mechanics of materials - university of pittsburghqiw4/academic/mems1082/chapter3-1 diode.pdf ·...

Department of Mechanical Engineering

MEMS1082

MechatronicsChapter 3-1 Semiconductor devices

Diode


Semiconductor: Si


Semiconductor


N-type and P-type SemiconductorsThere are two types of impurities: N-type - In N-type doping, phosphorus or arsenic is added to the silicon in small quantities. Phosphorus and arsenic each have five outer electrons, so they're out of place when they get into the silicon lattice. The fifth electron has nothing to bond to, so it's free to move around. It takes only a very small quantity of the impurity to create enough free electrons to allow an electric current to flow through the silicon. N-type silicon is a good conductor. Electrons have a negative charge, hence the name N-type. P-type - In P-type doping, boron or gallium is the dopant. Boron and gallium each have only three outer electrons. When mixed into the silicon lattice, they form "holes" in the lattice where a silicon electron has nothing to bond to. The absence of an electron creates the effect of a positive charge, hence the name P-type. Holes can conduct current. A hole happily accepts an electron from a neighbor, moving the hole over a space. P-type silicon is a good conductor.

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N-type and P-type Semiconductors


Semiconductor device-diodeA diode is the simplest possible semiconductor device. A diode allows current to flow in one direction but not the other. You may have seen turnstiles at a stadium or a subway station that let people go through in only one direction. A diode is a one-way turnstile for electrons.

When you put N-type and P-type silicon together as shown in this diagram, you get a very interesting phenomenon that gives a diode its unique properties.


Diodes

http://upload.wikimedia.org/wikipedia/commons/0/05/Diode_3D_and_ckt.png


Diode

Electron flow direction

Current direction


Diode depletion region

http://upload.wikimedia.org/wikipedia/commons/0/05/Diode_3D_and_ckt.png


pn junction

PN Junction

http://upload.wikimedia.org/wikipedia/commons/f/fa/Pn-junction-equilibrium-graphs.png


Diode depletion region


Diode forward and reverse bias


Shockley diode equation


Diode current and voltage

http://upload.wikimedia.org/wikipedia/commons/a/a5/Diode-IV-Curve.svg


Diode Characteristic


Diode Characteristic at different scale


Diode measurementMeter with a

“Diode check” function displays the forward voltage drop of 0.548 volts instead of a low resistance


Measurement of a diodeMeasuring forward voltage of a diode without “diode check” meter function: (a) Schematic diagram. (b) Pictorial diagram


Load line of diode A circuit with a diode


Example For circuit, determine the current i


Example Circuit

reduction to Théveninequivalent circuit


Example Thévenin equivalent circuit


Example Draw load line

to determine the diode voltage and current


Example Determine current i


Example Determine the current and voltage of the diode in the

circuit. The diode characteristic is given in the right figure.


Example


Piecewise-linear approximation and small signal analysis Diode is nonlinear resistor


Piecewise-linear approximation and small signal analysis Diode piecewise-linear approximation


Piecewise-linear approximation and small signal analysis


Piecewise-linear approximation and small signal analysis Small signal analysis


Piecewise-linear approximation and small signal analysis If we are only interested in the portion due to vs(t), we may

set Es=0, and Ef =0, then

Often, for practical purpose, we can assume Ef =0 in small signal equivalent circuit of a diode. For typical diodes, the value of Rf is quite small, between 1Ω and 100Ω. Thus Rfcan be neglected.


Piecewise-linear approximation and small signal analysis


The ideal diodes


The piecewise- linear model of a diode, using an ideal diode

Ideal diode


Example Nonlinear resistors with a wide range of characteristics can be

obtained, approximately, with circuit containing diodes, for example, a square-law device is two-terminal nonlinear resistor whose terminal voltage-current characteristic obeywhere k is normalization constant. The ideal characteristic is shown

2kvi =


Example This device may be used in modulator, e.g., to attain a voice

signal to high-frequency carrier wave, as is done in amplitude modulation (AM) radio transmission. Design a square-law device to approximate the ideal characteristics for

with a normalization constant k=0.001Vv 50 ≤≤


Example A circuit using ideal diodes D1 and D2

and voltage sources E1 and E2

Use V=5V; E1 < E2

Initially 0≤v≤ E1,the diodes are reverse biased and open, the curve will have slope 1/R3

For E1 ≤v≤ E2,D1 closes, and D2 open, the input resistance will be R3llR1

For E2 ≤v≤ 5V,D1 and D2 close, the input resistance will be R3llR1llR2

Suppose E1 =2.0V and E2=3.5V

mAkEI 4211 ==

mAkEI 25.12222 ==

mAkVI 252 ==


Example Noting the slope of each portion, we obtain

Ω== 5001

13 I

ER Ω=−−

= 18212

1221 II

EERR Ω= 2861R

Ω=−−

= 1182

2321 II

EVRRR Ω= 3332R

Replacing the actual diode with their piecewise-linear approximation using

VER ff 5.0,10 =Ω=

Ω= 5003RΩ= 2761R Ω= 3232R

E1 =1.5V and E2=3.0V


Ideal transformer


Rectifiers

Half-Wave Rectifier The transformer isolates the load from the source


Rectifiers

Half-Wave Rectifier

πωππωω20

0sin≤≤=≤≤=tv

ttVv

L

sL

( )

π

ωωπ

π

s

sL

V

tdtVV

=

= ∫0 sin21

The average dc value of vL


Rectifiers Representing the Half-Wave Rectifier voltage by Fourier series

.........2coscos......2sinsin 2121 ++++++= tbtbtataVv LL ωωωω

The Fourier coefficients can be determined as

( ) ( ) dttntvT

bdttntvT

aT

Ln

T

Ln ωω cos2;sin200 ∫∫ ==

( ) ( )2

sinsin1sin2001

ss

T

LVtdttVdtttv

Ta === ∫∫ ωωω

πω

π

For the Half-Wave Rectified voltage

( ) ( ) 0sinsin1sin200

=== ∫∫ tdtntVdttntvT

a s

T

Ln ωωωπ

ωπ


Rectifiers

0;152;0,

32;0 54321 =−==−== bVbbVbb ss

ππ

Thus the Fourier series for the Half-Wave Rectified signal

( ) .....4cos1522cos

32sin

2+−−+= tVtVtVVtv ssss

L ωπ

ωπ

ωπ


Rectifiers Filtering the Half-Wave Rectifier

Capacitor has lower impedance to higher frequencies


Rectifiers Filtering the Half-Wave Rectifier

Larger C can be used to increase the time constant RC


Rectifiers Effects of actual diodes


The Full-Wave Rectifiers The full-wave rectifier


The Full-Wave Rectifiers The full-wave rectifier

( )

π

ωωπ

π

s

sL

V

tdtVV

2

sin10

=

= ∫

The average dc value of vL

Thus the Fourier series for the Full-Wave Rectified signal

( ) .....4cos1542cos

342

+−−= tVtVVtv sssL ω

πω

ππ


The Full-Wave Rectifiers Effect of actual diodes


The Full-Wave Bridge Rectifier A bridge rectifier makes use of four diodes in a bridge

arrangement to achieve full-wave rectification. This is a widely used configuration, both with individual diodes wired as shown and with single component bridges where the diode bridge is wired internally.


Bridge Rectifiers

Various types of Bridge RectifiersNote that some have a hole through

their centre for attaching to a heat sink


The Full-Wave Bridge Rectifier Bridge Rectifier


The Full-Wave Bridge Rectifier Bridge Rectifier with RC Filter and LC filter


The Voltage Limiter Limiter using ideal diodes and batteries


The Voltage Limiter Limiter using ideal diode and batteries



( ) 12 VR

RRtvVR

RR

L

sLs

L

sL +<<

+−

Load voltage is limited for source voltage


Example For a limiter shown below, assume identical piecewise-

linear diodes with Rf=100Ω, Ef=0.5V, V1=V2=10V, RL=100Ω, Rs=100Ω, and vs(t)=50sinωt V, sketch vL(t)


Zener Diodes A Zener diode is a type of

diode that permits current not only in the forward direction like a normal diode, but also in the reverse direction if the voltage is larger than the breakdown voltage known as "Zener knee voltage" or "Zener voltage". The device was named after Clarence Zener, who discovered this electrical property.

http://upload.wikimedia.org/wikipedia/commons/e/e9/Zener_3D_and_ckt.png


Zener Diodes Piecewise-linear

characteristic Device characteristic

of Zener diode


Zener Diodes Piecewise-linear model


Zener Diode Regulator In this circuit, a typical voltage

reference or regulator, an input voltage, UIN, is regulated down to a stable output voltage UOUT. The intrinsic voltage drop of diode D is stable over a wide current range and holds UOUTrelatively constant even though the input voltage may fluctuate over a fairly wide range. Because of the low impedance of the diode when operated like this, Resistor R is used to limit current through the circuit.

IDiode = (UIN - UOUT) / R


Zener Diode Regulator R must be small enough that the current through D keeps D in reverse breakdown. The value of this current is given in the data sheet for D. For example, the common BZX79C5V6 device, a 5.6 V 0.5 W Zener diode, has a recommended reverse current of 5 mA. If insufficient current exists through D, then UOUT will be unregulated, and less than the nominal breakdown voltage. When calculating R, allowance must be made for any current through the external load, not shown in this diagram, connected across UOUT.

R must be large enough that the current through D does not destroy the device. If the current through D is ID, its breakdown voltage VB and its maximum power dissipation PMAX, then IDVB < PMAX.


Zener Diode regulator

L

z

zs

zs

RV

VP

RRVV

I +=+−

= max

min

max,max

L

z

s

zs

RV

RRVV

I =+−

=max

min,min


Example

ARV

RVV

VPI

L

zzs

z

18.0max,maxmax =−

−==

Ω=−

= 250min

min,max I

VVR zs

A source voltage varies between 120V and 75V. The source resistance is zero, and the load resistance is 1kΩ. It is desired to maintain the load voltage at 60V. Determine the value of a regulator resistor R that will accomplish this and the required power rating of the zener.

1. A zener having a zener voltage of 60V is selected2. The maximum value of regulator resistance

mARVI

L

z 601000

60min ===

3. The power rating is determined when Vs=Vs,max. And zener draw the maximum current

WP 8.10max =


Light Emitting Diode


Light Emitting DiodeAn LED will begin to emit light when the on-voltage is exceeded. Typical on voltages are 2–3 volts


Connect Light Emitting Diode in Series

Connecting LEDs in seriesIf you wish to have several LEDs on at the same time it may be possible to connect them in series. This prolongs battery life by lighting several LEDs with the same current as just one LED. All the LEDs connected in series pass the same current so it is best if they are all the same type. The power supply must have sufficient voltage to provide about 2V for each LED (4V for blue and white) plus at least another 2V for the resistor. To work out a value for the resistor you must add up all the LED voltages and use this for VL.

Example calculations: A red, a yellow and a green LED in series need a supply voltage of at least 3 × 2V + 2V = 8V, so a 9V battery would be ideal. VL = 2V + 2V + 2V = 6V (the three LED voltages added up). If the supply voltage VS is 9V and the current I must be 15mA = 0.015A, Resistor R = (VS - VL) / I = (9 - 6) / 0.015 = 3 / 0.015 = 200, so choose R = 220 (the nearest standard value which is greater).

mechanics of materials - university of pittsburghqiw4/academic/mems1082/chapter3-1 diode.pdf ·...

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