Diode Equation and Models

8/8/2019 Diode Equation and Models

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Diode Equation and ModelsThe general equation linking the diode

current I to the applied voltage V is:

-

! 1exp

nkT

eVII o


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Diode Equation and Models Here:

Io is the reverse saturation current.

k is Boltzmann's constant= 1.38 x 10-23 JK-1.

T is the working temperature in Kelvin.

e is the magnitude of the electronic charge.

n is called the ideality f actor. (n= 1 fromtheory. From experiments on silicon diodes n=2 at low current and 1 for large currents).


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Diode Equation and Models As an exercise satisfy yourself that this explains

the facts discussed in the Semiconductor Diodes

section of the module. (The exponential termcorresponds to majority carrier flow whilst the

1 term relates to the reverse saturation

component)

You can now tackle questions 1-4 on Example

Sheet1!


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Diode Equation and Models By plotting out this equation on a practical

scale we see that to a good approximation

-

}

nkT

eVII o exp


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Diode Equation and Models Diode eqn


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Diode Equation and Models An ideal diode would show an abrupt

transition from perfectly conducting (diode

short circuit) to perfectly non-conducting

(diode open circuit) states at 0V

I

V


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Diode Equation and Models It acts as switch since

In the ON state it is a short and in the OFF

state it is open circuit

I

V

ONOFF

Smith/Dorf symbol

for ideal diode


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Diode Equation and Models An silicon diode approximates this ideal

but the transition from conducting to non-

conducting circuit states is at around 0.6Vbecause of the barrier potential. This

voltage is called the cut-in voltageI

V0.6


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Diode Equation and Models Experiment


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Diode Equation and Models A closer approximation to the diode I-V

equation (experiment) also includes the bulk

resistance. This gives the diodes I-V curve

a finite slope above cut-in.

I

V0.6


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Diode Equation and Models Diodes formed in other materials have

different cut-in voltages.

Diodes breakdown for large reverse bias

(Breakdown voltage)


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Diode Equation and Models We are now in a position to draw some models

that represent diode behaviour.

We can use these models instead of the diodeequation in circuit analysis

Later on in the Module we will be developing

similar models (orequivalentcircuits) to represent

the behaviour of transistors when they are used as

linear amplifiers.


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Diode Equation and Models Diode circuit symbol

p nAnode Cathode


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Diode Equation and Models BS3939, IEC symbol (For information only,

Smith and Dorfs symbols will be used in

the module)


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Diode Equation and Models In forward bias the equivalent circuit is a

forward bias drop (Vc ~ 0.6V) in series with

a small (forward) resistance.

I

V0.6

+ -

V

VC Rf


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Diode Equation and Models In many cases Rf can be ignored.

I

V0.60.6V


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Diode Equation and Models In reverse bias (strictly in the off state

below Vc) the diode can be represented by a

very large resistor Rr.

We shall assume Rr. to be infinitely large so

that the piecewise linear model for the diode

is:


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Diode Equation and Models Incremental Diode Model

Anotherimportant principle that we will needfor transistor analysis is that of theincrementalmodelling of a non-linear device.

Basically this assumes the diode I-V curve is

linear forsmall variations in I and V about someoperatingor bias point. (Also known as the Qor quiescent point.)


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Diode Equation and Models We introduce important notation used

throughout the module. As noted, the

(small) a.c. signal sits on top of a d.c. biaslevel.

Lower-case symbols are used for the timevarying signals (i, v).

Upper-case symbols are used for the d.c.bias levels (I, V).


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Diode Equation and Models

Q

VQ

I, i

V, v

v

V, v

I, i i

t

t


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Diode Equation and Models The diode is biased to operate about a point

Q on the I-V curve

The small a.c. signal is superimposed onthis bias.

The diode can then be modelled by a

resistance equal to the inverse slope of thetangent to the bias point (Linearapproximation to diode curve)


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Diode Equation and Models


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Diode Equation and Models We will, in the examples class, use the diode

equation to show that, for an ideality factor of 1,

the dynamic (small signal) resistance is:

)(

25

Qatslope

1

(Ohms)

mAIdI

dVr

Q

D !!!


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Zener Diode

This is simply a diode whose breakdown

voltage is controlled to be a specific value.

It finds wide use in limiting and voltage

regulator circuits (see diode application

section of the module)

Diode Equation and Models

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