Physics of Bipolar Junction Transistors

Transcription

1 SUT Analog Circuits Physics of Bipolar Junction Transistors Prepared by: Siavash Kananian 1

2 Bipolar Transistor n the chapter, we will study the physics of bipolar transistor and derive large and small signal models. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 2

3 Voltage-Dependent Current Source A V V V out in KR L A voltage-dependent current source can act as an amplifier. f KR L is greater than 1, then the signal is amplified. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 3

4 Voltage-Dependent Current Source with nput Resistance Regardless of the input resistance, the magnitude of amplification remains unchanged. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 4

5 Exponential Voltage-Dependent Current Source A three-terminal exponential voltage-dependent current source is shown above. deally, bipolar transistor can be modeled as such. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 5

6 Structure and Symbol of Bipolar Transistor Bipolar transistor can be thought of as a sandwich of three doped Si regions. The outer two regions are doped with the same polarity, while the middle region is doped with opposite polarity. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 6

7 njection of Carriers Reverse biased PN junction creates a large electric field that sweeps any injected minority carriers to their majority region. This ability proves essential in the proper operation of a bipolar transistor. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 7

8 Forward Active Region Forward active region: V BE > 0, V BC < 0. Figure b) presents a wrong way of modeling figure a). Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 8

9 Accurate Bipolar Representation Collector also carries current due to carrier injection from base. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 9

10 Carrier Transport in Base Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 10

11 Collector Current C C S AE qdnn N W S E E B AE qdnn N W B 2 i V exp V BE T 2 i V exp V BE T 1 Applying the law of diffusion, we can determine the charge flow across the base region into the collector. The equation above shows that the transistor is indeed a voltage-controlled element, thus a good candidate as an amplifier. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 11

12 Parallel Combination of Transistors When two transistors are put in parallel and experience the same potential across all three terminals, they can be thought of as a single transistor with twice the emitter area. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 12

13 Simple Transistor Configuration Although a transistor is a voltage to current converter, output voltage can be obtained by inserting a load resistor at the output and allowing the controlled current to pass thru it. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 13

14 Constant Current Source deally, the collector current does not depend on the collector to emitter voltage. This property allows the transistor to behave as a constant current source when its base-emitter voltage is fixed. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 14

15 Base Current C B Base current consists of two components: 1) Reverse injection of holes into the emitter and 2) recombination of holes with electrons coming from the emitter. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 15

16 Emitter Current Applying Kirchoff s current law to the transistor, we can easily find the emitter current. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 16 B C C E B C E 1 1

17 Summary of Currents Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 17 1 exp 1 exp 1 exp T BE S E T BE S B T BE S C V V V V V V

18 Bipolar Transistor Large Signal Model A diode is placed between base and emitter and a voltage controlled current source is placed between the collector and emitter. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 18

19 Example: Maximum R L As R L increases, V x drops and eventually forward biases the collector-base junction. This will force the transistor out of forward active region. Therefore, there exists a maximum tolerable collector resistance. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 19

20 Characteristics of Bipolar Transistor Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 20

21 Example: V Characteristics Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 21

22 Transconductance g g g m m m d dv 1 V V T C T BE S V S exp V VBE exp V T BE T Transconductance, g m shows a measure of how well the transistor converts voltage to current. t will later be shown that g m is one of the most important parameters in circuit design. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 22

23 Visualization of Transconductance g m can be visualized as the slope of C versus V BE. A large C has a large slope and therefore a large g m. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 23

24 Transconductance and Area When the area of a transistor is increased by n, S increases by n. For a constant V BE, C and hence g m increases by a factor of n. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 24

25 Transconductance and c The figure above shows that for a given V BE swing, the current excursion around C2 is larger than it would be around C1. This is because g m is larger C2. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 25

26 Small-Signal Model: Derivation Small signal model is derived by perturbing voltage difference every two terminals while fixing the third terminal and analyzing the change in current of all three terminals. We then represent these changes with controlled sources or resistors. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 26

27 Small-Signal Model: V BE Change Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 27

28 Small-Signal Model: V CE Change deally, V CE has no effect on the collector current. Thus, it will not contribute to the small signal model. t can be shown that V CB has no effect on the small signal model, either. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 28

29 Small Signal Example g r m V g C T m Here, small signal parameters are calculated from DC operating point and are used to calculate the change in collector current due to a change in V BE. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 29

30 Small Signal Example n this example, a resistor is placed between the power supply and collector, therefore, providing an output voltage. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 30

31 Early Effect The claim that collector current does not depend on V CE is not accurate. As V CE increases, the depletion region between base and collector increases. Therefore, the effective base width decreases, which leads to an increase in the collector current. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 31

32 Early Effect llustration With Early effect, collector current becomes larger than usual and a function of V CE. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 32

33 Early Effect Representation Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 33

34 Early Effect and Large-Signal Model Early effect can be accounted for in large-signal model by simply changing the collector current with a correction factor. n this mode, base current does not change. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 34

35 Early Effect and Small-Signal Model r o V CE C S VA V exp V BE T V A C Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 35

36 Summary of deas 36 Physics of BJTs, Fundamentals of Microelectronics, B.Razavi

37 Bipolar Transistor in Saturation When collector voltage drops below base voltage and forward biases the collector-base junction, base current increases and decreases the current gain factor,. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 37

38 Large-Signal Model for Saturation Region Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 38

39 Overall /V Characteristics The speed of the BJT also drops in saturation. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 39

40 Example: Acceptable V CC Region V CC C R C ( V 400mV ) BE n order to keep BJT at least in soft saturation region, the collector voltage must not fall below the base voltage by more than 400mV. A linear relationship can be derived for V CC and R C and an acceptable region can be chosen. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 40

41 Deep Saturation n deep saturation region, the transistor loses its voltagecontrolled current capability and V CE becomes constant. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 41

42 PNP Transistor With the polarities of emitter, collector, and base reversed, a PNP transistor is formed. All the principles that applied to NPN's also apply to PNP s, with the exception that emitter is at a higher potential than base and base at a higher potential than collector. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 42

43 A Comparison between NPN and PNP Transistors The figure above summarizes the direction of current flow and operation regions for both the NPN and PNP BJT s. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 43

44 PNP Equations C B E S V exp V 1 S EB T S V exp V EB T V exp V EB T Early Effect C S V exp V EB T V 1 V EC A 44 Physics of BJTs, Fundamentals of Microelectronics, B.Razavi

45 Large Signal Model for PNP Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 45

46 PNP Biasing Note that the emitter is at a higher potential than both the base and collector. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 46

47 Small Signal Analysis Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 47

48 Small-Signal Model for PNP Transistor The small signal model for PNP transistor is exactly DENTCAL to that of NPN. This is not a mistake because the current direction is taken care of by the polarity of V BE. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 48

49 Small Signal Model Example Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 49

50 Small Signal Model Example Small-signal model is identical to the previous ones. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 50

51 Small Signal Model Example Since during small-signal analysis, a constant voltage supply is considered to be AC ground, the final small-signal model is identical to the previous two. Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 51

52 Small Signal Model Example V Physics of BJTs, Fundamentals of Microelectronics, B.Razavi 52

53 A little Frequency Response! Consider the common emitter circuit above. Derive the Vo-Vi characteristics for f=10hz. Oscilloscope Screen on right: Siavash Kananian Copyright 53

54 Raising the frequency and checking the screen again, give some unpredictable result! f = 1kHz f = 10kHz f = 100kHz Siavash Kananian Copyright 54

55 What happens? Do you remember from earlier experiments, the Lissajous Patterns? t seems that input and output at higher frequencies have some phase shift! Why on earth something like that would happen? s there a capacitor somewhere we don t see? The answer is yes! BJT internal capacitors is the key to the question. Siavash Kananian Copyright 55

56 BJT at high frequency At high frequency, capacitive effects come into play. C b represents the base charge, whereas C and C je are the junction capacitances. Since an integrated bipolar circuit is fabricated on top of a substrate, another junction capacitance exists between the collector and substrate, namely C CS. Siavash Kananian Copyright 56

57 Another look at Characteristics: SPCE Simulation f = 10Hz f = 1kHz f = 10kHz f = 100kHz Siavash Kananian Copyright 57

58 SPCE Code n case you want to discover new things yourself: Bc107_high_frequency.options spice vcc r k r k q bc107 v1 1 0 sin tran 100u 200m.probe v(3).model bc107 npn s=7.049f Xti=3 Eg=1.11 Vaf=116.3 Bf=375.5 se=7.049f Ne=1.281 kf=4.589 Nk=.5 Xtb=1.5 Br=2.611 sc=121.7p Nc=1.865 kr=5.313 Rc=1.464 Cjc=5.38p Mjc=.329 Vjc=.6218 Fc=.5 Cje=11.5p Mje=.2717 Vje=.5 Tr=10n Tf=451p tf=6.194 Xtf=17.43 Vtf=10.op.end Siavash Kananian Copyright 58