Bipolar Junction Transistors Physical Structure and Modes of

Bipolar Junction Transistors Physical Structure and Modes of Operation Emitter (E) Metal contact n-type p-type n-type Emitter region Base region Collecter region Emitter-base junction (EBJ) Mode Base (B) EBJ Cutoff Reverse Active Forward Saturation Forward © REP 12/3/2020 ENGR 224 Collecter (C) Collecter-base junction (CBJ) CBJ Reverse Forward Page BJT 4. 1 -1

Bipolar Junction Transistors Operation of the npn Transistor in the Active Mode p n E Injected electrons Diffusing electrons n Collected electrons C Injected holes (i. B 1) B © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -2

Bipolar Junction Transistors Current Flow § § Only diffusion-current components are considered Profiles of minority-carrier concentrations in the base and in the emitter of an npn transistor operating in the active mode; v. BE > 0 and v. CB 0. EBJ depletion region Carrier concentration Emitter (n) Base (p) CBJ depletion region Collector (n) Electron concentration np (ideal) Hole concentration pn 0 np(0) pn(0) np (with recombination) Distance (x) Effective base width W © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -3

Bipolar Junction Transistors The Collector Current § § § Most of the diffusing electrons will reach the boundary of the collector-base depletion region These successful electrons will be swept across the CBJ depletion region into the collector By convention, the direction of i. C is opposite to that of electron flow saturation current © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -4

Bipolar Junction Transistors The Base Current Two components of base current, i B 1 and i. B 2. Hole diffusivity in the emitter Hole diffusion length in the emitter minority-carrier lifetime Doping concentration of the emitter common-emitter current gain © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -5

Bipolar Junction Transistors The Emitter Current common-base current gain © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -6

Bipolar Junction Transistors First Order Equivalent Circuit Models § § The externally controlled signals for this model are Voltage Controlled Current Source Model the three currents shown outside the gray box. C The voltage VBE, exists internally as a result of the currents and can be externally measured. We can force a current and measure a voltage. The diode in the model is designated as DE since the current flowing through the diode is the same as the emitter current. The collector current is dependent on the base-emitter voltage VBE. B The model is a non-linear voltage controlled current source C § § § The externally controlled signals for this model are two currents and the voltage VBE shown outside the gray box. The current i. E exists internally as a result of the voltage VBE and can be externally measured. The collector current is dependent on the emitter current i. E. DE B DE E Current Controlled Current Source E © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -7

Bipolar Junction Transistors Equivalent Circuit Models, cont’d § § In this version of the model the diode conducts the BASE current which is beta times smaller. In one version the dependent current source is voltage controlled (v. BE), in the other version the dependent current source is current controlled (b). B C E Note connection point is now on the opposite side of the diode Voltage Controlled Current Source Model © REP 12/3/2020 ENGR 224 C B E Current Controlled Current Source Page BJT 4. 1 -8

Bipolar Junction Transistors Two Port Model of the Common-Base Configuration C B B E B Two port Network C B The base lead is common to both ports DE E E C B B If we switch the leads within the network the common base aspect is more apparent E C B B Two-Port representation of a BJT Transistor symbol in a common-base configuration © REP 12/3/2020 ENGR 224 The common-base current gain is a Page BJT 4. 1 -9

Bipolar Junction Transistors Two Port Model of the Common-Emitter Configuration C B B E Two port Network C E The emitter lead is common to both ports E i. C is out of phase with i. B B E C E Two-Port representation of a BJT Transistor symbol in a common-emitter configuration © REP 12/3/2020 ENGR 224 The common-emitter current gain is a Page BJT 4. 1 -10

Bipolar Junction Transistors Operation of the pnp Transistor in the Active Mode n p E Injected holes Diffusing holes p Collected holes C Injected electrons (i. B 1) B © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -11

Bipolar Junction Transistors Equivalent pnp Circuit Models E E DE B B C C © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -12

Bipolar Junction Transistors Circuit Symbols and Conventions - npn C C B B E E npn BJT © REP 12/3/2020 ENGR 224 Voltage polarities and current flow in a transistor biased in the active mode. Page BJT 4. 1 -13

Bipolar Junction Transistors Circuit Symbols and Conventions - pnp E E B B C C pnp BJT © REP 12/3/2020 ENGR 224 Voltage polarities and current flow in a transistor biased in the active mode. Page BJT 4. 1 -14

Bipolar Junction Transistors Example 4. 1 § The transistor in the circuit below has b = 100 and exhibits a v. BE of 0. 7 V at i. C = 1 m. A. Design the circuit so that a current of 2 m. A flows through the collector and a voltage of +5 V appears at the collector. © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -15

Bipolar Junction Transistors Graphical Representation of Transistor Characteristics § § Similar to diodes, except we talk about the voltage across one junction V BE and the current through the other terminal i. C. For most of the conditions we will encounter in working with BJTs the ideality factor, n will be considered to be 1. T 1 T T 3 2 T 1>T 2>T 3 0 0. 5 0. 7 i. C-v. BE characteristics Effect of temperature on i. C-v. BE characteristic. At a constant current, v. BE changes by – 2 m. V/o. C. 0 0. 5 0. 7 © REP 12/3/2020 ENGR 224 0 0. 5 0. 7 Page BJT 4. 1 -16

Bipolar Junction Transistors i. C versus v. CB Characteristics § npn transistor in active mode saturation Current controlled current source 0 1 2 3 -Vnp = forward bias +Vnp = reverse bias saturation See next page 0 1 2 3 © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -17

Bipolar Junction Transistors i. C=v. CE Characteristics § The Early Voltage (typically 50 -100 Volts), also known as the Base-Width Modulation parameter. § As the base-collector junction reverse bias is increased the depletion layer expands and consumes some of the base narrowing it and causing an increase in the collector current. Saturation region Active region © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -18

Bipolar Junction Transistors Example 4. 2 § We wish to analyze this circuit to determine all node voltages and branch currents. We will assume that b is specified to be 100. © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -19

Bipolar Junction Transistors Example 4. 2, cont’d § § We don’t know whether the transistor is in the active mode or not. A simple approach would be to assume that the device is in the active mode, and then check our results at the end 1 2 3 4 5 1 3 2 4 5 © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -20

Bipolar Junction Transistors Example 4. 3 § We wish to analyze the circuit shown below to determine the voltages at all nodes and the currents through all branches. Note that this circuit is identical to the previous circuit except that the voltage at the base is now +6 V. Assuming active-mode: 3 4 1 2 Collector voltage > base voltage saturation mode, not active mode © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -21

Bipolar Junction Transistors Example 4. 4 § We wish to analyze the circuit below to determine the voltages at all nodes and the currents through all branches. This circuit is identical to that considered in the previous two examples except that now the base voltage is zero. 3 5 4 2 1 © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -22

Bipolar Junction Transistors Example 4. 6 § We will analyze the following circuit to determine the voltages at all nodes and currents through all branches. Assume b=100. 1 3 2 3 4 4 2 © REP 12/3/2020 ENGR 224 5 5 Page BJT 4. 1 -23

Bipolar Junction Transistors Example 4. 7 § We want to analyze the circuit shown below to determine the voltages at all nodes and currents through all branches. Assume b=100. © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -24

Bipolar Junction Transistors Example 4. 7, cont’d © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -25

Bipolar Junction Transistors The BJT as an Amplifier § Objectives 1. Biasing 2. DC equations 3. Transconductance 4. Input resistance looking into the base 5. Input resistance looking into the emitter 6. Voltage gain 7. Gummel plots § Lesson 1. Biasing 1) For our amplifiers, the BJT must be biased in the FORWARD-ACTIVE 2) However, it’s a difficult challenge to establish a CONSTANT DC CURRENT 3) Our goal: A Q point insensitive to TEMPERATURE , ß , VBE. © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -26

Bipolar Junction Transistors The BJT as an Amplifier 2. DC Equations (learn ‘em now) 1) 2) 3) 4) 3. Transconductance (remember the small-signal approximation from before? ) - Valid only for v. BE< 10 m. V - Defined as the incremental change in output current for an incremental change in input voltage at a DC operating point…. . © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -27

Bipolar Junction Transistors The BJT as an Amplifier If vbe<< VT § Note that i. C = IC at v. BE = VBE, so…. . . © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -28

Bipolar Junction Transistors The BJT as an Amplifier Input Resistance “ looking into “ the Base ( highlight this in your text & on this page!) v Defined as the incremental change input voltage for an incremental change in base current at a DC operating point… v Other important relationships ( be prepared to use any of these!) © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -29

Bipolar Junction Transistors The BJT as an Amplifier Input Resistance “looking into “ the Emitter (hightlight this in your text & on this page) v Define as the incremental change in input voltage for an incremental change in emitter current at DC operating point…. . v Other important relationship ( be prepared to use either of them!) © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -30

Bipolar Junction Transistors The BJT as an Amplifier Relationship between r and re - The same input resistance. . . just “ viewed from two different places ! “ © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -31

Bipolar Junction Transistors The BJT as an Amplifier Lets look at Voltage Gain again v A BJT senses vbe v This is a and causes a proportional current gm vbe VOLTAGE - CONTROLED CURRENT SOURCE v So. . . How do we obtain an output voltage so that we get a voltage gain? Out of phase with the input © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -32

Bipolar Junction Transistors Voltage Gain Signal voltage: © REP 12/3/2020 ENGR 224 Voltage gain: Page BJT 4. 1 -33

Bipolar Junction Transistors Small-signal equivalent circuit models § § § Every current and voltage in the amplifier circuit is composed of two components: a dc component and a signal component. The dc components are determined from the dc circuit below on the left. By eliminating the dc voltages, we are left with the signal components (on the right). The resulting circuit is equivalent to the transistor as far as small-signal operation is concerned. + - Amplifier circuit with dc sources © REP 12/3/2020 ENGR 224 + - Amplifier circuit with dc sources eliminated Page BJT 4. 1 -34

Bipolar Junction Transistors The Hybrid-P Model current-controlled current source voltage-controlled current source C B E © REP 12/3/2020 ENGR 224 C B E Page BJT 4. 1 -35

Bipolar Junction Transistors The T Model § These models explicitly show the emitter resistance re rather than the base resistance rp featured in the hybrid- model. C B E voltage-controlled current source © REP 12/3/2020 ENGR 224 E current-controlled current source Page BJT 4. 1 -36

Bipolar Junction Transistors Application of the Small-Signal Equivalent Circuits § The availability of the small-signal BJT circuit models makes the analysis of transistor amplifier circuits a systematic process consisting of the following steps: v Determine the dc operating point of the BJT and in particular the dc collector current IC. v Calculate the values of the small-signal model parameters: v Eliminate the dc sources by replacing each dc voltage source with a short circuit and each dc current source with an open circuit. v Replace the BJT with one of its small-signal equivalent circuit models. Although any one of the models can be used, one might be more convenient than the others for the particular circuit being analyzed. This point will be made clearer later in this chapter. v Analyze the resulting circuit to determine the required quantities (e. g. , voltage gain, input resistance). © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -37

Bipolar Junction Transistors Example 4. 9 § We wish to analyze the transistor amplifier shown below to determine its voltage gain. Assume b = 100. 2 3 + - 1 2 1 3 © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -38

Bipolar Junction Transistors Example 4. 9, cont’d § Having determined the operating point, we now proceed to determine the small-signal model parameters + - B C E © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -39

Bipolar Junction Transistors A note about Output Signal Swing § § § The collector voltage (and vo) can have a maximum value of zero volts before the transistor goes from forward active mode to saturation mode since the base is grounded. When no input (ac) voltage is applied the output (collector) was found to be at a DC level of -5. 4 V. If we desire a symmetric output signal (about the -5. 4 V DC level) the signal would have to go to -5. 4 - 5. 4 or -10. 8 Volts (this is a large output signal swing). This causes a problem, since our lower voltage supply is only -10 V. In order to avoid possibly producing a distorted output signal the input signal range must be limited so that the output is not clipped as shown below. Limiting the input signal to smaller values to limit clipping is not the same as using a small signal to invoke the linear approximation as indicated in the next bullet item. Another important point to be made about the output signal is that it is shown to be linear in the figure below but in fact the i. C-vbe characteristic is not linear for a large output signal swing. t 0 -5. 4 -10 © REP 12/3/2020 ENGR 224 clipping Page BJT 4. 1 -40

Bipolar Junction Transistors Modifying the Hybrid-p Model to Include the Early Effect § § § The Early effect causes the collector current to depend on v. BE as well as v. CE. The dependence on v. CE is modeled by assigning a finite output resistance to the controlled current-source. By including ro in the equivalent circuit shown below, the gain will be somewhat reduced. voltage-controlled current source B current-controlled current source C E © REP 12/3/2020 ENGR 224 B C E Page BJT 4. 1 -41

Bipolar Junction Transistors Summary of the BJT Small-Signal Model Parameters § § Keep these at your fingertips (I. e. formula sheet for an exam or homework or in lab) v See Table 4. 3 Model parameters in terms of DC bias currents § Model parameters in terms of the transconductance, gm § Model parameters in terms of re § Relationships between the common-emitter current gain and the common-base gain © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -42

Bipolar Junction Transistors Graphical Analysis © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -43

Bipolar Junction Transistors Graphical Analysis (cont. ) © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -44

Bipolar Junction Transistors Graphical Analysis (cont. ) © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -45

Bipolar Junction Transistors Graphical Analysis (cont. ) © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -46

Bipolar Junction Transistors Single Power Supply § § § Biasing the BJT involves establishing a constant dc current in the emitter which is calculable, predictable, and insensitive to temperature variations and to b (for transistors of the same type). The bias point should allow for maximum output signal swing. To design for a stable IE, the design constraints (shown below) must be satisfied. Design constraints: Circuit topology for biasing a BJT amplifier © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -47

Bipolar Junction Transistors Single Power Supply, cont’d § From the previous page, our design constraints are as follows: § When biasing the BJT, we must make sure of the following: v VBB must not be too large, or it will lower the sum of voltages across R C and VCB v RC should be large enough to obtain high voltage gain and large signal swing v VCB (or VCE) should be large enough to provide a large signal swing § Rules of thumb: § We’d like for RB to be small, which is achieved by low values of R 1 and R 2. This could result in higher current drain from the power supply, hence lower input resistance (if the input signal is coupled to the base). This means that we want to make the base voltage independent of b and solely determined by the voltage divider. In order to achieve this, another rule of thumb is practiced: select R 1 and R 2 such that their current is in the range of © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -48

Bipolar Junction Transistors Example 4. 12 § We wish to design the bias network of the amplifier shown below to establish a current I E = 1 m. A using a power supply VCC = +12 V. neglecting base current: for voltage divider current = 0. 1 IE for nonzero base current: for voltage divider current = IE © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -49

Bipolar Junction Transistors Example 4. 12, cont’d § Depending on what the emitter current is, we can have two designs: v Design 1: the voltage divider current = 0. 1 IE, and v Design 2: the voltage divider current = IE Design 1 © REP 12/3/2020 ENGR 224 Design 2 Page BJT 4. 1 -50

Bipolar Junction Transistors Biasing Using Two Power Supplies § § § A somewhat simpler bias arrangement is possible if two power supplies are available. If the transistor is to be used with the base grounded, then R B can be eliminated altogether. If the input signal is to be coupled to the base, then R B is needed. Design constraints: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -51

Bipolar Junction Transistors An Alternative Biasing Arrangement © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -52

Bipolar Junction Transistors Biasing Using a Current Source § § § The BJT can be biased using a current source The advantage is that the emitter current is independent of the values b and RB Current-source biasing leads to significant design simplification © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -53

Bipolar Junction Transistors Common-Emitter Amplifier Circuit © REP 12/3/2020 ENGR 224 AC Hybrid -based model Page BJT 4. 1 -54

Bipolar Junction Transistors Common-Emitter Amplifier (cont. ) Input Resistance: Current Gain: Voltage Gain: Output Resistance: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -55

Bipolar Junction Transistors Exercise 4. 31 For a CE amplifier, let I=1 m. A, RC=5 k. W, b=100, VA=100 V, and Rs=5 k. W. Find Ri, Av, Ai, and Ro: What is Av if a 5 k. W load resistor is added to the circuit: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -56

Bipolar Junction Transistors Common-Emitter Amplifier with an Emitter Resistor © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -57

Bipolar Junction Transistors Common-Emitter Amplifier with an Emitter Resistor (cont. ) Input Resistance: © REP 12/3/2020 ENGR 224 Voltage Gain: Page BJT 4. 1 -58

Bipolar Junction Transistors Common-Emitter Amplifier with an Emitter Resistor (cont. ) Characteristics of CE amplifier with resistance Re: § § Output Resistance: § § § Input resistance is increased by the factor of (1+gm. Re) An input signal of (1+gm. Re) times larger can be applied to the input without inducing nonlinear distortion The voltage gain is reduced The voltage gain is less dependent on the value of b The high frequency response is significantly improved Current Gain: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -59

Bipolar Junction Transistors Exercise 4. 32 For a CE amplifier with Re, let I=1 m. A, RC=5 k. W, b=100, and Rs=5 k. W. Find Re such that the amplifier has an input resistence of 4 times that of the source. Find Av, Ai, and Ro: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -60

Bipolar Junction Transistors Exercise 4. 32 For the same CE amplifier, find the maximum vs without Re and with Re if vp is to be limited to 5 m. V: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -61

Bipolar Junction Transistors Common-Base Amplifier © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -62

Bipolar Junction Transistors Common-Base Amplifier (cont. ) Input Resistance: Current Gain: Voltage Gain: Output Resistance: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -63

Bipolar Junction Transistors Exercise 4. 33 For a CB amplifier with Re, let I=1 m. A, RC=5 k. W, b=100, and Rs=5 k. W. Find Ri. Av, Ai, and Ro: Note that Ri. Av, Ai are much lower than the CE amplifier using the same components although the voltage gain of the CB amplifier can be almost equivalent if Rs is low. © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -64

Bipolar Junction Transistors Common-Collector Amplifier - Emitter Follower © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -65

Bipolar Junction Transistors Common-Collector Amplifier - Emitter Follower (cont. ) © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -66

Bipolar Junction Transistors Common-Collector Amplifier - Emitter Follower (cont. ) Input Resistance: Voltage Gain: Current Gain: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -67

Bipolar Junction Transistors Common-Collector Amplifier - Emitter Follower (cont. ) Output Resistance: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -68

Bipolar Junction Transistors Common-Collector Amplifier - Emitter Follower (cont. ) Output Resistance (cont. ): Voltage Gain revisited: Open-circuit voltage gain: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -69

Bipolar Junction Transistors Exercise 4. 34 For an emitter follower with a load resistence, RL=1 k. W, let I=5 m. A, b=100, VA=100 V, and Rs=10 k. W. Find © REP 12/3/2020 ENGR 224 : Page BJT 4. 1 -70

Bipolar Junction Transistors Exercise 4. 34 (cont. ) For an emitter follower with a load resistence, RL=1 k. W, let I=5 m. A, b=100, VA=100 V, and Rs=10 k. W. Find © REP 12/3/2020 ENGR 224 : Page BJT 4. 1 -71

Bipolar Junction Transistors The BJT as a switch-cutoff and saturation § The BJT has 4 modes of operation: v Cutoff v Forward Active v Saturation v Inverse Active § So far, we have studied the forward active mode in great detail. Now we will look at the BJT in cutoff mode and at the BJT in saturation mode. These two extreme modes of operation are very useful if the transistor is used as a switch, such as in digital logic circuits. Mode EBJ Cutoff Reverse Forward Active Forward Saturation Forward Inverse Active Reverse © REP 12/3/2020 ENGR 224 CBJ Reverse Forward Page BJT 4. 1 -72

Bipolar Junction Transistors Cutoff Region § § Consider the circuit shown below. If voltage source v. I is goes lesss than about 0. 5 V, the Emitter-Base Junction will conduct negligible current (reverse-biased). The CBJ is also reverse-biased since VCC is positive. The device will be in the cutoff mode. It follows that: + - © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -73

Bipolar Junction Transistors Active Region § To turn the transistor on, v. I must be increased to above 0. 7 V. This gives base current: § The collector current is given by which applies only if the device is in active mode. At this point, we don’t know for sure, therefore we assume active mode and calculate the collector current from § Next, we check whether or not. In our case, just check whether or not. If so, then our original assumption is true. If not, the device is in saturation. + - © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -74

Bipolar Junction Transistors Saturation Region § Saturation occurs when we attempt to force a current in the collector higher than the collector circuit can support while maintaining active-mode operation. Maximum collector current MAXIMUM BASE current in forward active above , the collector § Increasing current will increase and the collector voltage will fall below that of the base. This will continue until the CBJ becomes forward-biased. Constant current + - IB is usually higher than IB(EOS) by a factor of 2 to 10 -- overdrive factor. EOS=edge of saturation This value can be set “at will. ” © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -75

Bipolar Junction Transistors Model for the Saturated BJT § A simple model for the npn and pnp transistors in saturation mode is shown on the left. § For quick approximate calculations one may consider VBE and VCEsat to be zero and use three-terminal short circuit shown on the right to model a saturated transistor. C B npn C B E E E approximate model C B pnp © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -76

Bipolar Junction Transistors Example 4. 13 § We wish to analyze the circuit to determine the voltages at all nodes and currents in all branches. Assume the transistor b is specified to be at least 50. Assuming saturation: 1 4 2 3 3 5 1 2 4 5 © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -77

Bipolar Junction Transistors Example 4. 14 § The transistor shown below is specified to have b in the range 50 to 150. Find the value of RB that results in saturation with an overdrive factor of at least 10. © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -78

Bipolar Junction Transistors Example 4. 15 § We want to analyze the circuit below to determine the voltages at all nodes and the currents through all branches. The minimum value of b is specified to be 30. © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -79

Bipolar Junction Transistors Example 4. 15, cont’d § Substituting in the equations on the previous page, we obtain the following: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -80

Bipolar Junction Transistors Introduction - Equation forms for use in SPICE § Consider the equation for the emitter current in an ideal pnp bipolar junction transistor § We can simplify the equations by collecting the terms into only a few constants, giving the coefficients different names, for example, half of the equation given above becomes; § The other half of the equation is similarly reduced § This allows the emitter current to be written in a much more compact form: © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -81

Bipolar Junction Transistors Equation forms for use in SPICE (continued) § Now consider the equation for the collector current in an ideal pnp bipolar junction transistor § The right half of the equation reduces to: § The left half of the equation is similarly reduced § This allows the collector current to be written in a much more compact form: § If we know two of the terminal currents we can find the current in the third terminal © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -82

Bipolar Junction Transistors The Ebers-Moll equations for an ideal PNP BJT § The key results are § The equivalent circuit (just another way to state the equations) IC C P IC a. FIF B C IR IB N a. RIR IF B IB IE IE © REP 12/3/2020 ENGR 224 E Page BJT 4. 1 -83

Bipolar Junction Transistors Use in SPICE § The current sources illustrate the interaction of the two junctions due to the narrow base region § § IS is one of the three required SPICE parameters for a BJT in SPICE 2 The reduced equations can be manipulated to show that: § Only three numbers, b. F , b. R and IS are needed for the Ebers-Moll equations to be completely specified. v All other parameters can be calculated from these three v The equations can be applied to all regions of operation Can be extended to the nonideal case by defining coefficients in front of the exponential terms § § For NPN transistors the diodes, currents and voltage polarities are reversed © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -84

Bipolar Junction Transistors An Alternative form of the Ebers-Moll Model, the Transport Model § § In this model the diodes DBE and DBC have saturation currents IS/b. F and IS/b. F respectively The base current, ib can be written as § i. T is the current component of i. C which arises from the minority carrier diffusion (transport) across the base, hence the name of this model C i. C DBC B § The transport model is exactly equivalent to the Ebers. Moll model but it highlights different aspects of BJT behavior. It uses one less circuit element and one less parameter in SPICE © REP 12/3/2020 ENGR 224 IS/b. R i. B i. T DBE IS/b. F i. E Page BJT 4. 1 -85 E

Bipolar Junction Transistors Common-Base Characteristics § First-Order i. C-v. CB Characteristics § Second-Order i. C-v. CB Characteristics © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -86

Bipolar Junction Transistors Common-Emitter Characteristics § Second-Order i. C-v. CE Characteristics (refer to lesson 17) © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -87

Bipolar Junction Transistors DC and ac b § “BETA DC” (spice) v More accurate than b. F, because its determined at Q v Common-emitter current gain at DC § “BETAAC” (spice) v Input ac signal results in Di. B Di. C. v Thus changes, because v Since v. CE is constant, bac=short-circuit current gain. v Typically, bac=bdc. Use bac in small-signal model. © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -88

Bipolar Junction Transistors “Complete” BJT Models § Low-frequency model § rx=base resistance of bulk Si § r = © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -89

Bipolar Junction Transistors “Complete” BJT Models § High-frequency model © REP 12/3/2020 ENGR 224 Page BJT 4. 1 -90