# 3.19 The diode

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A brief description of a diode and its inner workings.

The resistor, capacitor, and inductor are linear circuit elements in that their v-i relations are linear in the mathematical sense. Voltage and current sourcesare (technically) nonlinear devices: stated simply, doubling the current through a voltage source does not double the voltage. Amore blatant, and very useful, nonlinear circuit element is the diode ( learn more ). Its input-output relation has an exponential form.

$i(t)={I}_{0}(e^{\frac{q}{kT}v(t)}-1)$
Here, the quantity $q$ represents the charge of a single electron in coulombs, $k$ is Boltzmann's constant, and $T$ is the diode's temperature in $K$ . At room temperature, the ratio $\frac{kT}{q}=25$ mV. The constant ${I}_{0}$ is the leakage current, and is usually very small. Viewing this v-i relation in [link] , the nonlinearity becomes obvious. When the voltage is positive,current flows easily through the diode. This situation is known as forward biasing . When we apply a negative voltage, the current is quite small, and equals ${I}_{0}$ , known as the leakage or reverse-bias current. A less detailed model for the diode has any positive current flowing through the diode when it is forward biased, andno current when negative biased. Note that the diode's schematic symbol looks like an arrowhead; the direction of current flowcorresponds to the direction the arrowhead points.

Because of the diode's nonlinear nature, we cannot use impedances nor series/parallel combination rules to analyze circuits containing them. The reliablenode method can always be used; it only relies on KVL for its application, and KVL is a statement about voltage drops around aclosed path regardless of whether the elements are linear or not. Thus, for this simple circuit wehave

$\frac{{v}_{\mathrm{out}}}{R}={I}_{0}(e^{\frac{q}{kT}({v}_{\mathrm{in}}-{v}_{\mathrm{out}})}-1)$
This equation cannot be solved in closed form. We must understand what is going on from basic principles,using computational and graphical aids. As an approximation, when ${v}_{\mathrm{in}}$ is positive, current flows through the diode so long as the voltage ${v}_{\mathrm{out}}$ is smaller than ${v}_{\mathrm{in}}$ (so the diode is forward biased). If the source is negative or ${v}_{\mathrm{out}}$ "tries" to be bigger than ${v}_{\mathrm{in}}$ , the diode is reverse-biased, and the reverse-bias current flowsthrough the diode. Thus, at this level of analysis, positive input voltages result in positive output voltages with negativeones resulting in ${v}_{\mathrm{out}}=-(R{I}_{0})$ .

We need to detail the exponential nonlinearity to determine how the circuit distorts the input voltage waveform. We can ofcourse numerically solve [link] to determine the output voltage when the input is a sinusoid. Tolearn more, let's express this equation graphically. We plot each term as a function of ${v}_{\mathrm{out}}$ for various values of the input voltage ${v}_{\mathrm{in}}$ ; where they intersect gives us the output voltage. The left side, the current through the output resistor, does notvary itself with ${v}_{\mathrm{in}}$ , and thus we have a fixed straight line. As for the right side,which expresses the diode's v-i relation, the point at which the curve crosses the ${v}_{\mathrm{out}}$ axis gives us the value of ${v}_{\mathrm{in}}$ . Clearly, the two curves will always intersect just once for anyvalue of ${v}_{\mathrm{in}}$ , and for positive ${v}_{\mathrm{in}}$ the intersection occurs at a value for ${v}_{\mathrm{out}}$ smaller than ${v}_{\mathrm{in}}$ . This reduction is smaller if the straight line has a shallowerslope, which corresponds to using a bigger output resistor. For negative ${v}_{\mathrm{in}}$ , the diode is reverse-biased and the output voltage equals $-(R{I}_{0})$ .

What utility might this simple circuit have? The diode'snonlinearity cannot be escaped here, and the clearly evident distortion must have some practical application if the circuitwere to be useful. This circuit, known as a half-wave rectifier , is present in virtually every AM radio twice and each serves very different functions! We'll learn what functions later.

Here is a circuit involving a diode that is actually simpler toanalyze than the previous one. We know that the current through the resistor must equal that through the diode. Thus, thediode's current is proportional to the input voltage. As the voltage across the diode is related to the logarithm of itscurrent, we see that the input-output relation is

${v}_{\mathrm{out}}=-(\frac{kT}{q}\ln (\frac{{v}_{\mathrm{in}}}{R{I}_{0}}+1))$
Clearly, the name logarithmic amplifier is justified for this circuit.

what is the stm
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
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scanning tunneling microscope
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what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
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absolutely yes
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for teaching engĺish at school how nano technology help us
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Do somebody tell me a best nano engineering book for beginners?
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what is fullerene does it is used to make bukky balls
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fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
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