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This article has been tagged since February 2006. A diode I-V curve is clearly non-linear and this makes it difficult for diodes to be modelled in circuits. This text discusses two methods of analysing diode circuits ...
Graphical Analysis
Let us consider the following circuit: The diode is clearly forward biased and, assuming that the supply voltage is greater than the threshold voltage of the diode, a current, I, flows through the circuit. By Kirchhoff’s laws, we can find an equation for the current flowing in the circuit as follows:  Image File history File links Diode_Modelling_Image2. ...
Gustav Robert Kirchhoff (March 12, 1824 - October 17, 1887), a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. ...
The problem with this equation is that it has 2 unknowns, I and Vd. However, since the current flowing through the diode is the same as the current throughout the entire circuit, we can lay down another equation relating I and Vd, and this is the diode I-V characteristic:
When I >> IS, the formula can be simplified to:
Where IS is the saturation current of the diode (typically 10-12 A), q is the elementary charge value, 1.6x10-19C, n is known as the fiddle factor (for silicon diodes, n = 2), k is the Boltzmann constant, 1.38x10-23 and T is the temperature in Kelvin. attention Often the electrical current in a system increases with the voltage applied, but only up to a certain point. ...
The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ...
Ludwig Boltzmann Ludwig Boltzmann (February 20, 1844 – September 5, Austrian physicist famous for the invention of statistical mechanics. ...
The kelvin (symbol: K) is the SI unit of temperature, and is one of the seven SI base units. ...
If we were to go about solving this equation, we would substitute I from the second equation into the first equation, and then try and rearrange the resulting equation to get Vd. However, it turns out that this is impossible to do and the equations cannot be solved algebraically. The other method is to plot the two curves on a graph and the point of intersection will give the value of the current flowing through the circuit and the voltage across the diode.
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Piecewise Linear Modelling In practice, the graphical method is complicated and long and is impractical for complex circuits. The second method of modelling a diode is called piecewise linear (PWL) modelling. In mathematics, this means taking a function and breaking it down into several linear segments. The example below shows how a curve can be approximated by three linear segments, forming a three-segment PWL model: In mathematics, a piecewise linear function , where V is a vector space and is a subset of a vector space, is any function with the property that can be decomposed into finitely many convex polytopes, such that f is equal to a linear function on each of these polytopes. ...
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The same method is used to approximate the diode characteristic curve into linear segments. This enables us to substitute the real diode for an ideal diode, a voltage source and a resistor. The figure below shows a real diode I-V curve being approximated by a two segment piecewise linear model. Resistor symbols (US and Japan) Resistor symbols (Europe) A pack of resistors A resistor is a two-terminal electrical or electronic component that resists an electric current by producing a voltage drop between its terminals in accordance with Ohms law. ...
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Firstly, let us consider the ideal diode. In an ideal diode, if the diode is reverse biased, the current flowing through it is zero. The ideal diode starts conducting at 0V and an infinite current can flow through and the diode acts like a short circuit. The I-V characteristics of an ideal diode are shown below:
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Now let us consider the case when we add a voltage source in series with the diode in the form shown below:
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If the anode of the diode is connected to 0V, the voltage at the cathode will be at Vt and so the potential at the cathode will be greater than the potential at the anode and the diode will be reverse biased. In order to get the diode to conduct, the voltage at the anode will need to be taken to Vt. This circuit models the threshold voltage present in real diodes. The combined I-V characteristic of this circuit is shown below: Diagram of a zinc anode in a Daniells cell. ...
Diagram of a copper cathode in a Daniells cell. ...
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The last thing needed is a resistor to limit the current as shown below:
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The I-V characteristic of the final circuit looks like this:
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The real diode now be replaced with the ideal diode, voltage source and resistor and the circuit can now be modelled using just linear elements. When forward biased, the ideal diode is simply a short circuit and when reverse biased, an open circuit.
See also Diodes Types of diodes A diode functions as the electronic version of a one-way valve. ...
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