 (3), 306-314, 1999.
In article      View Article
 
[78]  Leung, V.W. and Roberts, G.W., “Analysis and Compensation of Log-Domain Biquadratic Filter Response Deviations due to Transistor Non-idealities”, Analog Integrated Circuits and Signal Processing, 22 (2-3), 147-162, 2000.
In article      View Article
 
[79]  Drakakis, E.M. and Payne, A.J., “A Bernoulli Cell-Based Investigation of the Non-Linear Dynamics in Log-Domain Structures”, Analog Integrated Circuits and Signal Processing, 22 (2-3), 127-146, 2000.
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