Bipolar Junction Transistors PDF

CHAPTER 3 Bipolar Junction Transistors 3.1 INTRODUCTION During the period 1904–1947, the vacuum tube was undoubtedly the electronic de-...

CHAPTER 3 Bipolar Junction Transistors 3.1 INTRODUCTION During the period 1904–1947, the vacuum tube was undoubtedly the electronic de- vice of interest and development. In 1904, the vacuum-tube diode was introduced by J. A. Fleming. Shortly thereafter, in 1906, Lee De Forest added a third element, called the control grid, to the vacuum diode, resulting in the first amplifier, the triode. In the following years, radio and television provided great stimulation to the tube in- dustry. Production rose from about 1 million tubes in 1922 to about 100 million in 1937. In the early 1930s the four-element tetrode and five-element pentode gained prominence in the electron-tube industry. In the years to follow, the industry became one of primary importance and rapid advances were made in design, manufacturing techniques, high-power and high-frequency applications, and miniaturization. On December 23, 1947, however, the electronics industry was to experience the advent of a completely new direction of interest and development. It was on the af- ternoon of this day that Walter H. Brattain and John Bardeen demonstrated the am- plifying action of the first transistor at the Bell Telephone Laboratories. The original transistor (a point-contact transistor) is shown in Fig. 3.1. The advantages of this three- terminal solid-state device over the tube were immediately obvious: It was smaller Co-inventors of the first transistor at Bell Laboratories: Dr. William Shockley (seated); Dr. John Bardeen (left); Dr. Walter H. Brat- tain. (Courtesy of AT&T Archives.) Dr. Shockley Born: London, England, 1910 PhD Harvard, 1936 Dr. Bardeen Born: Madison, Wisconsin, 1908 PhD Princeton, 1936 Dr. Brattain Born: Amoy, China, 1902 PhD University of Minnesota, 1928 All shared the Nobel Prize in 1956 for this contribution. Figure 3.1 The first transistor. (Courtesy Bell Telephone Laboratories.) 112 and lightweight; had no heater requirement or heater loss; had rugged construction; and was more efficient since less power was absorbed by the device itself; it was in- stantly available for use, requiring no warm-up period; and lower operating voltages were possible. Note in the discussion above that this chapter is our first discussion of devices with three or more terminals. You will find that all amplifiers (devices that increase the voltage, current, or power level) will have at least three terminals with one controlling the flow between two other terminals. 3.2 TRANSISTOR CONSTRUCTION The transistor is a three-layer semiconductor device consisting of either two n- and one p-type layers of material or two p- and one n-type layers of material. The former is called an npn transistor, while the latter is called a pnp transistor. Both are shown in Fig. 3.2 with the proper dc biasing. We will find in Chapter 4 that the dc biasing is necessary to establish the proper region of operation for ac amplification. The emit- ter layer is heavily doped, the base lightly doped, and the collector only lightly doped. The outer layers have widths much greater than the sandwiched p- or n-type mater- ial. For the transistors shown in Fig. 3.2 the ratio of the total width to that of the cen- ter layer is 0.150/0.001  1501. The doping of the sandwiched layer is also con- siderably less than that of the outer layers (typically, 101 or less). This lower doping level decreases the conductivity (increases the resistance) of this material by limiting the number of “free” carriers. Figure 3.2 Types of transistors: For the biasing shown in Fig. 3.2 the terminals have been indicated by the capi- (a) pnp; (b) npn. tal letters E for emitter, C for collector, and B for base. An appreciation for this choice of notation will develop when we discuss the basic operation of the transistor. The abbreviation BJT, from bipolar junction transistor, is often applied to this three- terminal device. The term bipolar reflects the fact that holes and electrons participate in the injection process into the oppositely polarized material. If only one carrier is employed (electron or hole), it is considered a unipolar device. The Schottky diode of Chapter 20 is such a device. 3.3 TRANSISTOR OPERATION The basic operation of the transistor will now be described using the pnp transistor of Fig. 3.2a. The operation of the npn transistor is exactly the same if the roles played by the electron and hole are interchanged. In Fig. 3.3 the pnp transistor has been re- drawn without the base-to-collector bias. Note the similarities between this situation and that of the forward-biased diode in Chapter 1. The depletion region has been re- duced in width due to the applied bias, resulting in a heavy flow of majority carriers from the p- to the n-type material. Figure 3.3 Forward-biased junction of a pnp transistor. 3.3 Transistor Operation 113  Let us now remove the base-to-emitter bias of the pnp transistor of Fig. 3.2a as shown in Fig. 3.4. Consider the similarities between this situation and that of the reverse-biased diode of Section 1.6. Recall that the flow of majority carriers is zero, resulting in only a minority-carrier flow, as indicated in Fig. 3.4. In summary, there- fore: One p-n junction of a transistor is reverse biased, while the other is forward biased. In Fig. 3.5 both biasing potentials have been applied to a pnp transistor, with the resulting majority- and minority-carrier flow indicated. Note in Fig. 3.5 the widths of the depletion regions, indicating clearly which junction is forward-biased and which is reverse-biased. As indicated in Fig. 3.5, a large number of majority carriers will diffuse across the forward-biased p-n junction into the n-type material. The question then is whether these carriers will contribute directly to the base current IB or pass directly into the p-type material. Since the sandwiched n-type material is very thin and has a low conductivity, a very small number of these carriers will take this path of high resistance to the base terminal. The magnitude of the base current is typically on the order of microamperes as compared to milliamperes for the emitter and col- lector currents. The larger number of these majority carriers will diffuse across the reverse-biased junction into the p-type material connected to the collector terminal as indicated in Fig. 3.5. The reason for the relative ease with which the majority carri- ers can cross the reverse-biased junction is easily understood if we consider that for the reverse-biased diode the injected majority carriers will appear as minority carri- ers in the n-type material. In other words, there has been an injection of minority car- riers into the n-type base region material. Combining this with the fact that all the minority carriers in the depletion region will cross the reverse-biased junction of a diode accounts for the flow indicated in Fig. 3.5. Figure 3.4 Reverse-biased junction of a pnp Figure 3.5 Majority and minority transistor. carrier flow of a pnp transistor. Applying Kirchhoff’s current law to the transistor of Fig. 3.5 as if it were a sin- gle node, we obtain IE  IC  IB (3.1) and find that the emitter current is the sum of the collector and base currents. The collector current, however, is comprised of two components—the majority and mi- nority carriers as indicated in Fig. 3.5. The minority-current component is called the leakage current and is given the symbol ICO (IC current with emitter terminal Open). The collector current, therefore, is determined in total by Eq. (3.2). IC  ICmajority  ICOminority (3.2) 114 Chapter 3 Bipolar Junction Transistors  For general-purpose transistors, IC is measured in milliamperes, while ICO is mea- sured in microamperes or nanoamperes. ICO, like Is for a reverse-biased diode, is tem- perature sensitive and must be examined carefully when applications of wide tem- perature ranges are considered. It can severely affect the stability of a system at high temperature if not considered properly. Improvements in construction techniques have resulted in significantly lower levels of ICO, to the point where its effect can often be ignored. 3.4 COMMON-BASE CONFIGURATION The notation and symbols used in conjunction with the transistor in the majority of texts and manuals published today are indicated in Fig. 3.6 for the common-base con- figuration with pnp and npn transistors. The common-base terminology is derived from the fact that the base is common to both the input and output sides of the con- figuration. In addition, the base is usually the terminal closest to, or at, ground po- tential. Throughout this book all current directions will refer to conventional (hole) flow rather than electron flow. This choice was based primarily on the fact that the vast amount of literature available at educational and industrial institutions employs conventional flow and the arrows in all electronic symbols have a direction defined by this convention. Recall that the arrow in the diode symbol defined the direction of conduction for conventional current. For the transistor: The arrow in the graphic symbol defines the direction of emitter current (con- ventional flow) through the device. All the current directions appearing in Fig. 3.6 are the actual directions as defined by the choice of conventional flow. Note in each case that IE  IC  IB. Note also that the applied biasing (voltage sources) are such as to establish current in the di- rection indicated for each branch. That is, compare the direction of IE to the polarity or VEE for each configuration and the direction of IC to the polarity of VCC. To fully describe the behavior of a three-terminal device such as the common- base amplifiers of Fig. 3.6 requires two sets of characteristics—one for the driving point or input parameters and the other for the output side. The input set for the common-base amplifier as shown in Fig. 3.7 will relate an input current (IE) to an in- put voltage (VBE) for various levels of output voltage (VCB). The output set will relate an output current (IC) to an output voltage (VCB) for var- ious levels of input current (IE) as shown in Fig. 3.8. The output or collector set of characteristics has three basic regions of interest, as indicated in Fig. 3.8: the active, Figure 3.6 Notation and sym- bols used with the common-base configuration: (a) pnp transistor; (b) npn transistor. Figure 3.7 Input or driving point characteristics for a common-base silicon transistor amplifier. 3.4 Common-Base Configuration 115  IC (mA) Active region (unshaded area) 7 mA 7 6 mA 6 5 mA 5 Saturation region 4 mA 4 3 mA 3 2 mA 2 I E = 1 mA 1 I E = 0 mA 0 Figure 3.8 Output or collector −1 0 5 10 15 20 V CB (V) characteristics for a common-base transistor amplifier. Cutoff region cutoff, and saturation regions. The active region is the region normally employed for linear (undistorted) amplifiers. In particular: In the active region the collector-base junction is reverse-biased, while the base-emitter junction is forward-biased. The active region is defined by the biasing arrangements of Fig. 3.6. At the lower end of the active region the emitter current (IE) is zero, the collector current is sim- ply that due to the reverse saturation current ICO, as indicated in Fig. 3.8. The current ICO is so small (microamperes) in magnitude compared to the vertical scale of IC (mil- liamperes) that it appears on virtually the same horizontal line as IC  0. The circuit conditions that exist when IE  0 for the common-base configuration are shown in Fig. 3.9. The notation most frequently used for ICO on data and specification sheets is, as indicated in Fig. 3.9, ICBO. Because of improved construction techniques, the level of ICBO for general-purpose transistors (especially silicon) in the low- and mid- power ranges is usually so low that its effect can be ignored. However, for higher power units ICBO will still appear in the microampere range. In addition, keep in mind that ICBO, like Is, for the diode (both reverse leakage currents) is temperature sensi- tive. At higher temperatures the effect of ICBO may become an important factor since Figure 3.9 Reverse saturation it increases so rapidly with temperature. current. Note in Fig. 3.8 that as the emitter current increases above zero, the collector cur- rent increases to a magnitude essentially equal to that of the emitter current as deter- mined by the basic transistor-current relations. Note also the almost negligible effect of VCB on the collector current for the active region. The curves clearly indicate that a first approximation to the relationship between IE and IC in the active region is given by IC  IE (3.3) As inferred by its name, the cutoff region is defined as that region where the collec- tor current is 0 A, as revealed on Fig. 3.8. In addition: In the cutoff region the collector-base and base-emitter junctions of a transis- tor are both reverse-biased. 116 Chapter 3 Bipolar Junction Transistors  The saturation region is defined as that region of the characteristics to the left of VCB  0 V. The horizontal scale in this region was expanded to clearly show the dra- matic change in characteristics in this region. Note the exponential increase in col- lector current as the voltage VCB increases toward 0 V. In the saturation region the collector-base and base-emitter junctions are forward-biased. The input characteristics of Fig. 3.7 reveal that for fixed values of collector volt- age (VCB), as the base-to-emitter voltage increases, the emitter current increases in a manner that closely resembles the diode characteristics. In fact, increasing levels of VCB have such a small effect on the characteristics that as a first approximation the change due to changes in VCB can be ignored and the characteristics drawn as shown in Fig. 3.10a. If we then apply the piecewise-linear approach, the characteristics of Fig. 3.10b will result. Taking it a step further and ignoring the slope of the curve and therefore the resistance associated with the forward-biased junction will result in the characteristics of Fig. 3.10c. For the analysis to follow in this book the equivalent model of Fig. 3.10c will be employed for all dc analysis of transistor networks. That is, once a transistor is in the “on” state, the base-to-emitter voltage will be assumed to be the following: VBE  0.7 V (3.4) In other words, the effect of variations due to VCB and the slope of the input charac- teristics will be ignored as we strive to analyze transistor networks in a manner that will provide a good approximation to the actual response without getting too involved with parameter variations of less importance. I E (mA) I E (mA) I E (mA) 8 8 8 7 7 7 Any V CB 6 6 6 5 5 5 4 4 4 3 3 3 2 2 2 1 1 0.7 V 1 0.7 V 0 0.2 0.4 0.6 0.8 1 VBE (V) 0 0.2 0.4 0.6 0.8 1 VBE (V) 0 0.2 0.4 0.6 0.8 1 VBE (V) (a) (b) (c) Figure 3.10 Developing the equivalent model to be employed for the base-to- emitter region of an amplifier in the dc mode. It is important to fully appreciate the statement made by the characteristics of Fig. 3.10c. They specify that with the transistor in the “on” or active state the voltage from base to emitter will be 0.7 V at any level of emitter current as controlled by the ex- ternal network. In fact, at the first encounter of any transistor configuration in the dc mode, one can now immediately specify that the voltage from base to emitter is 0.7 V if the device is in the active region—a very important conclusion for the dc analysis to follow. 3.4 Common-Base Configuration 117  EXAMPLE 3.1 (a) Using the characteristics of Fig. 3.8, determine the resulting collector current if IE  3 mA and VCB  10 V. (b) Using the characteristics of Fig. 3.8, determine the resulting collector current if IE remains at 3 mA but VCB is reduced to 2 V. (c) Using the characteristics of Figs. 3.7 and 3.8, determine VBE if IC  4 mA and VCB  20 V. (d) Repeat part (c) using the characteristics of Figs. 3.8 and 3.10c. Solution (a) The characteristics clearly indicate that IC  IE  3 mA. (b) The effect of changing VCB is negligible and IC continues to be 3 mA. (c) From Fig. 3.8, IE  IC  4 mA. On Fig. 3.7 the resulting level of VBE is about 0.74 V. (d) Again from Fig. 3.8, IE  IC  4 mA. However, on Fig. 3.10c, VBE is 0.7 V for any level of emitter current. Alpha () In the dc mode the levels of IC and IE due to the majority carriers are related by a quantity called alpha and defined by the following equation: I dc  C (3.5) IE where IC and IE are the levels of current at the point of operation. Even though the characteristics of Fig. 3.8 would suggest that   1, for practical devices the level of alpha typically extends from 0.90 to 0.998, with most approaching the high end of the range. Since alpha is defined solely for the majority carriers, Eq. (3.2) becomes IC  IE  ICBO (3.6) For the characteristics of Fig. 3.8 when IE  0 mA, IC is therefore equal to ICBO, but as mentioned earlier, the level of ICBO is usually so small that it is virtually un- detectable on the graph of Fig. 3.8. In other words, when IE  0 mA on Fig. 3.8, IC also appears to be 0 mA for the range of VCB values. For ac situations where the point of operation moves on the characteristic curve, an ac alpha is defined by IC ac   IE VCB  constant (3.7) The ac alpha is formally called the common-base, short-circuit, amplification factor, for reasons that will be more obvious when we examine transistor equivalent circuits in Chapter 7. For the moment, recognize that Eq. (3.7) specifies that a relatively small change in collector current is divided by the corresponding change in IE with the collector-to-base voltage held constant. For most situations the magnitudes of ac and dc are quite close, permitting the use of the magnitude of one for the other. The use of an equation such as (3.7) will be demonstrated in Section 3.6. Biasing The proper biasing of the common-base configuration in the active region can be de- termined quickly using the approximation IC  IE and assuming for the moment that 118 Chapter 3 Bipolar Junction Transistors  Figure 3.11 Establishing the proper biasing management for a common-base pnp transistor in the active region. IB  0 A. The result is the configuration of Fig. 3.11 for the pnp transistor. The ar- row of the symbol defines the direction of conventional flow for IE  IC. The dc sup- plies are then inserted with a polarity that will support the resulting current direction. For the npn transistor the polarities will be reversed. Some students feel that they can remember whether the arrow of the device sym- bol in pointing in or out by matching the letters of the transistor type with the ap- propriate letters of the phrases “pointing in” or “not pointing in.” For instance, there is a match between the letters npn and the italic letters of not pointing in and the let- ters pnp with pointing in. 3.5 TRANSISTOR AMPLIFYING ACTION Now that the relationship between IC and IE has been established in Section 3.4, the basic amplifying action of the transistor can be introduced on a surface level using the network of Fig. 3.12. The dc biasing does not appear in the figure since our in- terest will be limited to the ac response. For the common-base configuration the ac input resistance determined by the characteristics of Fig. 3.7 is quite small and typi- cally varies from 10 to 100 . The output resistance as determined by the curves of Fig. 3.8 is quite high (the more horizontal the curves the higher the resistance) and typically varies from 50 k to 1 M (100 k for the transistor of Fig. 3.12). The dif- ference in resistance is due to the forward-biased junction at the input (base to emit- ter) and the reverse-biased junction at the output (base to collector). Using a common value of 20  for the input resistance, we find that V 200 mV Ii  i    10 mA Ri 20  If we assume for the moment that ac  1 (Ic  Ie), IL  Ii  10 mA and VL  ILR  (10 mA)(5 k)  50 V Ii pnp IL E C + + B Ri Ro V i = 200 mV R 5 k Ω VL 20 Ω 100 k Ω – – Figure 3.12 Basic voltage amplification action of the common-base configuration. 3.5 Transistor Amplifying Action 119  The voltage amplification is VL 50 V Av      250 Vi 200 mV Typical values of voltage amplification for the common-base configuration vary from 50 to 300. The current amplification (IC/IE) is always less than 1 for the com- mon-base configuration. This latter characteristic should be obvious since IC  IE and  is always less than 1. The basic amplifying action was produced by transferring a current I from a low- to a high-resistance circuit. The combination of the two terms in italics results in the label transistor; that is, transfer  resistor → transistor 3.6 COMMON-EMITTER CONFIGURATION The most frequently encountered transistor configuration appears in Fig. 3.13 for the pnp and npn transistors. It is called the common-emitter configuration since the emit- ter is common or reference to both the input and output terminals (in this case com- mon to both the base and collector terminals). Two sets of characteristics are again necessary to describe fully the behavior of the common-emitter configuration: one for the input or base-emitter circuit and one for the output or collector-emitter circuit. Both are shown in Fig. 3.14. Figure 3.13 Notation and sym- bols used with the common-emit- ter configuration: (a) npn transis- tor; (b) pnp transistor. The emitter, collector, and base currents are shown in their actual conventional current direction. Even though the transistor configuration has changed, the current relations developed earlier for the common-base configuration are still applicable. That is, IE  IC  IB and IC  IE. For the common-emitter configuration the output characteristics are a plot of the output current (IC) versus output voltage (VCE) for a range of values of input current (IB). The input characteristics are a plot of the input current (IB) versus the input volt- age (VBE) for a range of values of output voltage (VCE). 120 Chapter 3 Bipolar Junction Transistors  IC (mA) 8 90 µA 7 80 µA 70 µA I B (µA) 6 VCE = 1 V 60 µA VCE = 10 V 100 (Saturation region) 5 50 µA VCE = 20 V 90 40 µA 80 4 70 30 µA 60 3 (Active region) 50 20 µA 2 40 30 10 µA 1 20 I B = 0 µA 10 0 5 10 15 20 VCE (V) 0 0.2 0.4 0.6 0.8 1.0 VBE (V) VCEsat (Cutoff region) ~ β I CBO I CEO = (a) (b) Figure 3.14 Characteristics of a silicon transistor in the common-emitter config- uration: (a) collector characteristics; (b) base characteristics. Note that on the characteristics of Fig. 3.14 the magnitude of IB is in microam- peres, compared to milliamperes of IC. Consider also that the curves of IB are not as horizontal as those obtained for IE in the common-base configuration, indicating that the collector-to-emitter voltage will influence the magnitude of the collector current. The active region for the common-emitter configuration is that portion of the upper-right quadrant that has the greatest linearity, that is, that region in which the curves for IB are nearly straight and equally spaced. In Fig. 3.14a this region exists to the right of the vertical dashed line at VCEsat and above the curve for IB equal to zero. The region to the left of VCEsat is called the saturation region. In the active region of a common-emitter amplifier the collector-base junction is reverse-biased, while the base-emitter junction is forward-biased. You will recall that these were the same conditions that existed in the active re- gion of the common-base configuration. The active region of the common-emitter configuration can be employed for voltage, current, or power amplification. The cutoff region for the common-emitter configuration is not as well defined as for the common-base configuration. Note on the collector characteristics of Fig. 3.14 that IC is not equal to zero when IB is zero. For the common-base configuration, when the input current IE was equal to zero, the collector current was equal only to the re- verse saturation current ICO, so that the curve IE  0 and the voltage axis were, for all practical purposes, one. The reason for this difference in collector characteristics can be derived through the proper manipulation of Eqs. (3.3) and (3.6). That is, Eq. (3.6): IC  IE  ICBO Substitution gives Eq. (3.3): IC  (IC  IB)  ICBO IB ICBO Rearranging yields IC     (3.8) 1  1  3.6 Common-Emitter Configuration 121  If we consider the case discussed above, where IB  0 A, and substitute a typical value of  such as 0.996, the resulting collector current is the following: (0 A) ICBO IC      1  1 0.996 ICBO    250ICBO 0.004 If ICBO were 1 A, the resulting collector current with IB  0 A would be 250(1 A)  0.25 mA, as reflected in the characteristics of Fig. 3.14. For future reference, the collector current defined by the condition IB  0 A will be assigned the notation indicated by Eq. (3.9). ICEO   ICBO 1    IB  0 A (3.9) In Fig. 3.15 the conditions surrounding this newly defined current are demonstrated with its assigned reference direction. For linear (least distortion) amplification purposes, cutoff for the common- emitter configuration will be defined by IC  ICEO. In other words, the region below IB  0 A is to be avoided if an undistorted out- put signal is required. When employed as a switch in the logic circuitry of a computer, a transistor will have two points of operation of interest: one in the cutoff and one in the saturation region. The cutoff condition should ideally be IC  0 mA for the chosen VCE voltage. Since ICEO is typically low in magnitude for silicon materials, cutoff will exist for switching purposes when IB  0 A or IC  ICEO for silicon transistors only. For ger- manium transistors, however, cutoff for switching purposes will be defined as those conditions that exist when IC  ICBO. This condition can normally be obtained for germanium transistors by reverse-biasing the base-to-emitter junction a few tenths of a volt. Recall for the common-base configuration that the input set of characteristics was approximated by a straight-line equivalent that resulted in VBE  0.7 V for any level of IE greater than 0 mA. For the common-emitter configuration the same approach can be taken, resulting in the approximate equivalent of Fig. 3.16. The result supports our earlier conclusion that for a transistor in the “on” or active region the base-to- emitter voltage is 0.7 V. In this case the voltage is fixed for any level of base current. I B (µA) 100 90 80 70 60 50 40 30 20 10 0 Figure 3.16 Piecewise-linear 0.2 0.4 0.6 0.8 1 V BE (V) Figure 3.15 Circuit conditions equivalent for the diode character- related to ICEO. 0.7 V istics of Fig. 3.14b. 122 Chapter 3 Bipolar Junction Transistors (a) Using the characteristics of Fig. 3.14, determine IC at IB  30 A and VCE  EXAMPLE 3.2 10 V. (b) Using the characteristics of Fig. 3.14, determine IC at VBE  0.7 V and VCE  15 V. Solution (a) At the intersection of IB  30 A and VCE  10 V, IC  3.4 mA. (b) Using Fig. 3.14b, IB  20 A at VBE  0.7 V. From Fig. 3.14a we find that IC  2.5 mA at the intersection of IB  20 A and VCE  15 V. Beta ( ) In the dc mode the levels of IC and IB are related by a quantity called beta and de- fined by the following equation: I dc  C (3.10) IB where IC and IB are determined at a particular operating point on the characteristics. For practical devices the level of typically ranges from about 50 to over 400, with most in the midrange. As for , certainly reveals the relative magnitude of one cur- rent to the other. For a device with a of 200, the collector current is 200 times the magnitude of the base current. On specification sheets dc is usually included as hFE with the h derived from an ac hybrid equivalent circuit to be introduced in Chapter 7. The subscripts FE are de- rived from forward-current amplification and common-emitter configuration, respec- tively. For ac situations an ac beta has been defined as follows: IC ac   IB  VCE  constant (3.11) The formal name for ac is common-emitter, forward-current, amplification factor. Since the collector current is usually the output current for a common-emitter con- figuration and the base current the input current, the term amplification is included in the nomenclature above. Equation (3.11) is similar in format to the equation for ac in Section 3.4. The procedure for obtaining ac from the characteristic curves was not described because of the difficulty of actually measuring changes of IC and IE on the characteristics. Equation (3.11), however, is one that can be described with some clarity, and in fact, the result can be used to find ac using an equation to be derived shortly. On specification sheets ac is normally referred to as hfe. Note that the only dif- ference between the notation used for the dc beta, specifically, dc  hFE, is the type of lettering for each subscript quantity. The lowercase letter h continues to refer to the hybrid equivalent circuit to be described in Chapter 7 and the fe to the forward current gain in the common-emitter configuration. The use of Eq. (3.11) is best described by a numerical example using an actual set of characteristics such as appearing in Fig. 3.14a and repeated in Fig. 3.17. Let us determine ac for a region of the characteristics defined by an operating point of IB  25 A and VCE  7.5 V as indicated on Fig. 3.17. The restriction of VCE  con- stant requires that a vertical line be drawn through the operating point at VCE  7.5 V. At any location on this vertical line the voltage VCE is 7.5 V, a constant. The change 3.6 Common-Emitter Configuration 123  I C (mA) 9 8 90 µA 80 µA 7 70 µA 6 60 µA 50 µA 5 40 µA 4 IC2 IB 2 30 µA 3 25 µA ∆ IC Q - pt. 20 µA IC1 2 IB1 10 µA 1 IB = 0 µA 0 5 10 15 20 25 VCE (V) VCE = 7.5 V Figure 3.17 Determining ac and dc from the collector characteristics. in IB (IB) as appearing in Eq. (3.11) is then defined by choosing two points on ei- ther side of the Q-point along the vertical axis of about equal distances to either side of the Q-point. For this situation the IB  20 A and 30 A curves meet the re- quirement without extending too far from the Q-point. They also define levels of IB that are easily defined rather than have to interpolate the level of IB between the curves. It should be mentioned that the best determination is usually made by keeping the chosen IB as small as possible. At the two intersections of IB and the vertical axis, the two levels of IC can be determined by drawing a horizontal line over to the ver- tical axis and reading the resulting values of IC. The resulting ac for the region can then be determined by IC IC2 IC1 ac   IB VCE  constant   IB2 IB1 3.2 mA 2.2 mA 1 mA     30 A 20 A 10 A  100 The solution above reveals that for an ac input at the base, the collector current will be about 100 times the magnitude of the base current. If we determine the dc beta at the Q-point: I 2.7 mA  C    108 dc IB 25 A 124 Chapter 3 Bipolar Junction Transistors  Although not exactly equal, the levels of ac and dc are usually reasonably close and are often used interchangeably. That is, if ac is known, it is assumed to be about the same magnitude as dc, and vice versa. Keep in mind that in the same lot, the value of ac will vary somewhat from one transistor to the next even though each transistor has the same number code. The variation may not be significant but for the majority of applications, it is certainly sufficient to validate the approximate approach above. Generally, the smaller the level of ICEO, the closer the magnitude of the two betas. Since the trend is toward lower and lower levels of ICEO, the validity of the foregoing approximation is further substantiated. If the characteristics had the appearance of those appearing in Fig. 3.18, the level of ac would be the same in every region of the characteristics. Note that the step in IB is fixed at 10 A and the vertical spacing between curves is the same at every point in the characteristics—namely, 2 mA. Calculating the ac at the Q-point indicated will result in IC  9 mA 7 mA 2 mA        200 ac IB VCE  constant 45 A 35 A 10 A Determining the dc beta at the same Q-point will result in I 8 mA  C    200 dc IB 40 A revealing that if the characteristics have the appearance of Fig. 3.18, the magnitude of ac and dc will be the same at every point on the characteristics. In particular, note that ICEO  0 A. Although a true set of transistor characteristics will never have the exact appear- ance of Fig. 3.18, it does provide a set of characteristics for comparison with those obtained from a curve tracer (to be described shortly). Figure 3.18 Characteristics in which ac is the same everywhere and ac  dc. For the analysis to follow the subscript dc or ac will not be included with to avoid cluttering the expressions with unnecessary labels. For dc situations it will sim- ply be recognized as dc and for any ac analysis as ac. If a value of is specified for a particular transistor configuration, it will normally be used for both the dc and ac calculations. 3.6 Common-Emitter Configuration 125  A relationship can be developed between and  using the basic relationships introduced thus far. Using  IC/IB we have IB  IC/ , and from   IC/IE we have IE  IC/. Substituting into IE  IC  IB I I we have C  IC  C  and dividing both sides of the equation by IC will result in 1 1   1    or      (  1) so that    (3.12a) 1  or   (3.12b) 1  In addition, recall that ICBO ICEO    1  but using an equivalence of 1   1 1  derived from the above, we find that ICEO  (  1)ICBO or ICEO  ICBO (3.13) as indicated on Fig. 3.14a. Beta is a particularly important parameter because it provides a direct link between current levels of the input and output circuits for a common-emitter configuration. That is, IC  IB (31.4) and since IE  IC  IB  IB  IB we have IE  (  1)IB (3.15) Both of the equations above play a major role in the analysis in Chapter 4. Biasing The proper biasing of a common-emitter amplifier can be determined in a manner similar to that introduced for the common-base configuration. Let us assume that we are presented with an npn transistor such as shown in Fig. 3.19a and asked to apply the proper biasing to place the device in the active region. The first step is to indicate the direction of IE as established by the arrow in the transistor symbol as shown in Fig. 3.19b. Next, the other currents are introduced as 126 Chapter 3 Bipolar Junction Transistors Figure 3.19 Determining the proper biasing arrangement for a common- emitter npn transistor configuration. shown, keeping in mind the Kirchhoff’s current law relationship: IC  IB  IE. Fi- nally, the supplies are introduced with polarities that will support the resulting direc- tions of IB and IC as shown in Fig. 3.19c to complete the picture. The same approach can be applied to pnp transistors. If the transistor of Fig. 3.19 was a pnp transistor, all the currents and polarities of Fig. 3.19c would be reversed. 3.7 COMMON-COLLECTOR CONFIGURATION The third and final transistor configuration is the common-collector configuration, shown in Fig. 3.20 with the proper current directions and voltage notation. The common-collector configuration is used primarily for impedance-matching purposes since it has a high input impedance and low output impedance, opposite to that of the common-base and common-emitter configurations. IE IE E E IB p IB n n V EE p V EE B B p n V BB V BB C IC C IC IE IE E E IB IB B B IC IC Figure 3.20 Notation and sym- C C bols used with the common-col- lector configuration: (a) pnp tran- (a) (b) sistor; (b) npn transistor. 3.7 Common-Collector Configuration 127  C A common-collector circuit configuration is provided in Fig. 3.21 with the load resistor connected from emitter to ground. Note that the collector is tied to ground even though the transistor is connected in a manner similar to the common-emitter B configuration. From a design viewpoint, there is no need for a set of common- collector characteristics to choose the parameters of the circuit of Fig. 3.21. It can E be designed using the common-emitter characteristics of Section 3.6. For all practi- R cal purposes, the output characteristics of the common-collector configuration are the same as for the common-emitter configuration. For the common-collector configura- tion the output characteristics are a plot of IE versus VEC for a range of values of IB. The input current, therefore, is the same for both the common-emitter and common- Figure 3.21 Common-collector configuration used for collector characteristics. The horizontal voltage axis for the common-collector con- impedance-matching purposes. figuration is obtained by simply changing the sign of the collector-to-emitter voltage of the common-emitter characteristics. Finally, there is an almost unnoticeable change in the vertical scale of IC of the common-emitter characteristics if IC is replaced by IE for the common-collector characteristics (since   1). For the input circuit of the common-collector configuration the common-emitter base characteristics are suffi- cient for obtaining the required information. 3.8 LIMITS OF OPERATION For each transistor there is a region of operation on the characteristics which will en- sure that the maximum ratings are not being exceeded and the output signal exhibits minimum distortion. Such a region has been defined for the transistor characteristics of Fig. 3.22. All of the limits of operation are defined on a typical transistor specifi- cation sheet described in Section 3.9. Some of the limits of operation are self-explanatory, such as maximum collector current (normally referred to on the specification sheet as continuous collector cur- rent) and maximum collector-to-emitter voltage (often abbreviated as VCEO or V(BR)CEO on the specification sheet). For the transistor of Fig. 3.22, ICmax was specified as 50 mA and VCEO as 20 V. The vertical line on the characteristics defined as VCEsat specifies Figure 3.22 Defining the linear (undistorted) region of operation for a transistor. 128 Chapter 3 Bipolar Junction Transistors the minimum VCE that can be applied without falling into the nonlinear region labeled the saturation region. The level of VCEsat is typically in the neighborhood of the 0.3 V specified for this transistor. The maximum dissipation level is defined by the following equation: PCmax  VCEIC (3.16) For the device of Fig. 3.22, the collector power dissipation was specified as 300 mW. The question then arises of how to plot the collector power dissipation curve specified by the fact that PCmax  VCEIC  300 mW or VCEIC  300 mW At any point on the characteristics the product of VCE and IC must be equal to 300 mW. If we choose IC to be the maximum value of 50 mA and substitute into the relationship above, we obtain VCEIC  300 mW VCE (50 mA)  300 mW 300 mW VCE    6 V 50 mA As a result we find that if IC  50 mA, then VCE  6 V on the power dissipation curve as indicated in Fig. 3.22. If we now choose VCE to be its maximum value of 20 V, the level of IC is the following: (20 V)IC  300 mW 300 mW IC    15 mA 20 V defining a second point on the power curve. If we now choose a level of IC in the midrange such as 25 mA, and solve for the resulting level of VCE, we obtain VCE(25 mA)  300 mW 300 mW and VCE    12 V 25 mA as also indicated on Fig. 3.22. A rough estimate of the actual curve can usually be drawn using the three points defined above. Of course, the more points you have, the more accurate the curve, but a rough estimate is normally all that is required. The cutoff region is defined as that region below IC  ICEO. This region must also be avoided if the output signal is to have minimum distortion. On some specification sheets only ICBO is provided. One must then use the equation ICEO  ICBO to es- tablish some idea of the cutoff level if the characteristic curves are unavailable. Op- eration in the resulting region of Fig. 3.22 will ensure minimum distortion of the out- put signal and current and voltage levels that will not damage the device. If the characteristic curves are unavailable or do not appear on the specification sheet (as is often the case), one must simply be sure that IC, VCE, and their product VCEIC fall into the range appearing in Eq. (3.17). 3.8 Limits of Operation 129  ICEO IC ICmax VCEsat VCE VCEmax (3.17) VCEIC PCmax For the common-base characteristics the maximum power curve is defined by the fol- lowing product of output quantities: PCmax  VCBIC (3.18) 3.9 TRANSISTOR SPECIFICATION SHEET Since the specification sheet is the communication link between the manufacturer and user, it is particularly important that the information provided be recognized and cor- rectly understood. Although all the parameters have not been introduced, a broad num- ber will now be familiar. The remaining parameters will be introduced in the chap- ters that follow. Reference will then be made to this specification sheet to review the manner in which the parameter is presented. The information provided as Fig. 3.23 is taken directly from the Small-Signal Transistors, FETs, and Diodes publication prepared by Motorola Inc. The 2N4123 is a general-purpose npn transistor with the casing and terminal identification appear- ing in the top-right corner of Fig. 3.23a. Most specification sheets are broken down into maximum ratings, thermal characteristics, and electrical characteristics. The electrical characteristics are further broken down into “on,” “off,” and small-signal characteristics. The “on” and “off” characteristics refer to dc limits, while the small- signal characteristics include the parameters of importance to ac operation. Note in the maximum rating list that VCEmax  VCEO  30 V with ICmax  200 mA. The maximum collector dissipation PCmax  PD  625 mW. The derating factor un- der the maximum rating specifies that the maximum rating must be decreased 5 mW for every 1° rise in temperature above 25°C. In the “off” characteristics ICBO is spec- ified as 50 nA and in the “on” characteristics VCEsat  0.3 V. The level of hFE has a range of 50 to 150 at IC  2 mA and VCE  1 V and a minimum value of 25 at a higher current of 50 mA at the same voltage. The limits of operation have now been defined for the device and are repeated be- low in the format of Eq. (3.17) using hFE  150 (the upper limit) and ICEO  ICBO  (150)(50 nA)  7.5 A. Certainly, for many applications the 7.5 A  0.0075 mA can be considered to be 0 mA on an approximate basis. Limits of Operation 7.5 mA IC 200 mA 0.3 V VCE 30 V VCEIC 650 mW In the small-signal characteristics the level of hfe ( ac) is provided along with a plot of how it varies with collector current in Fig. 3.23f. In Fig. 3.23j the effect of temperature and collector current on the level of hFE ( ac) is demonstrated. At room temperature (25°C), note that hFE ( dc) is a maximum value of 1 in the neighborhood of about 8 mA. As IC increased beyond this level, hFE drops off to one-half the value with IC equal to 50 mA. It also drops to this level if IC decreases to the low level of 0.15 mA. Since this is a normalized curve, if we have a transistor with dc  hFE  50 at room temperature, the maximum value at 8 mA is 50. At IC  50 mA it has dropped to 50/2  25. In other words, normalizing reveals that the actual level of hFE 130 Chapter 3 Bipolar Junction Transistors at any level of IC has been divided by the maximum value of hFE at that temperature and IC  8 mA. Note also that the horizontal scale of Fig. 3.23j is a log scale. Log scales are examined in depth in Chapter 11. You may want to look back at the plots of this section when you find time to review the first few sections of Chapter 11. Figure 3.23 Transistor specification sheet. 3.9 Transistor Specification Sheet 131  Before leaving this description of the characteristics, take note of the fact that the actual collector characteristics are not provided. In fact, most specification sheets as provided by the range of manufacturers fail to provide the full characteristics. It is expected that the data provided are sufficient to use the device effectively in the de- sign process. As noted in the introduction to this section, all the parameters of the specification sheet have not been defined in the preceding sections or chapters. However, the spec- ification sheet provided in Fig. 3.23 will be referenced continually in the chapters to follow as parameters are introduced. The specification sheet can be a very valuable tool in the design or analysis mode, and every effort should be made to be aware of the importance of each parameter and how it may vary with changing levels of cur- rent, temperature, and so on. Figure 1 – Capacitance Figure 2 – Switching Times 10 200 ts 7.0 100 5.0 70 Capacitance (pF) C ibo 50 3.0 Time (ns) 30 td tr 20 tf Cobo 2.0 VCC = 3 V 10.0 IC / IB = 10 7.0 VEB (off) = 0.5 V 1.0 5.0 0.1 0.2 0.3 0.5 0.7 1.0 2.0 3.0 5.0 7.0 10 20 30 40 1.0 2.0 3.0 5.0 10 20 30 50 100 200 Reverse bias voltage (V) I C , Collector current (mA) (b) (c) AUDIO SMALL SIGNAL CHARACTERISTICS NOISE FIGURE (VCE = 5 Vdc, TA = 25°C) Bandwidth = 1.0 Hz Figure 3 – Frequency Variations Figure 4 – Source Resistance 12 14 f = 1 kHz 10 Source resistance = 200 Ω 12 IC = 1 mA IC = 1 mA Source resistance = 200 Ω 10 MF, Noise figure (dB) MF, Noise figure (dB) 8 IC = 0.5 mA IC = 0.5 mA 8 Source resistance = 1 k Ω 6 IC = 50 µ A IC = 50 µ A 6 4 4 IC = 100 µ A 2 2 Source resistance = 500 Ω IC = 100 µ A 0 0 0.1 0.2 0.4 1 2 4 10 20 40 100 0.1 0.2 0.4 1.0 2.0 4.0 10 20 40 100 f, Frequency (kHz) R S , Source Resistance (kΩ ) (d) (e) Figure 3.23 Continued. 132 Chapter 3 Bipolar Junction Transistors  h PARAMETERS VCE = 10 V, f = 1 kHz, TA = 25°C Figure 5 – Current Gain Figure 6 – Output Admittance 300 100 h oe Output admittance (µ mhos) 200 50 h fe Current gain 20 100 10 70 5.0 50 2.0 30 1.0 0.1 0.2 0.5 1.0 2.0 5.0 10 0.1 0.2 0.5 1.0 2.0 5.0 10 I C , Collector current (mA) I C , Collector current (mA) (f) (g) Figure 7 – Input Impedance Figure 8 – Voltage Feedback Ratio 20 10 h re Voltage feedback ratio (× 10−4 ) 10 7.0 h ie Input impedance (kΩ) 5.0 5.0 3.0 2.0 2.0 1.0 0.5 1.0 0.7 0.2 0.5 0.1 0.2 0.5 1.0 2.0 5.0 10 0.1 0.2 0.5 1.0 2.0 5.0 10 I C , Collector current (mA) I C , Collector current (mA) (h) (i) STATIC CHARACTERISTICS (h) (i) STATIC CHARACTERISTICS Figure 9 – DC Current Gain 2.0 TJ = +125° C VCE = 1 V h FE DC Current gain (normalized) 1.0 +25° C 0.7 0.5 –55°C 0.3 0.2 0.1 0.1 0.2 0.3 0.5 0.7 1.0 2.0 3.0 5.0 7.0 10 20 30 50 70 100 200 I C , Collector current (mA) (j) Figure 3.23 Continued. 3.9 Transistor Specification Sheet 133  3.10 TRANSISTOR TESTING As with diodes, there are three routes one can take to check a transistor: curve tracer, digital meter, and ohmmeter. Curve Tracer The curve tracer of Fig. 1.45 will provide the display of Fig. 3.24 once all the con- trols have been properly set. The smaller displays to the right reveal the scaling to be applied to the characteristics. The vertical sensitivity is 2 mA/div, resulting in the scale shown to the left of the monitor’s display. The horizontal sensitivity is 1 V/div, re- sulting in the scale shown below the characteristics. The step function reveals that the curves are separated by a difference of 10 A, starting at 0 A for the bottom curve. The last scale factor provided can be used to quickly determine the ac for any re- gion of the characteristics. Simply multiply the displayed factor by the number of di- visions between IB curves in the region of interest. For instance, let us determine ac at a Q-point of IC  7 mA and VCE  5 V. In this region of the display, the distance between IB curves is 190 of a division, as indicated on Fig. 3.25. Using the factor spec- ified, we find that   9 200 ac   div   180 10 div 20 mA 18 mA Vertical 80 µ A per div 2 mA 16 mA 70 µA 14 mA 60 µA Horizontal per div 12 mA 1V 50 µA 10 mA 40 µA 8 mA Per Step 30 µA 10 µ A 6 mA 20 µA 4 mA B or gm 10 µA per div 2 mA 200 Figure 3.24 Curve tracer 0 µA response to 2N3904 npn 0 mA transistor. 0V 1V 2V 3V 4V 5V 6V 7V 8V 9V 10 V IC = 8 mA IB 2 = 40 µ A IC 2 = 8.2 mA ∆ IC ≅ 10 9 div Q-point ( IC = 7 m A, VCE = 5 V) IB 1 = 30 µ A Figure 3.25 Determining ac IC 1 = 6.4 mA for the transistor characteristics of Fig. 3.24 at IC  7 mA and VCE  5 V. IC = 6 mA VCE = 5 V 134 Chapter 3 Bipolar Junction Transistors Using Eq. (3.11) gives us IC IC2 IC1  8.2 mA 6.4 mA      ac IB VCE  constant IB2 IB1 40 A 30 A 1.8 mA    180 10 A verifying the determination above. Advanced Digital Meters Advanced digital meters such as that shown in Fig. 3.26 are now available that can provide the level of hFE using the lead sockets appearing at the bottom left of the dial. Note the choice of pnp or npn and the availability of two emitter connections to han- dle the sequence of leads as connected to the casing. The level of hFE is determined at a collector current of 2 mA for the Testmate 175A, which is also provided on the digital display. Note that this versatile instrument can also check a diode. It can mea- Figure 3.26 Transistor tester. sure capacitance and frequency in addition to the normal functions of voltage, cur- (Courtesy Computronics Technol- rent, and resistance measurements. ogy, Inc.) In fact, in the diode testing mode it can be used to check the p-n junctions of a transistor. With the collector open the base-to-emitter junction should result in a low voltage of about 0.7 V with the red (positive) lead connected to the base and the black (negative) lead connected to the emitter. A reversal of the leads should result in an OL indication to represent the reverse-biased junction. Similarly, with the emitter open, the forward- and reverse-bias states of the base-to-collector junction can be checked. Ohmmeter Low R An ohmmeter or the resistance scales of a DMM can be used to check the state of a Open transistor. Recall that for a transistor in the active region the base-to-emitter junction Ω B is forward-biased and the base-to-collector junction is reverse-biased. Essentially, + – therefore, the forward-biased junction should register a relatively low resistance while the reverse-biased junction shows a much higher resistance. For an npn transistor, the E forward-biased junction (biased by the internal supply in the resistance mode) from base to emitter should be checked as shown in Fig. 3.27 and result in a reading that Figure 3.27 Checking the will typically fall in the range of 100  to a few kilohms. The reverse-biased base- forward-biased base-to-emitter junction of an npn transistor. to-collector junction (again reverse-biased by the internal supply) should be checked as shown in Fig. 3.28 with a reading typically exceeding 100 k. For a pnp transis- High R tor the leads are reversed for each junction. Obviously, a large or small resistance in both directions (reversing the leads) for either junction of an npn or pnp transistor in- Ω dicates a faulty device. + – C If both junctions of a transistor result in the expected readings the type of tran- sistor can also be determined by simply noting the polarity of the leads as applied to the base-emitter junction. If the positive () lead is connected to the base and the B negative lead ( ) to the emitter a low resistance reading would indicate an npn tran- sistor. A high resistance reading would indicate a pnp transistor. Although an ohm- E meter can also be used to determine the leads (base, collector and emitter) of a tran- Figure 3.28 Checking the sistor it is assumed that this determination can be made by simply looking at the reverse-biased base-to-collector orientation of the leads on the casing. junction of an npn transistor. 3.10 Transistor Testing 135  3.11 TRANSISTOR CASING AND TERMINAL IDENTIFICATION After the transistor has been manufactured using one of the techniques described in Chapter 12, leads of, typically, gold, aluminum, or nickel are then attached and the entire structure is encapsulated in a container such as that shown in Fig. 3.29. Those with the heavy duty construction are high-power devices, while those with the small can (top hat) or plastic body are low- to medium-power devices. Figure 3.29 Various types of transistors: (a) Courtesy General Electric Company; (b) and (c) Courtesy of Motorola Inc.; (d) Courtesy International Rectifier Corpo- ration. Whenever possible, the transistor casing will have some marking to indicate which leads are connected to the emitter, collector, or base of a transistor. A few of the meth- ods commonly used are indicated in Fig. 3.30. Figure 3.30 Transistor terminal identification. The internal construction of a TO-92 package in the Fairchild line appears in Fig. 3.31. Note the very small size of the actual semiconductor device. There are gold bond wires, a copper frame, and an epoxy encapsulation. Four (quad) individual pnp silicon transistors can be housed in the 14-pin plastic dual-in-line package appearing in Fig. 3.32a. The internal pin connections appear in Fig. 3.32b. As with the diode IC package, the indentation in the top surface reveals the number 1 and 14 pins. 136 Chapter 3 Bipolar Junction Transistors Figure 3.31 Internal construction of a Fairchild transistor in a TO-92 package. (Courtesy Fairchild Camera and Instrument Corporation.) (Top View) C B E NC E B C 14 13 12 11 10 9 8 1 2 3 4 5 6 7 C B E NC E B C NC – No internal connection (a) (b) Figure 3.32 Type Q2T2905 Texas Instruments quad pnp silicon transistors: (a) appearance; (b) pin connections. (Courtesy Texas Instruments Incorporated.) 3.11 Transistor Casing and Terminal Identification 137  3.12 PSPICE WINDOWS Since the transistor characteristics were introduced in this chapter it seems appropri- ate that a procedure for obtaining those characteristics using PSpice Windows should be examined. The transistors are listed in the EVAL.slb library and start with the let- ter Q. The library includes two npn transistors and two pnp transistors. The fact that there are a series of curves defined by the levels of IB will require that a sweep of IB values (a nested sweep) occur within a sweep of collector-to-emitter voltages. This is unnecessary for the diode, however, since only one curve would result. First, the network in Fig. 3.33 is established using the same procedure defined in Chapter 2. The voltage VCC will establish our main sweep while the voltage VBB will determine the nested sweep. For future reference, note the panel at the top right of the menu bar with the scroll control when building networks. This option allows you to retrieve elements that have been used in the past. For instance, if you placed a re- sistor a few elements ago, simply return to the scroll bar and scroll until the resistor R appears. Click the location once, and the resistor will appear on the screen. Figure 3.33 Network employed to obtain the collector characteristics of the Q2N2222 transistor. Next, choose the Analysis Setup icon and enable the DC Sweep. Click on DC Sweep, and choose Voltage Source and Linear. Type in the Name VCC with a Start Value of 0 V and an End Value of 10 V. Use an Increment of 0.01 V to ensure a con- tinuous, detailed plot. Rather than click OK, this time we have to choose the Nested Sweep at the bottom left of the dialog box. When chosen, a DC Nested Sweep dialog box will appear and ask us to repeat the choices just made for the voltage VBB. Again, Voltage Source and Linear are chosen, and the name is inserted as VBB. The Start Value will now be 2.7 V to correspond with an initial current of 20 A as determined by VBB VBE 2.7 V 0.7 V IB