Course Roadmap Rectification Bipolar Junction Transistor• Course Roadmap • Rectification • Bipolar Junction Transistor 6.101 Spring 2020 Lecture 3 1 Acnowledgements: Neamen,

• Course Roadmap• Rectification• Bipolar Junction Transistor

6.101 Spring 2020 Lecture 3 1

Acnowledgements:Neamen, Donald: Microelectronics Circuit Analysis and Design, 3rd EditionThe Art Of Electronics by Horowitz and Hill

6.101 Course Roadmap

• Passive components: RLC – with RF• Diodes• Transistors: BJT, MOSFET, antennas• Op‐amps, 555 timer, ECG• Switch Mode Power Supplies• Fiber optics, PPG• Applications



Time Domain Analysis

])cos()[cos(2

cos

cos*)cos(

ttKAtAv

ttKAAv

mcmcm

cc

cmmc

Fourier Series ‐ Ramp


function [ t, sum ] = ramp(number)%generate a ramp based on fixed number of terms%t = 0:.1:pi*4; % display two full cycles with 0.1 spacing

sum = 0for n=1:number

sum = sum + sin(n*t)*(-1)^(n+1)/(n*pi);end

plot(t, sum)shg

end

Rectifier Circuits

6.101 Spring 2020 5

C F R L

1N4001

3a) Half-wave rectifier circuit diagram

120 V 60 Hz

+

v OUT

-

Pri Sec

12.6 VCT RMS

C F R L

3b) Full-wave rectifier circuit diagram

1N4001

+

v OUT

-

Pri Sec

12.6 VCT RMS

1N4001

120 V 60 Hz

R L

3c) Bridge rectifier circuit diagram

CF

+

v OUT

-

Pri Sec

12.6 VCT RMS120 V 60 Hz

4x 1N4001

+

+

+

Vout =

Vout =

Vout =

RC >> 16.6ms why?

Lecture 3

CT: center tap

Full Wave Bridge vs Center Tapped


Center tapped advantages:

• Lower diode voltage drop (high efficiency)

• Secondary windings carries ½ average current (thinner windings, easier to wind)

• Used in computer power supplies

Physical Wiring Matters


Power Supply Ripple Voltage Calculation

6.101 Spring 2020 8Lecture 3

D2 conduction angle in degrees

5 V Adapters


300 ma

1000 ma500 ma

Diode AC Resistance


Log Amplifier


-

+

+15

LF356

2

34

76

vin

vout+

_ -15

1.5k

1N914

0.1F

0.1F

ID

IR

bypass caps0.1uf caps (2)

ID IS (e

qVDkT

1) ISe

qVDkT

IR = - ID

Vout = - VD

6.101 Spring 2020 12

Bipolar Junction Transistors

• BJT can operate in a linear mode (amplifier) or can operate as a digital switch.

• Current controlled device• Two families: npn and pnp.• BJT’s are current controlled

devices• NPN – 2N2222• PNP – 2N2907• VCE ~30V, 500 mw power

NPN

PNP

base

emitter

collector

ib

ic = βib

ib + ic

Lecture 3

Why BJT’s ?

• Preferred device for demanding analog application, both integrated and discrete (lower noise)

• Great for high frequency applications; characteristics well understood.

• High reliability makes it a key device in automotive applications.

• Lower output resistance at emitter vs source• Larger gm compared to FET



BJT Symbols


2N22222N3904

12 3

2N3906P2N2222 pinout reversed

Packaging


TO-3TO-220

TO-18

BJT Current Relationship


NPN

base

emitter

collector

ic = βib

ib + ic

1

)1(

EC

BE

BC

BCE

iiii

iiiii

hFE = β = large signal (DC)gain at fixed current

hFE < hfe


max voltage

max continuous current

max power at 25o C


hFE = f(Ic) peaksat ~ 0.5-10ma

β

hFE @1.0ma < hfe @1.0ma


hFE & Current & Temperature Characteristics

NPN Common Emitter V‐I Relationship


β = ?

(James) Early Voltage


A large VA is desirable for high voltage gains ~ 30-50v.

VA is determined by transistor design and varies with base width, base and collector doping concentration.

Early effect: the rise of Ic due to base-width modulation.

Tek 575 Curve Tracer


• Vertical axis: current• Horizontal axis: voltage• Voltage sweep: positive

and negative with resistor current limit 0‐20v; 0‐200v!

• Input: fixed current steps (0.001‐200ma); 240 steps

• Tests: diodes, BJT, MOSFETs• Calibrate zero current step

Mcube


• Tests: – Diodes (forward

drop)– BJT (type, beta)– MOSFET (type,

VTH and more)

• Auto terminal identification

RLC – BJT MOSFET Testor


BJT Configurations

Voltage Gain

Current Gain

Power Gain

Common Emitter X X X

Common Collector X X

Common Base X X


Common emitter: hgh input impedance, for general amplification of voltage, current and power from low power, high impedance sources.

Common collector: aka "emitter follower" for high input impedance and current gain without voltage gain, as in an amplifier output stage.

Common base: low input impedance for low impedance sources, for high frequency response. Grounding the base short circuits the Miller capacitance from collector to base and makes possible much higher frequency response.

Circuit analysis by inspection


General Configuration


CommonEmitter

CommonCollector

CommonBase

Transistor Configurations


+15V

+

Vin

-

+

VOUT

-

RL

R1

+

+

R2

[a] Common Emitter Amplifier [b] Common Collector [Emitter Follower] Amplifier

RE RE

+15V

+Vin

-

+

VOUT

-

RL

R1

+

+

R2

+

[c] Common Base Amplifier

TRANSISTOR AMPLIFIER CONFIGURATIONS

R2

+15V

R 1

+

Vin

-

+VOUT

-

RE

+

+

Common Emitter Operation – Quiescent Point


Load Line – Operating Point


+20 V

910R2

2N3904

91 BFCR1

+

vout

-

ICQ • Find Vout open circuit voltage: 20V• Find ICQ max = 20/(910 +91) = ~20ma• Draw load line.

• For RE = 0, just choose Q at ½ VCC for maximum swing.

• For RE > 0, set Q at ½ [VCC – VRE]. • For ICQ = 10 mA, VRL = 9.1V, VRE = 0.91V,

VCE = 10V. For ICQ = 10.5mA, VRL = 9.6V, VRE = 0.96V, VCE = 9.5V

Transistor Bias Instability


I R V I R VI R V I R VI R R V V

IV VR R

IV V

R R

B B C E CC

B B F B E CC

B B F E CC

BCC

B F E

CF CC

B F E

0 70 7

0 7

0 71

0 72

.

..

.

.

RB

+15V

2N3904

IC = 4 mA

RE = 2200

IB

IE = 4 mA

CEBFE

BFCF

IIIIII

,1,100

R RV V

I

R V VmA

R k

R k kR k

B F EF CC

C

B

B

B

B

0 7

100 2200 100 15 0 74

220 14304

10

220 358138

3

.

.

8.8V

Variation of Collector Current with βOne Resistor


RB

+15V

2N3904

IC = 4 mA

RE = 2200

IB

IE = 4 mA

IC F2.9 mA 50

4.0 mA 100

5.0 mA 200

5.4 mA 300

IC=2.5 mA

Variation of Collector Current with Beta

IC F VCC 0.7V

RB F RE

2

Two Resistor Biasing


R2

RE =2200

+15V

R 1

2N3904

IC = 4 mA

IC = 4 mA

VTH= VB

RTH= RB

RE = 2200

2N3904

IC = 4 mA

VB

IB

+15V

RB

[a][b]

[c]

VB R1

R1 R2

Vcc 3 RB R1 / /R2 R1R2

R1 R2

4

Thevenin Circuit




R2

RE =2200

+15V

R 1

2N3904

IC = 4 mA

IC = 4 mA

VTH= VB

RTH= RB

RE = 2200

2N3904

IC = 4 mA

VB

IB

+15V

RB

[a][b]

[c]

V I R V I RV I R V I RV V I R I R I R R

IV VR R

IV V

R R

B B B C E

B B B F B E

B B B F B E B B F E

BB

B F E

CF B

B F E

0 7 00 7

0 7

0 75

0 76

..

.

.

.

VVV

VkmAVVkkmA

B

B

B

B

4.1010070968

7010024247.0100220224

Assume RB = 22kΩ,

βRE = 220kΩ and ignore RB



V RR R

V

R R R VV

R VV

R

R R RR R

B CC

CC

B

1

1 2

1 2 1 1 1

1 2 1

1 2

1510 4

145

1450 45

..

..

Given VB= 10.4 V and RB= 22kΩ, we can now solve equations (3) and (4) for R1 and R2.

R RR R

R k

R RR R

k

RR

k

R kR k use kR R k k use k

B1 2

1 2

1 1

1 1

12

1

1

1

2 1

22

0 450 45

22

0 45145

22

0 310 2270 9 680 45 0 45 70 9 319 33

.

.

.

..

.. . . .

Variation of Collector Current with βTwo Resistor Biasing


IC IC F

3.7 mA 2.9 mA 50

4.0 mA 4.0 mA 100

4.2 mA 5.0 mA 200

4.3 mA 5.4 mA 300

IC=0.6 mA IC=2.5 mA

Variation of Collector Current with Beta 67.0

EFB

BFC RR

VVI

I VkCF

F

10 4 0 722 2200

. .

Two Resistor One Resistor

Base Current – Resistor Divider


68K

33K

IC F

3.7 mA 50

4.0 mA 100

4.2 mA 200

4.3 mA 300

IC=0.6 mAib

Make small compared to the current through R2

ib

See handout: Transistor bias stability

Common Collector – Emitter Follower Biasing

• Β = 100, iB = 7.5ma/100 =‐ 75µa• Using Thevenin equivalent,

RB = R1||R2, VB =


+15V

R 1

2N3904

7.5 mA

1.0 k7.5 mA

R2

A

B

7.5 V

2N3904

7.5 mA

+15V

VB

RB

IB

21

115RR

R

VB = IBRB + 0.6V + 7.5VVB = [75 µA x 10k] + 0.6V + 7.5VVB = 750 mV + 0.6V + 7.5VVB = 8.9V

[15 R1] ÷ [R1 + R2] = 8.9V15 R1 = 8.9 x [R1 + R2][15−8.9] R1 = 8.9 R2R1 = 1.44 R2[R1 x R2] ÷ [R1 + R2] = 10 kΩ

[1.44R2 x R2] ÷ [1.44 R2 + R2] = 10kΩR2 = 16.9 kΩ (use 16 kΩ)R1 = 1.44 R2 = 24.4 kΩ (use 24 kΩ)

Common Collector – Emitter Follower Biasing

• With R1 = 24kΩ, R2 = 16 kΩ, the current through the voltage divider is 15 ÷ [40 kΩ] = 375 µA.

• The 75 µA base current is 20% of 375 µA.

• With R1 = 2 kΩ, will need a divider current that is ~ 4.1 mA. (75 µA is only ~2% of 4.1 mA, which is negligible)

• The voltage drop across R2 will be [15 V – 8.1 V] = 6.9 V; R2 = 1.7 kΩ

• But input impedance will be low = ~890Ω

• Use bootstrapping configuration


= 24.4 kΩ (use 24 kΩ)

+15V

R 1

2N3904

7.5 mA

8.1 V

1.0 k7.5 mA

R2

A

B

IDivider

Bootstrapping – Higher Input Impedance


Horowitz and Hill Figure 2.80

The base is connected to the emitter through with R3 and C2 . At signal frequency, C2 is a short so both ends of R3 are at the same voltage – so no current flows. Therefore R1 and R2 cannot load the input. So R3 appears to be very high.

In real life, there is a small AC voltage across R3. The AC current through R3 is 0.006 ÷ 4.7kΩ = 1.1 µA.

Result: “stiff” biasing with high input resistance at signal frequency.


“Our treatment of bipolar transistors is going to be quite different from that of many other books. It is a common practice to use the h-parameter (hybrid pi) model and equivalent circuit. In our opinion that is unnecessarily complicated and unintuitive. . . you also have the tendency to lose sight of which parameters of transistors behavior you can count on and more important, which ones can vary over large ranges.”

The Art of Electronics, Horowitz & Hill 3rd edition page 71

Commom Emitter – Hybrid π


RB

+15V

2N3904

ICRL

C +

vout

_

IB

+

TRANSISTOR AMPLIFIER CONFIGURATIONS WITH HYBRID- EQUIVALENT CIRCUITS

Rs

+vin

_

Rs

r

RL

ib

+

vout

_

c

e

b

+vin

_

RB

COMMON EMITTER AMPLIFER

0 g m r

gm ICQ

VTH

r0 VA

ICQ

Early Voltage

inv1

Lm

m

o

Lov

Lo

b

Lbo

in

outv

Rg

g

RAthen

rR

riRi

vvA

1

1

Common Emitter with Emitter Degeneration


• Input resistance (β+1)RE

• Voltage gain reduced by (1+gm RE)• Voltage gain less dependent on β

(linearity)

ELvEo

Eo

Lo

Eob

Lbo

in

outv

RRAthenRrif

RrR

RriRi

vvA

/;1

;111

1

outv1

inv1

Common Collector (Emitter Follower)


1;1

;1'

11'

11

1

vEo

Eos

Eo

Eosb

Ebo

in

outv

AthenRrif

RrRR

RrRiRi

vvA

• Buffer with unity gain• High input resistance driving low

output resistance (current gain).

mvVVI

g

rg

THTH

CQm

m

26

0

outv1inv1

Low Frequency Hybrid‐ Equation Chart


High gain, better high frequency responseLow input resistance

Unity gain, low output resistanceHigh input resist.

High gain applicationsModerate input resistance

High output resistance

Hybrid‐π Parameters


g mq

kT

IC

0 hfe (datasheet)C Cob (datasheet)

g m

2 (C C ) fT (transit frequency datasheet)

C g m

2 fTrC

rx (low frequency) : datasheet or estimate 50100(high frequency) : estimate 25

Miller Effect* – Common Emitter


)](1[ LCmM RRgCC

* Agarwal & Lang Foundations of Analog & Digital Electronics Circuits p 861

hfe and High Frequency Limits


Small signal current gain versus frequency, hfe, of a BJT biased in a common emitter configuration:

For hfe = 1 = fT, (transit frequency )

For 2N3904*, IC =1ma, VCE=10V , cπ=25pF, cμ=2pF

CrjCrjrg

ivghCjv

rvi m

b

bemfebe

beb

11

hT gm

2 ftCwhere C (c c )

kHzpFKcRgr

fRgofgainafor

MHzpF

mhof

LmhLm

T

3202)100(5.22

12

1100

240272

04.0

*Lundberg, Kent: Become One with the Transistor p29

Miller effect reduces high frequency limit!

Documents

Course Roadmap Rectification Bipolar Junction Transistor• Course Roadmap • Rectification • Bipolar Junction Transistor 6.101 Spring 2020 Lecture 3 1 Acnowledgements: Neamen,