• Course Roadmap • Rectification • Bipolar Junction Transistor

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

6.101 Spring 2020 Lecture 3 1 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

6.101 Spring 2020 Lecture 3 2 Time Domain Analysis 

 v  (Ac  KAm cosmt)*cosct KA  v  A cos t  m [cos(  )t  cos(  )t] c c 2 c m c m

6.101 Spring 2020 Lecture 3 3 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 = 0 for n=1:number sum = sum + sin(n*t)*(-1)^(n+1)/(n*pi); end

plot(t, sum) shg

end

6.101 Spring 2020 Lecture 3 4 CT: center tap Rectifier Circuits

+ 1N4001 12.6 VCT RMS + V = 120 V 60 Hz C F R L v OUT out

-

Pri Sec

3a) Half-wave rectifier circuit diagram 1N4001

+

12.6 VCT RMS 120 V 60 Hz C R F + L v OUT Vout = -

Pri Sec 1N4001 3b) Full-wave rectifier circuit diagram

4x 1N4001 +

12.6 VCT RMS 120 V 60 Hz CF R L v OUT Vout = + -

Pri Sec

3c) Bridge rectifier circuit diagram RC >> 16.6ms why?

6.101 Spring 2020 Lecture 3 5 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

6.101 Spring 2020 Lecture 3 6 Physical Wiring Matters

6.101 Spring 2020 Lecture 3 7 Power Supply Ripple Voltage Calculation

D2 conduction angle in degrees

6.101 Spring 2020 Lecture 3 8 5 V Adapters

500 ma 1000 ma

300 ma

6.101 Spring 2020 Lecture 3 9 Diode AC Resistance

6.101 Spring 2020 Lecture 3 10 Log Amplifier

bypass caps 0.1uf caps (2)

ID IR = - ID 1N914 IR Vout = - VD

0.1 F 1.5k  +15 2 - 7 LF356 6 qV  qV  vout  D   D  4  kT   kT  + I  I (e 1)  I e v 3 + D S S _ in 0.1F -15

6.101 Spring 2020 Lecture 3 11 Bipolar Junction Transistors

NPN collector • BJT can operate in a linear

ic = βib mode (amplifier) or can

ib operate as a digital switch. • Current controlled device

base • Two families: npn and pnp. i + i b c • BJT’s are current controlled emitter devices • NPN – 2N2222 • PNP – 2N2907

• VCE ~30V, 500 mw power PNP

6.101 Spring 2020 Lecture 3 12 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 2020 Lecture 3 13 6.101 Spring 2020 Lecture 3 14 BJT Symbols

2N2222 2N3904 2N3906 1 P2N2222 pinout reversed 2 3

6.101 Spring 2020 Lecture 3 15 Packaging

TO-18

TO-220 TO-3

6.101 Spring 2020 Lecture 3 16 BJT Current Relationship

NPN collector iE  iC  iB ic = βib  iC  iB  iE  ( 1)iB base ib + ic  iC  iE emitter    hFE = β = large signal (DC) gain at fixed current 1

hFE < hfe

6.101 Spring 2020 Lecture 3 17 max voltage

max continuous current

max power at 25o C

6.101 Spring 2020 Lecture 3 18 hFE = f(Ic) peaks at ~ 0.5-10ma β

hFE @1.0ma < hfe @1.0ma

6.101 Spring 2020 Lecture 3 19 hFE & Current & Temperature Characteristics

6.101 Spring 2020 Lecture 3 20 NPN Common Emitter V‐I Relationship

β= ?

6.101 Spring 2020 Lecture 3 21 (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.

6.101 Spring 2020 Lecture 3 22 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

6.101 Spring 2020 Lecture 3 23 Mcube

• Tests: – Diodes (forward drop) – BJT (type, beta) – MOSFET (type,

VTH and more)

• Auto terminal identification

6.101 Spring 2020 Lecture 3 24 RLC – BJT MOSFET Testor

6.101 Spring 2020 Lecture 3 25 BJT Configurations

Voltage Current Power Gain Gain 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.

6.101 Spring 2020 Lecture 3 26 Circuit analysis by inspection

6.101 Spring 2020 Lecture 3 27 General Configuration

Common Emitter

Common Common Base Collector

6.101 Spring 2020 Lecture 3 28 Transistor Configurations

TRANSISTOR AMPLIFIER CONFIGURATIONS

+15V +15V +15V

RL RL

R2 R2 R2

+ +

+ + + + + + + + + +

R + 1 VOUT VOUT V Vin R 1 RE V V in R OUT in R1 E RE ------

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

6.101 Spring 2020 Lecture 3 29 Common Emitter Operation – Quiescent Point

6.101 Spring 2020 Lecture 3 30 Load Line – Operating Point

+20 V

910 I R CQ 2 • Find Vout open circuit voltage: 20V

+ • Find I max = 20/(910 +91) = ~20ma 2N3904 CQ • Draw load line. vout

R 1 91 BFC -

• 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

6.101 Spring 2020 Lecture 3 31 Transistor Bias Instability

+15V IRBB 07. V IR CE V CC IRBB07. V FBE IR  V CC  IRBB  FE R V CC07. V

IC = 4 mA RB VVCC  07.  IB  1 RRBFE  2N3904 8.8V  FCCVV 07.  IB IC  2 RRBFE  I = 4 mA RE = 2200  E  FCCVV 07.  RRBFE IC 100 15VV 0. 7  R 100 2200  B 4mA  100, I   I 1430 F C F B Rk220 103 B 4 I E   F 1 I B , I E  IC RkB 220 358 k RkB  138 

6.101 Spring 2020 Lecture 3 32 Variation of Collector Current with β One Resistor

+15V F VCC  0.7V  IC  2 RB  F RE

IC = 4 mA RB

Variation of Collector Current with Beta 2N3904

IC F IB 2.9 mA 50 R = 2200  IE = 4 mA E 4.0 mA 100 5.0 mA 200 5.4 mA 300

IC=2.5 mA

6.101 Spring 2020 Lecture 3 33 Two Resistor Biasing

+15V +15V

IC = 4 mA IC = 4 mA R2

2N3904 IB 2N3904 RTH= RB

RB R = E V = V R 1 2200 TH B R = 2200 IC = 4 mA E VB

[b] [a] [c]

R1 R1R2 VB  Vcc 3 RB  R1 //R2  4 R1  R2 R1  R2

6.101 Spring 2020 Lecture 3 34 Thevenin Circuit

6.101 Spring 2020 Lecture 3 35 Two Resistor Biasing

VIRVIRBBB  07.  CE 0 +15V +15V VIRVBBB07.  FBE IR

VVIRIRIRRBBBFBEBBFE07.     IC = 4 mA IC = 4 mA R2

2N3904 IB 2N3904 RTH= RB R VVB  07.  B IB   5 R = E V = V RR R 1 2200 TH B R = 2200 BFE IC = 4 mA E VB

[b] [a] [c]  FBVV 07.  IC  6 RRBFE 

Assume RB = 22kΩ, 4mA22k  220k100VB  0.7V 

4mA 242k 100VB  70 βRE = 220kΩ and ignore RB 968  70 100VB

VB 10.4V

6.101 Spring 2020 Lecture 3 36 Two Resistor Biasing

RR12 RkB 22  Given VB= 10.4 V and RR12 R = 22kΩ, we can now RR 045. B 11 22k solve equations (3) and RR11 045. (4) for R1 and R2. 045. R2 1  22k 145. R1

0310. Rk1  22  Rkusek1  709.  68

RR210.... 45 0 45 70 9 k 319 kusek 33  R1 VBCC V RR12

VCC   15V  RR121 R   R 1   145. R 1  VB  10. 4V 

RR12145. R 1

045. RR12

6.101 Spring 2020 Lecture 3 37 Variation of Collector Current with β Two Resistor Biasing

 V  0.7V Variation of Collector Current with Beta I  F B 6 C R   R B F E Two Resistor One Resistor

IC IC F

 F 10.. 4 0 7V  3.7 mA 2.9 mA 50 IC  22k  F 2200 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

6.101 Spring 2020 Lecture 3 38 Base Current – Resistor Divider

IC F 3.7 mA 50 4.0 mA 100 68K 4.2 mA 200 4.3 mA 300 ib

IC=0.6 mA

33K Make i b small compared to the

current through R2

See handout: Transistor bias stability

6.101 Spring 2020 Lecture 3 39 Common Collector – Emitter Follower Biasing

+15V • Β = 100, iB = 7.5ma/100 =‐ 75µa 7.5 mA • Using Thevenin equivalent, R2  R  A 15 1  2N3904 RB = R1||R2, VB =    R1  R2 

R 1.0 k  1 7.5 mA VB = IBRB + 0.6V + 7.5V B VB = [75 µA x 10k] + 0.6V + 7.5V VB = 750 mV + 0.6V + 7.5V +15V VB = 8.9V

7.5 mA [15 R1] ÷ [R1 + R2] = 8.9V 15 R1 = 8.9 x [R1 + R2] 2N3904 [15−8.9] R = 8.9 R IB 1 2 RB R1 = 1.44 R2 7.5 V [R1 x R2] ÷ [R1 + R2] = 10 kΩ VB

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

6.101 Spring 2020 Lecture 3 40 Common Collector – Emitter Follower Biasing

• With R1 = 24kΩ, R2 = 16 kΩ, the +15V current through the voltage divider is 15 ÷ [40 kΩ] = 375 µA. 7.5 mA • The 75 µA base current is 20% of 375 R 2 IDivider µA.

A 8.1 V 2N3904 • 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 R 1.0 k 1 7.5 mA negligible)

B • 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)

6.101 Spring 2020 Lecture 3 41 Bootstrapping – Higher Input Impedance

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. Horowitz and Hill Figure 2.80

6.101 Spring 2020 Lecture 3 42 “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

6.101 Spring 2020 Lecture 3 43 Commom Emitter – Hybrid π

TRANSISTOR AMPLIFIER CONFIGURATIONS WITH HYBRID- EQUIVALENT CIRCUITS

COMMON EMITTER AMPLIFER

+15V  0  g m r

RL I IC CQ RB gm  C + 2N3904 + VTH Early Voltage I R B s v out VA + r  vin 0 _ _ ICQ

1 v in 1  v out  oib RL  o RL b c  Av  1   + v in ib r  r r  i   b  R  o RL s vout RB RL then Av   gm RL + o vin e _ _ gm

6.101 Spring 2020 Lecture 3 44 Common Emitter with Emitter Degeneration

1 v out  oib RL  o RL Av  1    ; v in ib r  o 1 RE r  o 1 RE    if r  o 1 RE ; thenAv  RL / RE 

1 • Input resistance (β+1)RE v out • Voltage gain reduced by (1+gm RE) 1 v in • Voltage gain less dependent on β (linearity)

6.101 Spring 2020 Lecture 3 45 Common Collector (Emitter Follower)

 0g mr

ICQ gm  VTH  26mv VTH

 1 v out  1i R o 1 RE A   o b E  ; v 1   v in ib R's r  o 1 RE R's r  o 1 RE



if r  o 1 RE ; then Av  1  

• Buffer with unity gain

1 • High input resistance driving low v in 1 v out output resistance (current gain).

6.101 Spring 2020 Lecture 3 46 Low Frequency Hybrid‐ Equation Chart

High gain applications Unity gain, low High gain, better high Moderate input resistance output resistance frequency response High output resistance High input resist. Low input resistance

6.101 Spring 2020 Lecture 3 47 Hybrid‐π Parameters

 q  g    I m  kT  C

0  hfe (datasheet)

C  Cob (datasheet)

g m  fT (transit frequency datasheet) 2(C C )

g m C  C 2 fT r

rx (low frequency):datasheet or estimate 50 100 (high frequency):estimate  25

6.101 Spring 2020 Lecture 3 48 Miller Effect* – Common Emitter

CM  C [1 gm (RC RL )]

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

6.101 Spring 2020 Lecture 3 49 hfe and High Frequency Limits 

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

vbe gmvbe gmr   ib   vbe j C hfe    r ib 1 jr C 1 jr C

g For h = 1 = f (transit frequency ) m fe T, hT  where C  (c  c )  2 ftC

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

0.04mho f   240MHz T 2 27 pF  1 1 for a gain of gm RL 100 fh     320kHz 2 r gm RLc 2 2.5K(100)2 pF Miller effect reduces high frequency limit!

*Lundberg, Kent: Become One with the Transistor p29

6.101 Spring 2020 Lecture 3 50