BJT - Principles of Operation

• Different concentrations of donors and acceptors in BJT regions

PE >> NB >> PC

• Very narrow base thickness compared with diffusion length LD

WB << LD

Emitter Base Collector (p++) (n+) (p)

Typical Doping [1/cm3]: PE~1020; NB~1018; PC~1017

• Current gain β = ∆iC / ∆iB

−⋅≈

D

B

B

E

LW

NP 1β

Bipolar Junction Transistor (BJT)

Symbolic representation of BJT in circuits VCB

IC Collector IB VCE Base VBE IE

Emitter • BJT is a three-terminal device

• The “arrow” shows the direction of current in an emitter

• Only two voltages and two currents are independent

VCE = VBE+ VCB

IE = IB + IC

Identification of BJT terminals

How to recognize the terminals using Ohmmeter • A stand alone transistor can be represented as two p-n

junctions. They can be tested separately

1) Type of BJT (n-p-n or p-n-p)

2) Which terminal is the base

n p

Base p Base n

n p

3) Which one is the emitter

• Emitter-Base is the most heavily doped p-n junction

Reverse Bias Resistance of B-E junction is much

lower than that of C-E junction: RBE << RCE

Types of BJT

• There are two basic types of BJT

n-p-n and p-n-p

C C n-type p-type

B B p-type n-type E E n-type p-type • This notation comes from the type and sequence of the

semoconductor layers

• Direction of the “arrow” specifies the type of BJT in

circuit diagrams

Regimes of BJT

+

+

• Forward active

•

n VCB > 0

p

VBE >0 N • B-E junction is forward biased, the typical VBE ≈ 0.7 V

iE

iC

iB

-

-

• C-B junction is reverse biased

• The most remarkable propety is that collector current

reflects the base current

∆iC = β . ∆iB

Typical current gain β ~ 70-200 •

• Collector and emitter currents close to each other iC ≈ iE

Family of Input characteristics of BJT

iC

n-p-n

iB (µA)

VCE

VBE

30

20

10

iB=f(VBE)

• Input characteristic

• iB(VBE) can be appr

+

VCE=const

VCE=10V VCE=0

VBE (V)

VCE=5V

0.7

BE

B

Vi

r ∆∆

=π

1

is a weak function of VCE

oximated as a step function at VBE ≈0

+

-

.

-

7V

Family of Output characteristics of BJT

iC=f(VCE)

n-p-n

VCE

iC (mA)

VBE

1

2

3

iB=const

0.5 • Saturation region:

• Active region: iC is

+

VCE

iB=10 µA

20 µA

30 µA

5 10 15

VCE < 0.5V

a weak function of VCE

+

-

-

(V)

Small signal parameters of BJT

collector base

iC=β iB iC =gm VBE

π

emitter

VA ≈ 100…200 V

iC

V0

Early voltage VA

1

• Current gain (empirical parameter) β ≈ 10…5• Transconductance gm=iC/VT gm ≈ 0.1…2• Input resistance rπ = β/gm= VT/iB rπ ≈ 10Ω…• Output resistance r0 =VA/ iC r0 ≈ 1…10

r0

r

CE

/ r0

00 A/V 1kΩ

0 kΩ

Configurations of BJT in stages

Vin Vout • One node in common for input and output circuits

Common emitter

Common Collector

Common Base

Biasing of BJT with constant iB

• A FORWARD ACTIVE regime requires a forward

biased B-E junction and a reverse biased C-B junction

+VCC

RB* iC

VBE ≈ 0.7V

iB • RB defines the base current in steady state conditions

B

CCB R

Vi 7.0−=

Loading of BJT

• RC converts the current iC into output voltage

• The vol

RB*

VBE ≈ 0.7V

tage drop across R

VCE =

RC

+VCC iB

C decreases VC

VCC – iC.RC

iC

VCE

E

Biasing of BJT with constant VBE

• The voltage divider (R1, R2) stabilises VBE +VCC

R1 RC

iB

iC • The values of R1 and R

1) to satisfy i1 >> iB

2) to provide proper bi

VBE

R2

i1

2 are chosen:

V

R RiCCB

1 2+>>

asing V VR

R RVBE CC=

+=2

1 20 7.

Thermal stabilization with RE

• Introducing RE is an effective way of thermal

stabilization of iC

+VCC

• Increase of iC with te

drop across RE and le

respectively

VB = V

RC

VBE

R1

R2

RE

VB = const

mperature i

ads to the r

BE +iERE

VRE = RE iE

ncreases the voltage

eduction of VBE, iB and iC

= const

High gain with good temperature stability

• Capacitor CE shunts RE for AC (signal) current

• The capacitor value shoul

RE at the lowest frequency

CE >>

RC

DC

d be large enough

fL of AC signal

f RL E

12π

iC

R1

R2

RE

to sho

CE

AC

rt out

BJT gain stage Amplitude and phase relationships

∆VE

VOU

VE

VIN

∆VC

t

iC RC 2k

VOUT

VC

VB

R1 8k2

RE 1k

R2 2k

C1

VCE

VCC +10V

iE

∆VE

t

RG 100k

∆VB

t

VC = VCC - iCRC

VE = iERE ≈ +iCRE

E

C

B

C

RR

VV

−≈∆∆

; ∆ϕCB=1800

1=∆∆

B

E

VV

; ∆ϕEB=0

BJT in gain stages

I. COMMON EMITTER • High Voltage gain AV +VCC

Vin

RB Vout

RB

t

RB

RB

t

t

• High Current gain AI

II. COMM

III. COMM

Vin

Vin

RC

RE

t

RC

+VCC

Vout

t

t

+VCC

Vout

t

• Low Rin, high Rout

• Inverting: ∆ϕ = 180o

ON BASE • Voltage gain AV in high

frequency bandwidth

• No Current gain: AI = 1

• Low Rin, high Rout

• Inverting: ∆ϕ = 180o

ON COLLECTOR

• High Rin, low Rout

• No Voltage gain: AV = 1

• High Current gain AI

• Non-inverting: ∆ϕ = 0o

R

Small signal parameters of BJT stage

n

R1 R2 rπ

Rin = R1 || R2 || rπ

• For AC current the resistances a

parallel

+VCC (const)

∆Vi

r0 ∆iro

∆iR2

r

Rout = R

re connec

rπ

∆iR1

∆iB

∆Vout

∆iRc

o RC

C || ro

ted in

Temperature dependence of BJT characteristics

• The input characteristic is a strong function of

temperature

iB (µA)

VBE (V) 0.7

T1 T2 > T1

- 2mV/oC

30

20

10

• Current gain β increases with temperature

Steady state collector current iC requires

temperature stabilization

BJT equivalent circuit for small signals

VBE= 0.7 + Vincos(ωt)

IB= 10 + Iincos(ωt)

0.7 V

10 µA

~ ~Vin

rπ is a differential input resistance

B

E

B

E

Vin

⇒

BJT Input Resistance rπ

IB Operating point (bias)

VBE 0.7 V

Vin

BE

B

VI

r ∂∂

=π

1

Iin

in

in

IV

r =π

rπ

BJT equivalent circuit for small signals

VCE= 5 + Voutcos(ωt)

IC= 1 + Ioutcos(ωt)

BJT Output Resistance r0

r0 is a differential output resistance

C

E~

Vout ⇒

5 V

C

E

Vout ~

IC Operating point

VCE 5 V

1 mA

Vout

CE

C

VI

r ∂∂

=0

1

out

out

IVr =0

Iout

r0

Small signal parameters of BJT

• Current gain (empirical parameter) β ≈ 10…500 • Transconductance gm=iC/VT gm ≈ 0.1…2A/V • Input resistance rπ = β/gm= VT/iB rπ ≈ 10Ω…1kΩ • Output resistance r0 =VA/ iC r0 ≈ 1…100 kΩ

base

r0

iC=β iB iC =gm VBE

rπ

collector

emitter

VA ≈ 100…200 V

iC

VCE 0

Early voltage VA

1/ r0

Stage with Common Emitter

+VCC

Vin

RB

t

• High Volta

• High Curre

• Inverting: ∆

• Low Rin,≈

• High Rout ≈

RC

Vout

t

ge gain AV

nt gain AI

ϕ = 180o

rπ

(ro || RC)

Stage with Common Collector

• Suitable as a current buffer

+VCC

VB

Vin

• High input res

Vin = VBE +VE = iB [rπ +

• Low output re

• No Voltage ga

RB

E

Vout

Vin

RE VE

istance Rin = Vin/iB ≈ β RE

= iB rπ + (iB + iC) RE = (1+β)RE] ≈ iBβ RE

sistance Rout

in AV ≈ 1

Stage with Common Base

+VCC

RB RC

Vout

t Vin

• High bandwidth of voltage gain

• Low input resistance Rin,≈ rπ

• High output resistance Rout ≈ (ro || RC)

• Inverting: ∆ϕ = 180o

• No Current Gain: α = ∆iC / ∆iE ≤ 1

11

≈+

=β

βα

Load line and Q-point of the gain stage

VCE =VCC - iC RC

• The load line can be determined using two points:

1) VCE = VCC at iC = 0

2) iC= VCC /RC at VCE = 0

iC (mA)

0.5 5

1

2 t

tan ϕ= 1/

3

• Quiescent (or Q) point is the int

the corresponding output charac

• The slope of the load line equal

• Setting the Q-point in the middl

obtain the maximum swing of o

Q-poin

Load line

ϕ

10

RC

ersection of th

teristic

s 1/RC

e of the load li

utput signal

iB = 20 µA

VCE (V) 15

e load line with

ne allows to

Load Line

Load line iC (mA)

Q-poin

∆iB

time

0.5 5 10

1

2

3

• The load line defines the relationsh

variation of iB and the variation of V

30 µA

t

ip

B

20 µA

time

b

E

10 µA

VCE (V) ∆VCE

15

etween the

Optimization of the Q-point

iC (mA)

VCE (V)

Optimum Q

Q1

t

Q2

∆VCE

t

t

0.5 5 10 15

1

2

3

• The maximum undistorted swing of the output voltage

depends on the position of Q-point

1) Optimum Q 2) Q1 or Q2

Operating point of a BJT stage +VCC

CCB RRRVV =+

=21

2

Ci

CEV = • The desirable oper

RC

RE

VBE

R1

R2

VB = const

BE iV +

E

B

RV −

≈

CCC iV −

ating po

VRE = RE iE

ECEE RiR +≈ 7.0

7.0

][ CE RR +

int is VCE ≈ VCC/2

Load line and Q-point for AC signal

• If capacitor CE is in parallel to RE, the AC load line is

CCCE RiVV −= *

iC (mA)

VCE (V)

iCQ

0.5 5 10 15

V* VCC

max Vout

1

2

3

1/(RC+RE)

Q-point

AC Load line

DC Load line

1/RC

• Q-point is the same for DC and AC load lines

• , iECQCC RiVV −=*CQ

- the current corresponding to Q-point

Properties of BJT at High Frequencies

• At high frequencies the gain is mainly limited by the

diffusion time τD of minor carriers through the base

β dB static gain 103 30

102 20 10 10 1

fT

slope 10 dB/dec

0.1 1 10 100 f (GHz)

• Cut–off frequency fT corresponds to unity gain β =1

f TD

=1

2πτ

• Gain-bandwidth product β .∆f =fT allows to estimate

the number of stages to obtain the required gain in the

specified bandwidth