Log-domain filters, translinear circuits and the Bernoulli cell

Drakakis, Emmanuel M.; Payne, A.J.; Toumazou, C.

doi:10.1109/iscas.1997.608784

Cited by 44 publications

(24 citation statements)

References 15 publications

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“…Because ELIN filters are in general quite nonlinear internally, classic linear filter theory is not directly applicable. Nevertheless, a fairly complete theory for externally linear filters has begun to develop, with notable contributions found in [2]- [4], regarding state space synthesis, in [5] and [6] regarding dynamic translinear analysis, and in [7] and [8] regarding modular analysis, although a number of interesting contributions have been made elsewhere. The current interest in ELIN filters was spawned in part by the pioneering work found in [9] and [10].…”

Section: Introductionmentioning

confidence: 99%

“…In order to facilitate the design, we will offer a new formulation which combines the exponential mappings introduced in [2] with the translinear ideas described elsewhere-for example, in [5], [6], and [19]. First, observe that the translational mappings in Section II provide a simple systematic way to guarantee that all of the system variables-that is, , and each of the state variables-will remain strictly positive at all times.…”

Section: A Introductionmentioning

confidence: 99%

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Syllabic-companding log domain filters

Frey

Tsividis

Efthivoulidis

et al. 2001

IEEE Trans. Circuits Syst. II

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Abstract-A general theory for companding log domain filters is proposed which combines not only exponential mappings, but also a new translational mapping approach which guarantees suitable operating conditions in any log domain filter. The filter equations resulting from the use of the theory ultimately contain translinear terms which are known to be realizable using translinear techniques. A discussion of the design of the companding filters, regarding the economical use of translinear loops and the convenient selection of system parameters, is offered which leads to first-and second-order circuit designs. Finally, the noise performance of an example design is investigated using a carefully crafted large-signal simulation technique, showing clearly the advantage of the companding filter approach.

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Section: Introductionmentioning

confidence: 99%

Section: A Introductionmentioning

confidence: 99%

Syllabic-companding log domain filters

Frey

Tsividis

Efthivoulidis

et al. 2001

IEEE Trans. Circuits Syst. II

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“…Construction of higher-order log-domain circuits from simple component cells has been described in various ways, such as the Bernoulli cell of [5] and the E and EÀ cells of [8]. We generate higher-order functions in a similar way, factoring the desired current transfer function into equations which can directly be implemented by the ®rst-order subcircuit of Fig.…”

Section: Designing Second-order Sectionsmentioning

confidence: 99%

“…This``dynamic translinear principle'' was developed in Mulder et al [4], and is worth paraphrasing here in the context of our method of circuit synthesis, where it allows us to synthesize ®lter circuits without resorting to state-space manipulation (cf. [5]). …”

Section: Introductionmentioning

confidence: 99%

Synthesis of Log-Domain Filters from First-Order Building Blocks

Edwards¹,

Cauwenberghs²

2000

Research Perspectives on Dynamic Translinear and Log-Domain Circuits

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Abstract. Log-domain ®lters are an important class of current-mode circuits having large-signal linearity and increased tuning range over voltage-mode ®lter circuits of similar complexity. In this paper we describe synthesis of a single-ended, ®rst-order ®lter circuit from static and dynamic translinear circuit principles, and show how higher-order ®lters can be easily constructed from the ®rst-order building block. We address additional issues related to low-frequency (audio-frequency) ®lter design and present results measured from test circuits and a complete 15-channel ®lterbank system fabricated in 2 mm and 1.2 mm BiCMOS processes.

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“…For example, in [1][2] and [13][14] cytomorphic/cytomimetic electronics are introduced. The logarithmic behaviour [15][16][17][18][19][20][21][22] of weakly inverted MOS devices is exploited. Log-domain circuits have been shown able to produce a variety of nonlinear dynamics [23][24].…”

Section: Introductionmentioning

confidence: 99%

Systematic Computation of Nonlinear Bilateral Dynamical Systems With a Novel Low-Power Log-Domain Circuit

Jokar

Soleimani

Drakakis

2017

IEEE Trans. Circuits Syst. I

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Simulation of large-scale nonlinear dynamical systems on hardware with a high resemblance to their mathematical equivalents has been always a challenge in engineering. This paper presents a novel currentinput current-output circuit supporting a systematic synthesis procedure of log-domain circuits capable of computing bilateral dynamical systems with considerably low power consumption and acceptable precision. Here, the application of the method is demonstrated by synthesizing four different case studies: 1) a relatively complex two-dimensional (2-D) nonlinear neuron model, 2) a chaotic 3-D nonlinear dynamical system Lorenz attractor having arbitrary solutions for certain parameters, 3) a 2-D nonlinear Hopf oscillator including bistability phenomenon sensitive to initial values and 4) three small neurosynaptic networks comprising three FHN neuron models variously coupled with excitatory and inhibitory synapses. The validity of our approach is verified by nominal and Monte Carlo simulated results with realistic process parameters from the commercially available AMS 0.35 µm technology. The resulting continuous-time, continuous-value and low-power circuits exhibit various bifurcation phenomena, nominal time-domain responses in good agreement with their mathematical counterparts and fairly acceptable process variation results (less than 5% STD).

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Log-domain filters, translinear circuits and the Bernoulli cell

Cited by 44 publications

References 15 publications

Syllabic-companding log domain filters

Syllabic-companding log domain filters

Synthesis of Log-Domain Filters from First-Order Building Blocks

Systematic Computation of Nonlinear Bilateral Dynamical Systems With a Novel Low-Power Log-Domain Circuit

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