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July09LessonTwo

July09LessonTwo - Key Lecture Concepts for CoE225/EE...

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Key Lecture Concepts for CoE225/EE 271 (Mostly Digital Electronics) 1 LESSON 2: Analysis of Circuits with Two-Terminal Nonlinear Devices Using LOAD CURVES and Mathematical Model (TRIAL AND ERROR) Lesson Overview: This lesson has three learning objectives. The first is to master a trial and error method to find the Q point of a diode in series with a resistor using the diode equations. Trial and error is an important technique to use to solve any nonlinear problem which requires the solution of a transcendental equation. By this method the diode current and voltage can be found with high precision by using just two assumptions or “educated guesses” of either the value of the current or voltage. It is an alternative to grinding out a mathematical solution or relying on computer analysis; it enables the engineer to quickly visualize the system that is being designed or analyzed. Exercising the trial and error method will give you a feeling for the typical small changes in diode voltage values required for large changes in diode current. The second learning objective is to use graphical methods to find the Q-pt. of nonlinear devices in series or in parallel. Graphical approaches are particularly useful when i/v characteristics can not be described mathematically; they are also important for designing and inventing new circuits and devices and for understanding the factors involved in high-speed switching. The graphical analyses taught in this lesson will be used throughout the course. It is well worth the effort to struggle a little to learn how to use graphical analysis versus relying only on mathematical equations. The third learning objective is to analyze circuits with more than one nonlinear device, e.g. multi-diode circuits. For multi-diode circuits it is necessary to make an assumption for each diode on whether its Q-point is in the 1 st or 3 rd quadrant. Then the circuit is analyzed based on these assumptions and the results checked by comparing the Q-point location of each diode versus the original assumption. If the assumption is wrong, the analysis must be repeated using a new set of assumptions for the states of each of the diodes. The analysis is not as difficult as it may seem, because a “feeling” for the best initial assumptions and how to modify them to use a correct set of assumptions does develop after solving problems. A “short or open” approximation to the state of the diode (the previously described ideal diode characteristic) can be used to simplify the analysis. A) Analysis by Iteration (Trial and Error Method) The iteration method will be taught by solving the problem of finding the voltage and current of a forward biased diode in series with a 10K resistor driven by a total applied voltage of ten volts. The applied voltage could be from a 10 volt supply line and ground or alternatively from plus and minus five volt lines. The circuits are shown in the margin. The parameters for the diode will be taken to be I S = 10 10 [mA] and nV T = 0.025 [v].

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