Transistor models
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Transistors are complicated devices. In order to ensure the reliable operation of circuits employing transistors, it is necessary to model the physical phenomena observed in their operation analytically using transistor models. There exists a variety of different models, that range in complexity.
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[edit] Usage
Transistor models are used for almost all modern electronic design work. Analog circuit simulators such as SPICE use models to predict the behavior of a design. Most design work is related to integrated circuit designs which have a very large tooling cost, primarily for the masks used to create the devices, and there is a large economic incentive to get the design working without any iterations. Complete and accurate models allow a large percentage of designs to work the first time.
Modern designs are usually very complex or for some application that requires low power, high speed, or some other specialized performance that is difficult to predict without accurate models of the devices used. Comprehensive models include the primary terminal current-voltage characteristics, capacitances between terminals, and parasitic capacitance, resistance, and inductance, time delays, and temperature effects.
[edit] Types
Non-linear, or large signal transistor models fall into three main types [1]:
- Physical models - These are models based upon device physics, describing in detail the specific physical phenomena within a transistor. Parameters within these models are based upon physical properties such as oxide thicknesses, substrate doping concentrations, carrier mobility, etc.
- Empirical models - This type of model is entirely based upon curve fitting techniques, using whatever equations most accurately fits the measured data to specify the operation of the transistor in simulation. Unlike the previous model, the parameters within such a model have no basis on physical constants and are instead simply the coefficients, exponents, etc., used in the measured data curve-fitting expressions.
- Table models - The third type is model is a form of look-up table containing a large number of values for common device parameters such as drain current and device parasitics. These values are indexed in reference to their corresponding bias voltage combinations. Thus, model accuracy is increased by inclusion of additional data points within the table. The chief advantage of this type of model is decreased simulation time (see article look-up table for discussion of the computational advantages of look-up tables).
Non-linear models are used with a computer simulation program, such as SPICE. The use of non-linear models, which describe the entire operating area of a transistor, is required for digital designs and large signal circuits such as power amplifiers.
Small signal, or linear, models are still often used to evaluate stability and gain in circuits where the signal is much smaller than the bias voltages. A big advantage of small signal models is they can be solved directly, while large signal non linear models must be iterated with a computer simulator. The tools for designing with transistor parameters include simultaneous equations, determinants, and matrix theory (often studied as part of linear algebra), especially Cramer's rule.
[edit] Models
See also Bipolar junction transistor theory and modelling
[edit] Modern models
[edit] Other transistor parameters
A transistor’s parameters represent its electrical properties. Engineers employ transistor parameters in production-line testing and circuit design. A group of a transistor’s parameters sufficient to predict circuit gain, input impedance, and output impedance is also referred to as its small-signal model. Small signal models were the first type of models used. A small signal model is generated by taking derivatives of the current-voltage curves about a bias point. As long as the signal is small relative to the bias voltage the derivatives do not vary significantly. Small signal models are still used to design circuits such as radio receivers and audio pre-amplifiers.
Two-by-two parameter matrices receive designations such as
- T parameters,
- h-parameter,
- z (impedance) parameter,
- y (admittance) parameter, and
- s (scattering parameters) models.
These parameters can all be mathematically derived from Scattering Parameter data. Scattering Parameters, or S Parameters, can be measured for a transistor at a given bias point with a Vector Network Analyzer.
[edit] References
[1] Y. Tsividis, Operation and Modeling of The MOS Transistor, 2nd edition, Oxford University Press, New York, New York, 1999. ISBN 0-1951-7014-8
[edit] External Links
- Agilent EEsof EDA, IC-CAP Parameter Extraction and Device Modeling Software http://eesof.tm.agilent.com/products/iccap_main.html
