The Ebers-moll Model-based Transistor Modeling

A transistor model has been set up on the basic of the Ebers-Moll model. When the input signal is low-frequency small-signal, low-frequency large-signal, high-frequency small-signal, or high-frequency large-signal, the waveform of the output signal has been analyezed. At the same time, the generating function of the Bessel function has been used to do the output harmonic analysis.When the input signal is Low-frequency small-signal, considering the base body resistance, making the problem of solving the direct current(DC) bias voltage of the inputting Ebers-Moll model part into a transcendental equation. Using Newton iteration analysis solution may get the DC bias voltage of inputting Ebers-Moll Model. Subsequently alternating current(AC) resistor (this resistor will be introduced in the chapter 3) can be get, finally the output signal of the whole model can be calculated. At that moment, the transistor can be regarded as a linear device.When the amplitude of the signal becomes larger, the output signal will contain much harmonic wave. At this time the transistor should not be treated as a linear device. The Newton iteration method still be used to get the DC bias voltage of the inputting Ebers-Moll model part. However, the solving the signal of the inputting Ebers-Moll model part contains a lot of a transcendental equations. Newton iteration method can not be used in many of these equations. The reason is when solving these equations, the Newton iteration method is diverged, and it is replaced by the dichotomy method.When the input signal is the high-frequency small-signal,two kinds of methods are used to get the result of the model. When the signal is High-frequency, the effects of junction capacitance must be considered, and the circuit equations are listed to solve the problem. At this time, the transistor can also be treated as a linear device. The frequency domain method mainly use the Fourier transformation for the frequency domain analysis, time domain method directly analyzes the time-domain to give the final results. The final results of both methods are consistent, because the same problem are analyzed from two different angles.When the input signal is relatively high frequency and large amplitude, the problem will become complicated. The problem of Ebers-Moll model of input signal and output signal are solving a first-order non-linear non-homogeneous differential equation. Similarly, the numerical method is used to solve problem. Based on an overall consideration, the improved Euler algorithm, as is called the prediction-correction method is adopted to solve the differential equations. Finally input and output signals of the Ebers-Moll model are get.In addition, the dynamic range of the model is introduced. The limitation of the input signal which is to define the small-signal or large-signal is narrated, which decides treating a transistor as a non-linear device or a linear device, is also showed. The limits which is used to distinct High-frequency or low frequency is described too. in the main are not to want to consider the problem of junction capacitance. And more, the treatment method of discontinuous points in the model is explained.Finally, some complement about the problem, which is caused by the arbitrary input signal, is made.