6.101 Course Roadmap Time Domain Analysis

6.101 Course Roadmap

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

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 Spring 2020 Lecture 3 2

Time Domain Analysis Fourier Series ‐ Ramp 

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

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 3 6.101 Spring 2020 Lecture 3 4 CT: center tap Rectifier Circuits Full Wave Bridge vs Center Tapped

+ 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 Center tapped advantages: 1N4001 3b) Full-wave rectifier circuit diagram • Lower diode voltage drop (high efficiency)

4x 1N4001 + • Secondary windings carries ½ average

12.6 VCT RMS 120 V 60 Hz CF R L v OUT Vout = current (thinner windings, easier to wind) + - Pri Sec • Used in computer power supplies 3c) Bridge rectifier circuit diagram RC >> 16.6ms why?

6.101 Spring 2020 Lecture 3 5 6.101 Spring 2020 Lecture 3 6

Power Supply Ripple Voltage Calculation Physical Wiring Matters

D2 conduction angle in degrees

6.101 Spring 2020 Lecture 3 7 6.101 Spring 2020 Lecture 3 8 5 V Adapters Diode AC Resistance

500 ma 1000 ma

300 ma

6.101 Spring 2020 Lecture 3 9 6.101 Spring 2020 Lecture 3 10

Log Amplifier Bipolar Junction Transistors

bypass caps 0.1uf caps (2) NPN collector • BJT can operate in a linear

ic = βib mode (amplifier) or can ID i IR = - ID b operate as a digital switch. 1N914 • IR Current controlled device Vout = - VD base • Two families: npn and pnp. 0.1 F 1.5k  +15 i + i 2 b c • BJT’s are current controlled - 7 LF356 6 qV  qV  vout  D   D  emitter devices 4  kT   kT  + I  I (e 1)  I e v 3 + D S S • _ in 0.1F -15 NPN – 2N2222 • PNP – 2N2907

• VCE ~30V, 500 mw power PNP

6.101 Spring 2020 Lecture 3 11 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 Packaging

TO-18

TO-220 TO-3

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

6.101 Spring 2020 Lecture 3 15 6.101 Spring 2020 Lecture 3 16 BJT Current Relationship

max voltage NPN collector iE  iC  iB ic = βib  iC  iB max continuous  current iE  ( 1)iB base max power at 25o C ib + ic  iC  iE emitter    hFE = β = large signal (DC) gain at fixed current 1

hFE < hfe

6.101 Spring 2020 Lecture 3 17 6.101 Spring 2020 Lecture 3 18

hFE & Current & Temperature hFE = f(Ic) peaks at ~ 0.5-10ma Characteristics β

hFE @1.0ma < hfe @1.0ma

6.101 Spring 2020 Lecture 3 19 6.101 Spring 2020 Lecture 3 20 NPN Common Emitter V‐I Relationship (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- β = ? width modulation.

6.101 Spring 2020 Lecture 3 21 6.101 Spring 2020 Lecture 3 22

Tek 575 Curve Tracer Mcube

• Vertical axis: current • Tests: • Horizontal axis: voltage – Diodes (forward • Voltage sweep: positive drop) and negative with resistor – BJT (type, beta) current limit 0‐20v; 0‐200v! – MOSFET (type, VTH and more) • Input: fixed current steps (0.001‐200ma); 240 steps • Auto terminal • Tests: diodes, BJT, MOSFETs identification • Calibrate zero current step

6.101 Spring 2020 Lecture 3 23 6.101 Spring 2020 Lecture 3 24 RLC –BJT MOSFET Testor 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 25 6.101 Spring 2020 Lecture 3 26

General Configuration Transistor Configurations

TRANSISTOR AMPLIFIER CONFIGURATIONS Common

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

6.101 Spring 2020 Lecture 3 27 6.101 Spring 2020 Lecture 3 28 Common Emitter Operation –Quiescent Point 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 29 6.101 Spring 2020 Lecture 3 30

Variation of Collector Current with β Transistor Bias Instability One Resistor

+15V IR07. V IR  V BB CE CC +15V IRBB07. V FBE IR  V CC  F VCC  0.7V IRBB  FE R V CC07. V IC  2 IC = 4 mA RB RB  F RE VVCC  07.  I  1 IC = 4 mA B RB RRBFE  2N3904 8.8V VV 07.  Variation of Collector Current with Beta FCC 2N3904 IB IC  2 RRBFE  IC F IB R = 2200  IE = 4 mA E 2.9 mA 50  VV 07.  FCC R = 2200  IE = 4 mA RRBFE E 4.0 mA 100 IC 100 15VV 0. 7  5.0 mA 200 R 100 2200  B 4mA 5.4 mA 300  F 100, IC   F I B 1430 3 Rk220 10 IC=2.5 mA B 4 I E   F 1 I B , I E  IC RkB 220 358 k RkB  138 

6.101 Spring 2020 Lecture 3 31 6.101 Spring 2020 Lecture 3 32 Two Resistor Biasing Two Resistor Biasing

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

VVIRIRIRRBBBFBEBBFE07.     IC = 4 mA I = 4 mA IC = 4 mA R C I = 4 mA 2 R C 2N3904 2 IB 2N3904 R = R TH B VV 07. I 2N3904 R  B  B B IB   5 2N3904 R = R = R E RR TH B R 2200 VTH= VB BFE 1 I = 4 mA RE = 2200 C V RB B [b]  R = [a] [c] E V = V VV 07. R 2200 TH B R = 2200 FB  1 I = 4 mA E I  6 C V C B RRBFE  [b] [a] [c]

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

4mA 242k 100VB  70 R1 R1R2 βRE = 220kΩ and ignore RB VB  Vcc 3 RB  R1 //R2  4 968  70 100VB R1  R2 R1  R2 VB 10.4V

6.101 Spring 2020 Lecture 3 33 6.101 Spring 2020 Lecture 3 34

Two Resistor Biasing Variation of Collector Current with β Two Resistor Biasing RR12 RkB 22  Given VB= 10.4 V and RR12 R = 22kΩ, we can now RR 045. B 11 22k Variation of Collector Current with Beta solve equations (3) and RR11 045.  F VB  0.7V IC  6 (4) for R1 and R2. 045. R2 R   R 1  22k B F E Two Resistor One Resistor 145. R1 IC IC F 0310. Rk1  22   10.. 4 0 7V  3.7 mA 2.9 mA 50 Rkusek 709.  68 I  F 1 C 22k  2200 RR0.... 45 0 45 70 9 k 319 kusek 33  F 4.0 mA 4.0 mA 100 R 21 V  1 V 4.2 mA 5.0 mA 200 BCCRR 12 4.3 mA 5.4 mA 300 V  15V CC   I =0.6 mA I =2.5 mA RR121 R   R 1   145. R 1  C  C  VB  10. 4V 

RR12145. R 1

045. RR12

6.101 Spring 2020 Lecture 3 35 6.101 Spring 2020 Lecture 3 36 Base Current –Resistor Divider Common Collector –Emitter Follower Biasing

+15V • Β = 100, iB = 7.5ma/100 =‐ 75µa 7.5 mA • Using Thevenin equivalent, R I  2 C F  R  A 15 1  3.7 mA 50 2N3904 RB = R1||R2, VB =    R1  R2  4.0 mA 100 68K R 1 1.0 k  7.5 mA 4.2 mA 200 VB = IBRB + 0.6V + 7.5V B 4.3 mA 300 VB = [75 µA x 10k] + 0.6V + 7.5V ib VB = 750 mV + 0.6V + 7.5V IC=0.6 mA +15V VB = 8.9V

7.5 mA [15 R1] ÷ [R1 + R2] = 8.9V 33K 15 R1 = 8.9 x [R1 + R2] Make small 2N3904 [15−8.9] R = 8.9 R ib IB 1 2 compared to the RB R1 = 1.44 R2 [R x R ] ÷ [R + R ] = 10 kΩ current through R2 7.5 V 1 2 1 2 VB

[1.44R2 x R2] ÷ [1.44 R2 + R2] = 10kΩ R = 16.9 kΩ (use 16 kΩ) See handout: Transistor bias stability 2 R1 = 1.44 R2 = 24.4 kΩ (use 24 kΩ)

6.101 Spring 2020 Lecture 3 37 6.101 Spring 2020 Lecture 3 38

Common Collector –Emitter Follower Biasing Bootstrapping –Higher Input Impedance

• With R1 = 24kΩ, R2 = 16 kΩ, the +15V current through the voltage divider is The base is connected to the emitter 15 ÷[40 kΩ] = 375 µA. through with R3 and C2 . At signal 7.5 mA • The 75 µA base current is 20% of 375 frequency, C2 is a short so both ends of R3 R 2 IDivider µA. are at the same voltage – so no current

A flows. Therefore R1 and R2 cannot load 8.1 V 2N3904 • With R1 = 2 kΩ, will need a divider the input. So R3 appears to be very high. current that is ~ 4.1 mA. (75 µA is only ~2% of 4.1 mA, which is R 1 1.0 k In real life, there is a small AC voltage 7.5 mA negligible) across R3. The AC current through R3 is B • The voltage drop across R2 will be [15 V –8.1 V] = 6.9 V; R2 = 1.7 kΩ 0.006 ÷ 4.7kΩ = 1.1 µA. • But input impedance will be low = ~890Ω Result: “stiff” biasing with high input • Use bootstrapping configuration resistance at signal frequency. Horowitz and Hill Figure 2.65

= 24.4 kΩ (use 24 kΩ)

6.101 Spring 2020 Lecture 3 39 6.101 Spring 2020 Lecture 3 40 Commom Emitter –Hybrid π

TRANSISTOR AMPLIFIER CONFIGURATIONS WITH HYBRID- EQUIVALENT CIRCUITS

COMMON EMITTER AMPLIFER

“Our treatment of bipolar transistors is going to be quite different +15V from that of many other books. It is a common practice to use the  0  g m r h-parameter (hybrid pi) model and equivalent circuit. In our RL I I R C CQ opinion that is unnecessarily complicated and unintuitive. . . you B gm  also have the tendency to lose sight of which parameters of C + 2N3904 + VTH Early Voltage transistors behavior you can count on and more important, which I R B s v ones can vary over large ranges.” out VA + r  vin 0 _ _ I The Art of Electronics, Horowitz & Hill 3rd edition page 71 CQ

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 41 6.101 Spring 2020 Lecture 3 42

Common Emitter with Emitter Degeneration Common Collector (Emitter Follower)

 0g mr

ICQ gm  VTH  26mv VTH

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

1 • Input resistance (β+1)RE v out • Voltage gain reduced by (1+gm RE) • Buffer with unity gain 1 v in • Voltage gain less dependent on β 1 • High input resistance driving low v in 1 (linearity) v out output resistance (current gain).

6.101 Spring 2020 Lecture 3 43 6.101 Spring 2020 Lecture 3 44 Low Frequency Hybrid‐ Equation Chart 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 r (low frequency):datasheet or estimate 50 100 High gain applications Unity gain, low High gain, better high x Moderate input resistance output resistance frequency response (high frequency):estimate  25 High output resistance High input resist. Low input resistance

6.101 Spring 2020 Lecture 3 45 6.101 Spring 2020 Lecture 3 46

hfe and High Frequency Limits Miller Effect* – Common Emitter 

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 CM  C [1 gm (RC RL )] 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! * Agarwal & Lang Foundations of Analog & Digital Electronics Circuits p 861 *Lundberg, Kent: Become One with the Transistor p29

6.101 Spring 2020 Lecture 3 47 6.101 Spring 2020 Lecture 3 48