• Course Roadmap• Rectification• Bipolar Junction Transistor

6.101 Spring 2017 Lecture 3 1

Acnowledgements:Neamen, Donald: Microelectronics Circuit Analysis and Design, 3rd Edition

6.101 Spring 2017 Lecture 3 2

Time Domain Analysis

])cos()[cos(2

cos

cos*)cos(

ttKAtAv

ttKAAv

mcmcm

cc

cmmc

Fourier Series ‐ Ramp

6.101 Spring 2017 Lecture 3 3

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

6.101 Course Roadmap

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

6.101 Spring 2017 Lecture 3 4

Rectifier Circuits

6.101 Spring 2017 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 tapPower Supply Ripple Voltage Calculation

6.101 Spring 2017 6Lecture 3

D2 conduction angle in degrees

5 V Adapters

6.101 Spring 2017 Lecture 3 7

300 ma

1000 ma500 ma

Diode AC Resistance

6.101 Spring 2017 8Lecture 3

Log Amplifier

6.101 Spring 2017 Lecture 3 9

-

+

+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 2017 10

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

6.101 Spring 2017 Lecture 3 11 6.101 Spring 2017 12Lecture 3

BJT Symbols

6.101 Spring 2017 Lecture 3 13

2N22222N3904

12 3

2N3906P2N2222 pinout reversed

Packaging

6.101 Spring 2017 Lecture 3 14

TO-3TO-220

TO-18

BJT Current Relationship

6.101 Spring 2017 Lecture 3 15

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

6.101 Spring 2017 Lecture 3 16

max voltage

max continuous current

max power at 25o C

6.101 Spring 2017 Lecture 3 17

hFE = f(Ic) peaksat ~5-10ma

β

hFE @1.0ma < hfe @1.0ma

6.101 Spring 2017 Lecture 3 18

hFE & Current & Temperature Characteristics

NPN Common Emitter V‐I Relationship

6.101 Spring 2017 Lecture 3 19

β = ?

(James) Early Voltage

6.101 Spring 2017 Lecture 3 20

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

VAis 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

6.101 Spring 2017 Lecture 3 21

• 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

6.101 Spring 2017 Lecture 3 22

• Tests: – Diodes (forward

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

VTH and more)

• Auto terminal identification

RLC – BJT MOSFET Testor

6.101 Spring 2017 Lecture 3 23

BJT Configurations

Voltage Gain

Current Gain

Power Gain

Common Emitter X X X

Common Collector X X

Common Base X X

6.101 Spring 2017 Lecture 3 24

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.

General Configuration

6.101 Spring 2017 Lecture 3 25

CommonEmitter

CommonCollector

CommonBase

Transistor Configurations

6.101 Spring 2017 Lecture 3 26

+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

6.101 Spring 2017 Lecture 3 27

Load Line – Operating Point

6.101 Spring 2017 Lecture 3 28

+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

6.101 Spring 2017 Lecture 3 29

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

6.101 Spring 2017 Lecture 3 30

RB

+15V

2N3904

IC = 4 mA

RE = 2200

IB

IE = 4 mA

IC F

2.9 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

6.101 Spring 2017 Lecture 3 31

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

Two Resistor Biasing

6.101 Spring 2017 Lecture 3 32

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

Two Resistor Biasing

6.101 Spring 2017 Lecture 3 33

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= 22kW, 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

6.101 Spring 2017 Lecture 3 34

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

6.101 Spring 2017 Lecture 3 35

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

6.117 2104 IAP Lecture 3 36

BJT Switching Models

+15v +15v

input signalinput

signal

off state on state

Forced beta reduces Vce satStored charges in base emitter junction slows turn off.

Common Collector – Emitter Follower Biasing

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

RB = R1||R2, VB =

6.101 Spring 2017 Lecture 3 37

+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

6.101 Spring 2017 Lecture 3 38

= 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

6.101 Spring 2017 Lecture 3 39

Horowitz and Hill Figure 2.65

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.

6.101 Spring 2017 Lecture 3 40

“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

6.101 Spring 2017 Lecture 3 41

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

6.101 Spring 2017 Lecture 3 42

• 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)

6.101 Spring 2017 Lecture 3 43

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

6.101 Spring 2017 Lecture 3 44

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

6.101 Spring 2017 Lecture 3 45

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

6.101 Spring 2017 Lecture 3 46

)](1[ LCmM RRgCC

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

hfe and High Frequency Limits

6.101 Spring 2017 Lecture 3 47

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!