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DAEs assume smooth characteristics for individual components; for example, a diode can be modeled/represented in a MNA with DAEs via the Shockley equation, but one cannot use an apparently simpler (more ideal) model where the sharply exponential forward and breakdown conduction regions of the curve are just straight vertical lines.
The Shockley diode equation relates the diode current of a p-n junction diode to the diode voltage .This relationship is the diode I-V characteristic: = (), where is the saturation current or scale current of the diode (the magnitude of the current that flows for negative in excess of a few , typically 10 −12 A).
Shockley derives an equation for the voltage across a p-n junction in a long article published in 1949. [2] Later he gives a corresponding equation for current as a function of voltage under additional assumptions, which is the equation we call the Shockley ideal diode equation. [3]
Includes many practical applications, problems and examples emphasizing troubleshooting, design, and safety to provide a solid foundation in the field of electronics. Assuming that readers have a basic understanding of algebra and trigonometry , the book provides a thorough treatment of the basic principles, theorems , circuit behavior and ...
The answer is not obvious, since the terminal voltage will not be V θ after Z e is connected. Instead, we imagine that we attach, in series with impedance Z e, a source with electromotive force E equal to V θ but directed to oppose V θ, as shown in Figure 2b. No current will then flow through Z e since E balances V θ.
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The characteristic curve (curved line), representing the current I through the diode for any given voltage across the diode V D, is an exponential curve. The load line (diagonal line) , representing the relationship between current and voltage due to Kirchhoff's voltage law applied to the resistor and voltage source, is
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