Bipolar transistor circuit analysis using the Lambert W-function

Banwell, T.C.

doi:10.1109/81.895330

Cited by 60 publications

(29 citation statements)

References 14 publications

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“…However, instead of solving it either numerically or approximately [2], [3], the current and voltage of this modified single-exponential equation may be explicitly solved in terms of the Lambert functions [4]. The Lambert W function, which is defined as the solution to the equation W(x) exp[W(x)] = x [5], is being increasingly used in electronics problems, in particular, for diode [6]- [10], solar cell [11]- [18], bipolar transistor [19], and metal-oxide-semiconductor field-effect transistor (MOSFET) [20]- [22] modeling purposes.…”

Section: Introductionmentioning

confidence: 99%

An Explicit Multiexponential Model as an Alternative to Traditional Solar Cell Models With Series and Shunt Resistances

Ortíz‐Conde

Lugo-Muñoz

Sánchez

2012

IEEE J. Photovoltaics

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Classical analyses of various conventional solar cell models are examined. They are unified through the separation of their linear and nonlinear components and the application of Thevenin's theorem to the linear terms. An explicit multiexponential model with series and shunt resistances is proposed as an alternative to conventional implicit multiexponential models commonly used to describe significant parallel conduction mechanisms in real solar cells. The proposed model is better suited than conventional models for repetitive simulation applications because of its inherently higher computational efficiency. Its explicit nature is a very useful feature for direct analytic differentiation and integration. The model's applicability has been assessed by parameter extraction and subsequent playback using synthetic I-V characteristics of a hypothetical solar cell at various illumination levels chosen purely for illustrative purposes.

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Section: Introductionmentioning

confidence: 99%

An Explicit Multiexponential Model as an Alternative to Traditional Solar Cell Models With Series and Shunt Resistances

Ortíz‐Conde

Lugo-Muñoz

Sánchez

2012

IEEE J. Photovoltaics

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“…12 It has also been used in laser and passive electro-optic systems to obtain a solution of the ladar-lidar equation. 13,14 In solar physics, new views of solar wind have been found with the W function, allowing the analytical derivation of both the outflow speed and the mass loss rate of the solar wind for certain illustrative approximations. 15 In the present work, we present yet another application of the W function to mathematical physics in the context of quantum statistics.…”

Section: Introductionmentioning

confidence: 99%

The Lambert W function and quantum statistics

Valluri

Gil

Jeffrey

et al. 2009

Journal of Mathematical Physics

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We present some applications of the Lambert W function ͑W function͒ to the formalism of quantum statistics ͑QS͒. We consider the problem of finding extrema in terms of energy for a general QS distribution, which involves the solution of a transcendental equation in terms of the W function. We then present some applications of this formula including Bose-Einstein systems in d dimensions, MaxwellBoltzmann systems, and black body radiation. We also show that for the appropriate parameter values, this formula reduces to an analytic expression in connection with Wien's displacement law that was found in a previous study. In addition, we show that for Maxwell-Boltzmann and Bose-Einstein systems, the W function allows us to express the temperature of the system as a function of the thermodynamically relevant chemical potential, the particle density, and other parameters. Finally, we explore an indirect relationship of the W function to the polylogarithm function and to the Lambert transform.

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“…This special function is commonly used in MOSFET modeling [25][26][27] and in electronics. 28 Equation (3) can be written in the general form of ln…”

Section: Analytical Drain Current Modelmentioning

confidence: 99%

Analytical surface-potential-based drain current model for amorphous InGaZnO thin film transistors

Tsormpatzoglou

Hastas

Choi

et al. 2013

Journal of Applied Physics

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A fully analytical surface-potential-based drain current model for amorphous InGaZnO (α-IGZO) thin film transistors (TFTs) has been developed based on a Gaussian distribution of subgap states, with the central energy fixed at the conduction band edge, which is approximated by two exponential distributions. This model includes both drift and diffusion components to describe the drain current in all regions of operation. Using an empirical mobility relationship that depends on both horizontal and vertical electric field, it is demonstrated that the model describes accurately the experimental transfer and output characteristics, making the model suitable for the design of circuits using α-IGZO TFTs.

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Bipolar transistor circuit analysis using the Lambert W-function

Cited by 60 publications

References 14 publications

An Explicit Multiexponential Model as an Alternative to Traditional Solar Cell Models With Series and Shunt Resistances

An Explicit Multiexponential Model as an Alternative to Traditional Solar Cell Models With Series and Shunt Resistances

The Lambert W function and quantum statistics

Analytical surface-potential-based drain current model for amorphous InGaZnO thin film transistors

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