semiconductors

Tom Penick [email protected] www.teicontrols.com/notes 06/12/98

SEMICONDUCTORSELTE 1403

Forward biased diode:

N

cathode

P

depletion layer+

electronflow

anode

An ideal diode acts like a closed switch when forwardbiased and an open switch when reverse biased. 1stapproximation calculations assume an ideal diode.2nd approximation calculations take into account thevoltage drop across the diode. 3rd approximationcalculations additionally take into account bulkresistance.

Voltage Drop silicon diode .7V germanium diode .3VBulk Resistance rB = ∆E/∆IA digital multimeter won't measure the resistance on a

diode due to insufficient voltage. The diode checkfunction of a digital multimeter reads the kneevoltage. The knee voltage is the voltage at which aforward biased diode begins to conduct.

Diode Ratings:PIV Reverse Breakdown VoltageIf Forward Current LimitIS Saturation Current - minority carrier current of a

reverse-biased diodeRf Forward ResistanceVk Knee Voltage

Light Emitting Diode When forward-biased,free electrons combine with holes near thejunction. As they move from an area ofhigher energy to lower energy, they emitradiation. Assume 2V drop unlessspecified.

LED

Schottky Diode has almost no chargestorage, so can switch on and off muchfaster than an ordinary diode. Hasmetallic/silicon junction; low powerhandling; .25V offset voltage; used for highfrequencies.

Schottky

Varactor is a silicon diode optimized for itsvariable capacitance when reversed-biased. Used for tuning frequency-dependent equipment.

Varactor

Zener Diode is designed to operate in thebreakdown region; used for voltageregulation.

Zener

Avalanche Effect Reverse voltage exceeds thebreakdown voltage and the minority carriers are givenenough energy to dislodge valence electrons fromtheir orbits. These free electrons then dislodgeothers.

Zener Effect The electric field becomes strong enoughacross the junction of a heavily-doped reverse-biaseddiode to pull valence electrons from their shells. Forbreakdown voltages below 5V, the Zener effectdominates, above 6V the avalanche effect dominates.

Second Approximation for a Zener Diode

IV V

R Rzin z

s z

=−+

Iz = zener currentVin = supply voltageVz = zener voltageRs = source resistanceRz = zener resistance

Zener Resistance is the small series resistance of azener diode when it operates in the breakdown region.

∆ ∆V I Rout z z= ∆V = change in output voltage∆Iz = change in zener currentRz = zener resistance

Half-Wave Rectifier:π

=π

=2rmsp

dc

VVV

diode reverse voltage: PIV = Vp

diode forward current: I Idcdiode =

Half-Wave Rectifier WithCapacitor Filter:

PIV = 2Vp

V V Vdc p rms= = 2

Full-Wave Rectifier:π

=π

=2rmsp

dc

VVV

Vp is the voltage across the full secondary winding)

diode reverse voltage: PIV = Vp

diode forward current: I Idcdiode = 12


Full-Wave Rectifier WithCapacitor Filter:

V V Vdc p rms= =12

12 2

Bridge Rectifier: VV V

dc

p rms= =2 2 2

π πdiode reverse voltage: PIV = Vp

diode forward current: I Idcdiode = 12

Bridge Rectifier WithCapacitor Filter:

V V Vdc p rms= = 2

Further refined to includethe effect of ripple voltage: V V

Vdc p

rip= −

2

Ripple Formula for acapacitor-input filter

VI

f Cripdc=

Vrip = peak-to-peak rippleIdc = dc peak load currentf = ripple frequency (twice

the input frequency for afull-wave rectifier)

C = filter capacitance

A choke is an iron-core inductor with alarge value of L in Henrys. Thechoke has an inductive reactance inohms of:

LfX L π= 2

A capacitor has an inductive reactancein ohms of:

CfX C π

=2

1

The resonant frequency of an inductorand capacitor (or varactor) inparallel: LC

fπ

=2

1

Clipper: Removes either the positive or negative peaksof a sine wave by shorting through a diode.

Clamper: Raises or lowers the sine wave so that itbecomes mostly positive or mostly negative.

Or Gate: Output goes high when any input is high.And Gate: Output goes high when all inputs are high

TRANSISTORS

elec

tron

flow

I ICE IB

forward biased reverse biased

Base

lightlydoped

pn

heavilydoped

Emitter

n

Collector

pnp

n

p p

npn

n n

p

(the n is next tothe arrow)

I I IE B C= + V V I RCE CC C C= −

Bias: difference in potential between base and emitter.

DC Alpha:(slightly lessthan 1) E

CDC I

I=α

1+ββ

=αDC

DCDC

DC Beta:(usually 50 -300)

βDC =I

IC

B

hFE is the same as βDC, the collectorto emitter current gain

The four operating regions of a transistor are saturation,active, cutoff, and breakdown.

CE(CUTOFF)

VCE

V

LrCQI+CEQV

DC and AC Load Lines, Q Point

Q

AC load lineDC load line

ICQCEQV

+

C(SAT)IrL

IC

The DC Load Line is a graph representing all possible dcoperating points of the transistor for a specific loadresistor. VCE is the x-axis and IC is the y-axis. Theequation is V V I RCE CC C C= − . The horizontal

intercept will be the supply voltage VCC and thevertical intercept will be the collector current when thetransistor is saturated, i.e. the collector/emitter isconsidered a closed switch.

The Q Point is the operating point of the transistor,usually located near the middle of the DC Load Line

AC Load Line The Q pointmoves along the AC loadline. Steeper than the DCload line.

i IV

rc sat CQ

CEQ

L( ) = +

v V I rce cutoff CEQ CQ L( ) = +AC Compliance - maximum peak to peak AC output

voltage without clipping. AC Compliance iscalculated by finding the smaller of the following:

Cutoff Clipping:PP I rCQ L= 2

Saturation Clipping:PP VCEQ= 2

When the Q point is centered on the DC load line, cutoffclipping occurs first because the AC load line is alwayssteeper than the DC load line.

DC Compliance is the DC voltage range over which thetransistor can operate; in other words VCC.

= .7VBEVIE

V V

RB

IB

BB

RC

IC

CC

Base Bias


Voltage Divider Bias: The Base Biascircuit above is usually impracticalin linear circuits because the Qpoint is unpredictable due tovariations in βDC. The VoltageDivider Bias shown at right solvesthis problem. When βDC is known,IE may be calculated as:

dcE

BEBE RRR

VVI

β+−

≅/)( 21

But when dc

E

RRR

β>> 21 ,

the equation may be reduced to: IV V

REB BE

E

≅−

1) Calculate the voltage at the base2) The emitter voltage is .7 less than the base3) Calculate IE

4) IC ≅ IE

5) Calculate voltage drop across RC

When designing the voltage divider bias amplifier, thecurrent through the voltage divider should be at least10 times the current through the base.

To center Q on the DC load line, VCE will be ½VCC, VE willbe about .1VCC.

To center Q on the ACload line, use theformula:

IV

R R rCQCC

C E L

=+ +

Other Biasing Methods

EmitterFeedback Bias

CollectorFeedback Bias

Emitter Bias

RE

IE

ICIB

R RCB

VCC

IE

VCC

ICIB

RB

RC

-VEE

RR E

IE

B

IB

RC

IC

CCV

dcBE

BECCC RR

VVI

β+−

≅/ dcBC

BECCC RR

VVI

β+−

≅/

IV V

REEE BE

E

≅−

AC Resistance of a Diode:where I is the dc current through thediode. To a second approximation,consider the .7V drop across thediode in calculating the value I.

rIac =

25mV

AC Emitter Resistance of a Transistor:′ =r

IeE

25mV

AC Beta: Called β as opposed to βdc (DCBeta). Referred to as hfe as opposed tohFE for DC Beta. b

c

i

i=β

CE Characteristics:Output is out of

phase with inputHigh voltage gain is

possibleMay be used with a

swamping resistorto stabilize thevoltage gain

In a matched loadcondition, RL = RC

RL

CCV

RR2 E

R1 RC

Common Emitter

AC Input Impedance of CEAmplifier: ein rRRz ′β= 21

AC Voltage Gain (CE) when theemitter is AC ground: A

V

V

r

rout

in

L

e

= =′

Swamping Resistor Todesensitize a CE amplifier tochanges in r’e, a resistor rE isadded between the emitter andac ground. This stabilizes theamount of gain, but alsoreduces it.

)()( eEbasein rrz ′+β=

)(21 eEin rrRRz ′+β=

Ar

r rL

E e

=+ ′

Heavy Swamping The value ofrE is much larger than the value

of r’e:

Ein rRRz β= 21

Ar

rL

E

=

AC Input Voltage when a sourceresistor (a resistor in series withthe input) is present.

vv z

R zbin in

s in

=+

AC Load Resistance, rL, rc, or rLac, is the parallelcombination of all AC paths from collector to ground.Remember the battery and capacitors are consideredshorts.

AC Power delivered to the load (class A amplifier):where VL is rms:

PV

RLL

L

=2

using peak to peak volts:

PV

RLPP

L

=2

8Quiescent Power Dissipationof a transistor:

P V IDQ CEQ CQ=

Efficiency of a stage:PL is load power at ACcompliance

%100(max) ×=ηCC

L

P

P

Total Current Drain is the voltagedivider current plus the collector current:

I I ICC CQ= +1

Cascaded Stages Gain: A A A A= 1 2 3

Cascaded Stages The AC loadresistance of one stage is affected bythe impedance of the following stage:

r R zL C in=

RR2 E

IE

V

R1 RC

IC

CC


CC Characteristics:Voltage gain < 1High input impedanceAC output is in phaseLow-distortionHas power gainCan be placed at the

output of a CEamplifier to reduceoutput loading andthereby increase thegain.

CC

RR 2 E

R 1

RL

V

Common Collector(Emitter Follower)

Input Impedance (high) of a CC: R R r rL e1 2 β( )+ ′AC Voltage Gain of a CC is slightly

less than 1: Ar

r rL

L e

=+ ′

AC Power Gain of a CC:G

r

r rAL

L e

=+ ′

= ≅β β β

AC Output Power of a CC: P i rout e L= 2

The DarlingtonAmplifierconsists ofcascaded CC’sfor a very largeincrease ininputimpedance.

1

RE RL

CCV

2

Darlington Pair

R

R

The Zener Follower is avoltage regulator circuitthat offers improved loadhandling over the zenerregulator. Voltage outputis .7V less than the valueof the zener diode.

R L

Zener Follower

Vin-

+

CB Characteristics:Low input impedanceLarge voltage gainAC output in phaseUseful at high

frequenciesNot as popular as CE

or CCA differential

amplifier is a CBdriven by a CE

RL

Common Base

VCC

Field Effect Transistors

Junction Field Effect Transistor JFETN channel P channel

G

S

D

G

S

D

Creating adepletion regionby reverse biasingthe gate reduces(pinches) currentbetween the drainand the source.

n

nDrain

pp

Neverforward biased

VGG VDDSource

Gate

Metal Oxide Silicon Field Effect Transistors

N channel

G

Enhancement-type MOSFET

B GS

DBS

D

P channel

G GateD DrainB Substrate*S Source

*usuallyconnectedinternally tothe source

Thin silicondioxide layer

Source

Metal

Gate pn

nSubstrate

Drain

P channel

Depletion-type MOSFET

G

N channel

BS GD

BS

D

MOSFET’s donot have thermalrunaway.

Gate may bepositive ornegative

p

Source

n

Depletion-type MOSFET

SubstrateGaten

Drain

semiconductors

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