Ebers-Moll Model Research Articles

The Minimum AC Signal Model of Bipolar Transistor in Amplification Region for Weak Signal Detection.

This paper presents a minimum signal model via the AC small-signal model and the uncertainty principle, which reveals the minimum AC signal that can be amplified by a bipolar transistor. The Ebers—Moll model (EM3) can describe the small signal amplification process, but it is difficult to define the minimum amplifiable signal of the bipolar transistor. In this study, the correspondence relationship between the non-equilibrium carrier and the electric injection is proved, and the relationship between the life of the non-equilibrium carrier and the measurable signal is proposed by the uncertainty principle. Next, the limit of perceived minimum voltage is also derived in this paper. Then, combining with EM3 model, the minimum AC signal model of bipolar transistor is presented to calculate the minimum voltage signal of bipolar transistor that can be amplified. Finally, a number of the simulation and experiment results show that when the minimum signal in the model is used as input, the carrier concentration of the bipolar transistor does not change and the base electrode cannot perceive the signal, which verifies the validity of the minimum AC signal model.

Wave Digital Modeling of Nonlinear 3-terminal Devices for Virtual Analog Applications

We propose a novel modeling method for circuits containing arbitrary nonlinear 3-terminal devices, which operates in the wave digital (WD) domain. This approach leads to the definition of a general and flexible WD model for 3-terminal devices, whose number of ports varies from 1 to 6. The generality of the method is confirmed by the fact that the WD models of 3-terminal devices already discussed in the literature can be seen as particular cases of the model that we present here. As examples of applications of our method, we develop WD models of the three most widespread types of transistors in audio circuitry, i.e., the MOSFET, the JFET and the BJT. These models are here designed to be used in Virtual Analog audio applications; therefore, their derivation is aimed at minimizing computational complexity while avoiding implicit relations between port variables, as far as possible. Proposed MOSFET and JFET models are characterized by third-order polynomial equations; hence, explicit closed-form wave scattering relations are obtained. On the other hand, the Ebers–Moll model describing the BJT results in transcendental equations in the WD domain that cannot be solved analytically. In order to cope with this problem, we propose a modified Newton–Raphson (NR) method for solving the implicit Ebers–Moll equations in the WD domain. Such iterative method exhibits a significantly higher robustness and convergence rate with respect to the traditional NR method, without compromising its efficiency. Finally, WD implementations of some audio circuits containing transistors are discussed.

State Estimation of Common Emitter Amplifier using Iterated Extended Kalman Filters

This paper presents the output voltage estimation of bipolar junction transistor (BJT) common emitter (CE) using iterated extended Kalman filter (IEKF). For this, state space model has been derived using Kirchhoff's current law (KCL) and Ebers-Moll model of the transistor. The performance of IEKF has been compared with extended Kalman filter (EKF). The simulation results show large signal to noise ratio (SNR) and small root mean square error (RMSE) using IEKF as compared to EKF, as IEKF considers the error due to linearization. The advantage of the proposed method is that the derived extended state space equation can be used for parameter estimation of both, the transistor state and transistor parameters as the derivation includes transistor model.

High frequency realization of non-autonomous nonlinear transistor circuit

In this paper, an electronic implementation of a non-autonomous nonlinear transistor circuit is presented. This nonlinear circuit topology requires a minimal number of components, which consists of two resistors, two capacitors, and a single NPN bipolar junction transistor (BJT). This topology is of interest because it is relatively simple to construct and could be used for potential applications such as random number generators (RNGs) or noise signal generators (NSGs). The transistor portion of the circuit was analyzed using the Ebers-Moll model for a BJT. Using this model, time domain and phase space plots that qualitatively match the original systems dynamics were created. This model was also used to create bifurcation diagrams of the base voltage versus both frequency and amplitude, where periodic and chaotic solutions exist. The hardware realization was built using commercial-off-the-shelf (COTS) components with two different printed circuit board (PCB) designs. This PCB included the forcing function on the board with the transistor circuit. This circuit topology functioned over a wide range of frequencies, with an upper limit of approximately 5.1 MHz. Many potential applications could benefit from this high operation frequency.

A Distributed Extended Ebers–Moll Model Topology for SiGe Heterojunction Bipolar Phototransistors Based on Drift–Diffusion Hydrodynamic Behavior

This paper proposes a novel type of compact circuit model for silicon germanium (SiGe) heterojunction phototransistor (HPT) that is justified from the distributed nature of both its electrical and optical behaviors. The proposed model is based on a modified Ebers–Model structure and contains 28 different parameters. It is independent of the nature of the base bias (current or voltage), as opposed to existing models. The method to identify that the architecture of the model is original as it makes use of a drift–diffusion numerical simulation of a SiGe HPT adjusted to experimental data. A good fit of the model both in amplitude and phase is obtained through the nine optomicrowave S-parameters.

Modeling nonlinear wave digital elements using the Lambert function

A large class of transcendental equations involving exponentials can be made explicit using the Lambert W function. In the last fifteen years, this powerful mathematical tool has been extensively used to find closed-form expressions for currents or voltages in circuits containing diodes. Until now almost all the studies about the W function in circuit analysis concern the Kirchhoff (K) domain, while only few works in the literature describe explicit models for diode circuits in the Wave Digital (WD) domain. However explicit models of NonLinear Elements (NLEs) in the WD domain are particularly desirable, especially in order to avoid the use of iterative algorithms. This paper explores the range of action of the W function in the WD domain; it describes a procedure to search for explicit wave mappings, for both one-port and multi-port NLEs containing diodes. WD models, describing an arbitrary number of different parallel and anti-parallel diodes, a transformerless ring modulator and some BJT amplifier configurations, are derived. In particular, an extended version of the BJT Ebers-Moll model, suitable for implementing feedback between terminals, is introduced.

Compact Electrothermal Reliability Modeling and Experimental Characterization of Bipolar Latchup in SiC and CoolMOS Power MOSFETs

In this paper, a compact dynamic and fully coupled electrothermal model for parasitic BJT latchup is presented and validated by measurements. The model can be used to enhance the reliability of the latest generation of commercially available power devices. BJT latchup can be triggered by body-diode reverse-recovery hard commutation with high dV/dt or from avalanche conduction during unclamped inductive switching. In the case of body-diode reverse recovery, the base current that initiates BJT latchup is calculated from the solution of the ambipolar diffusion equation describing the minority carrier distribution in the antiparallel p-i-n body diode. For hard commutation with high dV/dt , the displacement current of the drain-body charging capacitance is critical for BJT latchup, whereas for avalanche conduction, the base current is calculated from impact ionization. The parasitic BJT is implemented in Simulink using the Ebers–Moll model and the temperature is calculated using a thermal network matched to the transient thermal impedance characteristic of the devices. This model has been applied to CoolMOS and SiC MOSFETs. Measurements show that the model correctly predicts BJT latchup during reverse recovery as a function of forward-current density and temperature. The model presented, when calibrated correctly by device manufacturers and applications engineers, is capable of benchmarking the robustness of power MOSFETs.

Multiple Soft Fault Diagnosis of Bjt Circuits

Abstract This paper deals with multiple soft fault diagnosis of nonlinear analog circuits comprising bipolar transistors characterized by the Ebers-Moll model. Resistances of the circuit and beta forward factor of a transistor are considered as potentially faulty parameters. The proposed diagnostic method exploits a strongly nonlinear set of algebraic type equations, which may possess multiple solutions, and is capable of finding different sets of the parameters values which meet the diagnostic test. The equations are written on the basis of node analysis and include DC voltages measured at accessible nodes, as well as some measured currents. The unknown variables are node voltages and the parameters which are considered as potentially faulty. The number of these parameters is larger than the number of the accessible nodes. To solve the set of equations the block relaxation method is used with different assignments of the variables to the blocks. Next, the solutions are corrected using the Newton-Raphson algorithm. As a result, one or more sets of the parameters values which satisfy the diagnostic test are obtained. The proposed approach is illustrated with a numerical example.

Design for Drive Circuit of Solid Micro-Thruster Ignition System

Aiming at the lack of standard design method and the shortcomings of main functions of the existing drive circuit, a “Element-level Design under Transmission Voltage Switch Theory” is set forth and a smallest circuit structure namely as drive-unit, which contains Superstratum-unit, Substratum-unit and LC-unit, is designed in this paper to achieve the necessary functions. The drive circuit of n×n ignition bridges has been got from the structure expansion formula along with the expected life estimation. The Ebers-Moll Model of transistor and the internal circuit of MOSFET were used to make a theoretical analysis and the conclusion of such analysis was verified by simulation subsequently. Actual measurement has been made and the results show that the circuit in simple structure has provided a strong loading ability and accurate output; some elements of the circuit have been heated when the circuit was working; and the response time of the circuit was of the microsecond-level.

Ultra reliable infrared absorption water vapor detection through the all-electronic feedback stabilization

Single-beam balanced radiometric detection (BRD) system with all-electronic feedback stabilization has been proposed for high reliability water vapor detection under rough environmental conditions, which is insensitive to the fluctuation of transmission loss of light. The majority of photocurrent attenuation caused by the optical loss can be effectively compensated by automatically adjusting the splitting ratio of probe photocurrent. Based on the Ebers–Moll model, we present a theoretical analysis which can be suppressed the photocurrent attenuation caused by optical loss from 0.5552dB to 0.0004dB by using the all-electronic feedback stabilization. The deviation of the single-beam BRD system is below 0.29% with the bending loss of 0.31dB in fiber, which is obviously lower than the dual-beam BRD system (5.96%) and subtraction system (11.3%). After averaging and filtering, the absorption sensitivity of water vapor at 1368.597nm has been demonstrated, which is 7.368×10−6.

A Contraction Method for Locating All the DC Solutions of Circuits Containing Bipolar Transistors

The paper is devoted to the analysis of diode–transistor circuits having multiple DC solutions. The transistors are characterized by the Ebers–Moll model and the circuits are described by the Sandberg–Willson equation, without any piecewise-linear approximations. A new method for finding bounds on the location of all the solutions is offered. The method contracts a hyperrectangular region that includes the solutions in a systematic manner, considering in succession all the individual equations. It does not require much computation power and is very fast. The method is very useful as a preliminary step of the algorithms for finding all the DC solutions, making them more efficient. A numerical example is given to illustrate the proposed approach.

Wavelet Based Transistor Parameter Estimation Using Second Order Volterra Model

In this paper, we present a wavelet based parameter estimation technique to estimate the transistor parameter in a common emitter amplifier circuit. The method uses the closed form expression of the second order Volterra model of a common emitter amplifier circuit derived using perturbation technique and the Ebers–Moll model. Simulations show that the proposed method gives more accurate parameter estimation with smaller data storage requirement as compared to the conventional least squares method because the wavelet method is adapted to time frequency resolution. Also, the parameter estimation using a nonlinear model gives an SNR improvement of approximately 2-dB compared to the parameter estimation using only a linear part of the model.

Magnetoamplification in a Bipolar Magnetic Junction Transistor

We have demonstrated the first bipolar magnetic junction transistor using a dilute magnetic semiconductor. For an InMnAs p-n-p transistor magnetoamplification is observed at room temperature. The observed magnetoamplification is attributed to the magnetoresistance of the magnetic semiconductor InMnAs heterojunction. The magnetic field dependence of the transistor characteristics confirm that the magnetoamplification results from the junction magnetoresistance. To describe the experimentally observed transistor characteristics, we propose a modified Ebers-Moll model that includes a series magnetoresistance attributed to spin-selective conduction. The capability of magnetic field control of the amplification in an all-semiconductor transistor at room temperature potentially enables the creation of new computer logic architecture where the spin of the carriers is utilized.

Wavelet-Based Transistor Parameter Estimation

In this paper a wavelet-based parameter estimation method has been proposed for the common emitter transistor amplifier circuit and compared with the least squares method. As the maximal precision of simulation requires the modeling of electronic circuits in terms of device parameters and circuit components, the Volterra model of the common emitter amplifier circuit derived using the Ebers–Moll model and perturbation technique has been used for parameter estimation. The advantage of the proposed method is a smaller data storage requirement and accurate parameter estimation as compared to the least squares method because the wavelet method is adapted to time-frequency resolution.

Temperature Dependence of Current Gain, Ideality Factor, and Offset Voltage of AlGaAs/GaAs and InGaP/GaAs HBTs

This paper elucidates the stabilities of the dc current gain, ideality factor, and offset voltage against variations in temperature and currents for GaAs-based heterojunction bipolar transistors (HBTs). The InGaP/GaAs HBT markedly reduces the offset voltage and improves the temperature stability of the dc current gain relative to those of AlGaAs/GaAs benchmark devices. The relative insensitivity of the offset voltage in the InGaP/GaAs HBT to the temperature is established by comparison with AlGaAs/GaAs counterparts. One of the more intriguing aspects of these two HBTs is the replacement of the AlGaAs emitter with the InGaP emitter to improve the temperature stability of the offset voltage. Specifically, the effect of the base current on the offset voltage is abnormal in these devices. In this paper, the conventional Ebers-Moll model cannot account completely for our observed phenomena. Accordingly, the results herein (improved temperature stability of the offset voltage in the InGaP emitter HBT and the uncommon base current effect in these two devices) are interpreted in terms of a physics-based analytical model. A strong consistency existed between the experimental data and the theory. Additionally, some reasonable predictions (not obtained from the measured data) of the specific physically based model are presented. The large-signal model provides a description of device performance that will be of use to device engineers and designers.

The Ebers–Moll model for magnetic bipolar transistors

The equivalent electrical circuit of the Ebers–Moll-type is introduced for magnetic bipolar transistors. In addition to conventional diodes and current sources, the new circuit comprises two novel elements due to spin-charge coupling. A classification scheme of the operating modes of magnetic bipolar transistors in the low bias regime is presented.

Computing Multivalued Input–Output Characteristics in the Circuits Containing Bipolar Transistors

The paper deals with dc circuits including bipolar transistors represented by the Ebers-Moll model. An important question how to efficiently compute multivalued input-output characteristics of these circuits is considered. A switching variables approach for tracing a multivalued single-branched characteristic, which can be considered as some kind of continuation method, is developed. A new strategy of switching variables is proposed and the generalized implicit function theorem is used as the mathematical background. Unfortunately, this approach suffers from major shortcomings when it is directly applied to bipolar transistor circuits, due to specific nonlinearities of the transistor model, causing the sharp-turning-point problem. To overcome this problem, a variable transformation is proposed, which leads to smooth solution curves. An efficient algorithm combining the developed variant of switching variable method with the proposed transformation is described. A generalized version of the algorithm enables us to compute multivalued characteristics composed of disconnected branches, under the assumption that at least one point on each branch can be found. It is illustrated via four examples of realistic transistor circuits including a voltage regulator, the Schmitt trigger, a line receiver, and their combination.

A model for multi-finger HBTs including current gain collapse effects

A common-emitter equivalent circuit model which represents both the self-heating and the current collapse as feedback from the collector current to the base–emitter voltage is developed for multi-finger InGaAs/GaAs HBTs. The modified Ebers–Moll model is verified by comparing the simulated and measured results. Good agreement is also achieved for the scattering parameters and I– V characteristics confirming the validity of the model for high frequency applications.

Modelling and characterisation of transistors

Models and characterisation of active devices that control the flow of energy operating within and outside the active region of the operating domain are presented. Specifically, the incremental charge carrier and Ebers Moll models of the bipolar junction transistor are presented and the parameters of electrical behaviour of the device at the terminals were measured and analysed. The parameters determined could be employed to evaluate input and output impedances, current, voltage and power gains of the device at appropriate operating points. The measured parameters compare favourably with published manufacturers' data to within 5%. Keywords: Modelling Bipolar Junction Transistor (Global Journal of Pure and Applied Sciences: 2003 9(2): 303-310)

Ebers-Moll model of bipolar transistor with idealized diodes

The conventional DC Ebers-Moll model of the bipolar transistor with three different types of piecewise-linear characteristics of the emitter and collector diodes is analysed. Separate necessary and sufficient conditions in the form of inequalities relating the current gains and the characteristics or weakly no-gain are derived. They are of practical importance in various theoretical and computational studies of diode-transistor circuits.