3-(08 august 2014)-bjt

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 Page 1 of 34 L6, L7, & L8 (08 August 2014) Transistors The invention of the transistor by John Bardeen (1908   1991), Walter Brattain (1902   1987), and William Shockley (1910   1989) in 1948 totally revolutionized the world of electronics. For this work, these three men shared the Nobel Prize in Physics in 1956. By 1960, the transistor had replaced the vacuum tube in many electronic applications. The advent of the transistor created a multitrillion-dollar industry that produces such popular devices as personal computers, wireless keyboards, smartphones, electronic book readers, and computer tablets (Serway & Jewett, 2014),  p.1368. I maging the world without this amazing electronics building block, your ce llphone wou ld  be t he size of a washing machine, your laptop wouldn' t fit on your lap (or a single room), an your iPod would still be a gleam in Steve Jobs's eye. A transistor  is a solid-state switch that opens or closes a circuit. Unlike an electromechanical relay, the switching action in a transistor is caused by non-mechanical motion and is due to the change in the electrical characteristics of the device. In addition, they enabled the miniaturization of electronics, leading to the development of cellphones, iPods, GPS systems - and much more. You can say, transistors are the heart of nearly every electronic device in the world, quietly working away without taking up much space, generating a lot of heat, or breaking down every so often. In fact, they were the salient invention that led to the electronic age, integrated circuits, and ultimately the entire digital world. They basically do just two things in electronic circuits: switch and amplify. But those two jobs are the key to getting things done. The beauty of transistors is the way they can control electric current flow in a manner similar to the way a faucet controls the flow of water. With a faucet, the flow of water is controlled by a control knob. With a transistor, a small voltage and/or current applied to a control lead acts to control a larger electric flow t hrough its other two leads. For example, if you can switch electron flow on and off, you have control over the flow, and you can build very involved circuits by incorporating lots of switches in the right places. On the other hand, if you can amplify an electrical signal, then you can store and transmit tiny signals and boost them when you need them to make so mething happen. The diagrams in figure below show some common transistor cases (also called packages). The cases  protect the semiconductor chip on which the t ransistor is built and provide leads t hat can be used to connect it to other components. For each transistor, the diagrams show the lead designations and how to identify them based on the package design. Figure 1. Common transistors (Boysen & Kybett, 2012), p.93.

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Introduction to BJT calcs

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  • Page 1 of 34

    L6, L7, & L8 (08 August 2014)

    Transistors The invention of the transistor by John Bardeen (19081991), Walter Brattain (19021987), and William Shockley (19101989) in 1948 totally revolutionized the world of electronics. For this work, these three men shared the Nobel Prize in Physics in 1956. By 1960, the transistor had replaced the vacuum tube in many electronic applications. The advent of the transistor created a multitrillion-dollar industry that produces such popular devices as personal computers, wireless keyboards, smartphones, electronic book readers, and computer tablets (Serway & Jewett, 2014), p.1368. Imaging the world without this amazing electronics building block, your cellphone would be the size of a washing machine, your laptop wouldn't fit on your lap (or a single room), an your iPod would still be a gleam in Steve Jobs's eye. A transistor is a solid-state switch that opens or closes a circuit. Unlike an electromechanical relay, the switching action in a transistor is caused by non-mechanical motion and is due to the change in the electrical characteristics of the device. In addition, they enabled the miniaturization of electronics, leading to the development of cellphones, iPods, GPS systems - and much more. You can say, transistors are the heart of nearly every electronic device in the world, quietly working away without taking up much space, generating a lot of heat, or breaking down every so often. In fact, they were the salient invention that led to the electronic age, integrated circuits, and ultimately the entire digital world. They basically do just two things in electronic circuits: switch and amplify. But those two jobs are the key to getting things done. The beauty of transistors is the way they can control electric current flow in a manner similar to the way a faucet controls the flow of water. With a faucet, the flow of water is controlled by a control knob. With a transistor, a small voltage and/or current applied to a control lead acts to control a larger electric flow through its other two leads. For example, if you can switch electron flow on and off, you have control over the flow, and you can build very involved circuits by incorporating lots of switches in the right places. On the other hand, if you can amplify an electrical signal, then you can store and transmit tiny signals and boost them when you need them to make something happen. The diagrams in figure below show some common transistor cases (also called packages). The cases protect the semiconductor chip on which the transistor is built and provide leads that can be used to connect it to other components. For each transistor, the diagrams show the lead designations and how to identify them based on the package design.

    Figure 1. Common transistors (Boysen & Kybett, 2012), p.93.

  • Page 2 of 34

    Nowadays, there are many different types of transistors. The three most common types of transistors are: v Bipolar junction transistors (BJTs). v Field-effect transistors (FETs). v Metal-oxide semiconductor field effect transistors (MOSFETs).

    The major difference between the BJTs and FETs is that bipolar transistors require a biasing input (or output) current at their control leads, whereas FETs require only a voltagepractically no current. [Physically speaking, bipolar transistors require both positive (holes) and negative (electrons) carriers to operate, whereas FETs only require one charge carrier.]

  • Page 3 of 34

    Example: Transistors.

    (a) How many leads are there on most transistors?

    (b) Where there are only two leads, what takes the place of the third lead?

    (c) What are the three leads or connections called?

    (d) Why should you take care when soldering transistors into a circuit? Solution:

    (a) Three. (b) The case can be used instead, as indicated in the diagram on the right side of figure above. (This type of case is used for power transistors.) (c) Emitter, base, and collector. (d) Excessive heat can damage a transistor.

    L7.1. Bipolar Junction Transistors-(also see textbook p.90) 1. The Definition and Structure of Bipolar Junction Transistors The bipolar junction transistors (BJTs) were invented in 1945 by Shockley, Brattain, and Bardeen at Bell Laboratories, subsequently replacing vacuum tubes in electronic systems and paving the way for integrated circuits. B consist of two pn -junctions fused together to form a three-layer sandwich-like structure. In other words, you can think of a BJT as functioning like two diodes, connected back-to-back, as illustrated in figure below.

    Figure 2. The structure of two pn-junctions (Boysen & Kybett, 2012), p.94.

  • Page 4 of 34

    However, in the construction process, one important modification is made. Instead of two separate p regions, as shown in figure above, only one thin region is used, as shown in figure below.

    Figure 3. A transistor.

    As we saw, a BJT is a three-terminal device. One terminal is used as the control input, another is connected to the load voltage, while the third is connected to ground or a constant potential. They connect as shown in figure below.

    Figure 4. The three terminals of a transistor (Boysen & Kybett, 2012), p.95.

    When talking about a transistor as two diodes, you refer to the diodes as the base-emitter diode and the base-collector diode. By controlling the voltage applied to the base-emitter junction, you control how that junction is biased (forward or reverse), ultimately controlling the flow of electrical current through the transistor. Shown in figure below is an example comprising of a p layer sandwiched between two n regions and called an " npn " transistor.

    Figure 5. An npn BJT.

  • Page 5 of 34

    Of course, it is also possible to make an " pnp " transistor as well. Both npn and pnp type transistors can be made from either silicon or germanium.

    Figure 6. A pnp BJT.

    v npn BJTs: A thin piece of typep - semiconductor is sandwiched between two thicker pieces of typen - semiconductor, and leads are attached to each of the three sections.

    Figure 7. Schematic of an npn BJT.

    v pnp BJTs: A thin piece of typen - semiconductor is sandwiched between two thicker pieces of typep - semiconductor, and leads are attached to each of the three sections.

    Figure 8. Schematic of a pnp BJT.

    The circuit symbol for the both BJTs are shown in figure below.

    Figure 9. Circuit symbol of an npn BJT.

    As denoted by the bold n in figure above, the typen - silicon in the emitter is more heavily doped than the collector, so the collector and emitter are not interchangeable.

  • Page 6 of 34

    Figure 10. Circuit symbol of a pnp BJT.

    Some general characteristics of a BJT are: v A BJT is an active device that requires power to operate. v The BJT is a current-controlled device whose operation depends on the magnitude of the

    current supplied to the base. v A small base current allows a much larger current to flow between the collector and the

    emitter. v The BJT has three states of operation. These include the off or non-conducting state, the

    linear state, and the saturation state. These states of operation are determined by the magnitude of the BEV and CEV voltage. The former is set by the current supplied to the base.

    v The voltage at the emitter ( EV ) is always lower than the voltage at the base ( BV ) by about 0.6 V.

    v The collector voltage ( CV ) has to be more positive than the emitter voltage ( EV ). v If AC voltages are applied to the base input, then a DC offset voltage (called a bias voltage)

    needs to be added in series to the AC voltage to enable the transistor to be controlled by both the positive and negative parts of the AC signal.

    Example: Transistors.

    (a) Why dont two diodes connected back-to-back function like a transistor?

    (b) Which transistor terminal includes an arrowhead?

    (c) Draw a circuit symbol for both an npn and a pnp transistor.

    (d) Which of the transistors represented by these symbols might be silicon?

  • Page 7 of 34

    (e) Are silicon and germanium ever combined in a transistor? Solution:

    (a) The transistor has one thin p region, whereas the diodes share two thick p regions. (b) The emitter. (c) See figure below.

    (d) Either or both could be silicon. (Either or both could also be germanium) (e) Silicon and germanium are not mixed in any commercially available transistors. However, researchers are attempting to develop ultra-fast transistors that contain both silicon and germanium.

    2. How Bipolar Transistors Work

    Before continuing with the BJT, it is instructive to study an interesting effect in pn -junctions. Figure below is a schematic representation of a pnp BJT along with its attendant circuitry. A very thin typen - base region is sandwiched in between typep - emitter and collector regions. The circuit that includes the emitter-based junction (junction 1) is forward biased, whereas a reverse bias voltage is applied across the base-collector junction (junction 2).

    Figure 11. Schematic diagram of a pnp BJT and its associated circuitry, including input and output voltage-time characteristics showing voltage amplification (Callister & Rethwisch, 2010),

    p.751.

    Figure below illustrates the mechanics of operation in terms of the motion of charge carriers.

  • Page 8 of 34

    Figure 12. For a BJT, the distributions and directions of electron and hole motion (a) When no

    potential is applied; and (b) With appropriate bias for voltage amplification (Callister & Rethwisch, 2010), p.751.

    Because the emitter is typep - and junction 1 is forward biased, large numbers of holes enter the base region. These injected holes are minority carriers in the typen - base, and some will combine with the majority electrons. However, if the base is extremely narrow and the semiconducting materials have been properly prepared, most of these holes will be swept through the base without recombination, then across junction 2 and into the typep - collector. The holes now become a part of the emittercollector circuit. A small increase in input voltage within the emitterbase circuit produces a large increase in current across junction 2. This large increase in collector current is also reflected by a large increase in voltage across the load resistor, which is also shown in the circuit (see Figure 11). Thus, a voltage signal that passes through a junction transistor experiences amplification; this effect is also illustrated in figure above by the two voltagetime plots.

    Similar reasoning applies to the operation of an npn BJT, except that electrons instead of holes are injected across the base and into the collector.

  • Page 9 of 34

    Figure 13. The simple work model of an npn BJT (Scherz & Monk, 2013), p.431.

    Consider the reverse-biased junction depicted in figure below and recall from last class that the depletion region sustains a strong electric field. Now suppose an electron is somehow injected from outside into the right side of the depletion region. What happens to this electron? Serving as a minority carrier on the p side, the electron experiences the electric field and is rapidly swept away into the n side. The ability of a reverse-biased pn -junction to efficiently collect externally-injected electrons proves essential to the operation of the bipolar transistor.

  • Page 10 of 34

    Figure 14. Injection of electrons into depletion region (Razavi, 2014), p.125.

    3. Bipolar Transistor Water Analogy

    Figure 15. Bipolar transistor water analogy (Scherz & Monk, 2013), p.436.

    4. Bipolar Transistor Physics Theory

  • Page 11 of 34

    Let us label the voltages applied to the B, C, and E terminals as BV , CV , and EV , respectively (see figure below). The transistor is labelled 1Q here.

    Figure 16. (a) Structure; and (b) Circuit symbol of an npn BJT (Razavi, 2014), p.124.

    Let us further define the following voltage differences and current:

    BE B EV V V= - . (1)

    CE C EV V V= - . (2)

    E C BI I I= + . (3)

    For the transistor to be on, the base-to-emitter junction must be forward biased ( 0.6 VBEV = , so 0.6 VB EV V= + ). When this is the case, a large collector current can flow ( 0CI > ) with a small

    base current ( B CI I ), electrons diffuse from the emitter typen - region to the base typep - region. On the other hand, because the base-to-collector junction is reverse biased ( C BV V> ), there is a depletion region that would ordinarily prevent the flow of electrons from the base region into the collector region. However, because the base region is manufactured to be very thin and the emitter typen - region is more heavily doped than the base, most of the electrons from the emitter accelerate through the base region with enough momentum to cross the depletion region into the collector region without recombining with holes in the base region. For example, on the average, out of every 200 electrons injected by the emitter, one recombines with a hole. Remembering that conventional current is in the opposite direction of electron motion, the result is that a small base current ( BI ) flows from the base to the emitter and a larger current ( CI ) flows from the collector to the emitter. In other words, the base current ( BI ) must supply holes for both reverse injection into the emitter and recombination with the electrons travelling toward the collector (see figure below).

  • Page 12 of 34

    Figure 17. Base current resulting from holes; (a) Crossing to emitter; and (b) Recombining

    with electrons (Razavi, 2014), p.132.

    The small base current controls a larger collector current, and therefore the BJT functions as a current amplifier. This characteristic can be approximated with the following equation:

    or C B C FE BI I I h Ib= = . (4)

    which states that the collector current is proportional to the base current with an amplification factor known as the beta ( b ) for the transistor. In general, it is called current gain, because it shows how much the base current is amplified. Manufacturers often use the symbol FEh instead of b . Now, if you combine this equation with E C BI I I= + , you can come up with an equation relating the emitter and base currents:

    ( )1E FE BI h I= + . (5)

    As you can see, this equation is almost identical to the current-gain equation ( C FE BI h I= ), with exception of the +1 term. In practice, the +1 is insignificant as long as FEh is large (which is almost always the case). For typical BJTs, b is on the order of 100, but it can vary significantly among transistors (range from 50 to 1000). This means that you can make the following approximation:

    E CI I . (6)

    In addition, b is also temperature and voltage dependent; therefore, a precise relationship should not be assumed when designing specific transistor circuits.

  • Page 13 of 34

    Now, it is important to note that the current-gain formula applies only if rules1 and 2 are met, i.e., assuming the transistor is within the active region. Finally, in mathematical form, the rule expresses as the follows:

    0.6 ( )0.6 ( )

    BE B E

    BE B E

    V V V V npnV V V V pnp

    = - == - = -

    . (7)

    Figure 18. The relationship between emitter, collector, and base (Scherz & Monk, 2013), p.433.

    One final note with regard to bipolar transistor theory involves what is called transresiststance ( trr ). Transresistance represents a small resistance that is inherently present within the emitter junction region of a transistor. Two things that determine the transresistance of a transistor are temperature and emitter current flow. The following equation provides a rough approximation of the trr :

  • Page 14 of 34

    0.026tr

    E

    VrI

    = . (8)

    In many cases, trr is insignificantly small (usually well below 1000 ) and does not pose a major threat to the overall operation of a circuit. However, in certain types of circuits, treating trr as being insignificant will not do. In fact, its presence may be the major factor determining the overall behaviour of a circuit. We will take a closer look at transresistance later on in this chapter. In addition, BJTs have certain parameters that should not be exceeded. These parameters include maximum collector current and the power dissipation capability. These parameters are listed in table below for three common npn BJTs.

    Table 1. CHARATERISTICS OF COMMON npn BJT TRANSISTORS

    Note that the power dissipation capability of a transistor is dependent on the environment temperature. In table above, the power is listed for air temperature of 25C. The power dissipation decreases with increasing temperature. 5. Darlington Transistor

    The TIP102 transistor is called a Darlington transistor and it consists of two cascaded BJT transistors to amplify the collector current (see figure below). The advantage of this combination is that the current gain is the product of the two individual transistor gains and can exceed 10,000. They may often be found in power circuits for mechatronics systems.

    Figure 19. Schematic of a Darlington transistor (Scherz & Monk, 2013), p.443.

  • Page 15 of 34

    By attaching two transistors together as shown here, a larger current-handling, larger FEh equivalent transistor circuit is formed. The combination is referred to as a Darlington pair. The equivalent FEh for the pair is equal to the product of the individual transistors FEh values ( 1 2FE FE FEh h h= ). Darlington pairs are used for large current applications and as input stages for amplifiers, where big input impedances are required. Unlike single transistors, however, darlington pairs have slower response times (it takes longer for the top transistor to turn the lower transistor on and off) and have twice the base-to- emitter voltage drop (1.2 V instead of 0.6 V) as compared with single transistors. Darlington pairs can be purchased in single packages. 6. Basic Operation

    Transistor Switch

    In the pnp circuit, everything is reverse; current must leave the base in order for a collector current to folw.

  • Page 16 of 34

    Current Source

    Current Biasing Methods

  • Page 17 of 34

    Voltage Regulator

    In addition, two of the most common standard BJT circuits are called common emitter circuit and the emitter follower circuit. These circuits are discussed next. 7. Common Emitter Transistor Circuit If a BJT's emitter is grounded and an input voltage is applied to the base, the result is the common emitter circuit, because both the emitter and the supply voltage ground are connected to the same common point. The transistor switch or common emitter circuit is shown in figure below. In this circuit, inV is the control voltage, outV is the output voltage, and CCV is the supply voltage. In this circuit, a resistor ( CR ) is always placed between the supply voltage lead and the collector. In practice, this resistor represents the resistance of a load (such as an LED or motor) that needs to be switched on and off, and hence, the name of this circuit.

  • Page 18 of 34

    Figure 20. Common emitter circuit (Jouaneh, 2013), p.43.

    The transfer and output characteristics of a BJT are shown in figure below. In figure below (a), the collector current ( CI ) is plotted against BEV . The figure shows that the collector current ( CI ) is zero unless BEV exceeds 0.6 V, at which point CI starts increasing.

    Figure 21. (a) Transfer; and (b) Output characteristics of a BJT (Jouaneh, 2013), p.43.

    Figure above (b) shows the relationship between CI and CEV as a function of the base current ( BI ).The figure shows that away from the vertical axis or in the linear region, the collector current is mainly a function of the base current and does not change appreciably with an increase in CEV . Close to the vertical axis or in the saturation region, CI is a function of both CEV and BI . Some important terms used to describe a transistors operation include saturation region, cutoff region, linear (or active) region, bias, and quiescent point (Q-point)

    Saturation region refers to a region of operation where maximum collector current flows and the transistor acts much like a closed switch from collector to emitter.

    Cutoff region refers to the region of operation near the voltage axis of the collector characteristics graph, where the transistor acts like an open switch only a very small leakage current flows in this mode of operation.

  • Page 19 of 34

    Linear (or active) region describes transistor operation in the region to the right of saturation and above cutoff, where a near-linear relationship exists between terminal currents ( , ,B C EI I I ).

    Bias refers to the specific DC terminal voltages and current of the transistor to set a desired

    point of active-mode operation, called the quiescent point, or Q-point. In general, a BJT has three states of operations: v When 0.6 VBEV < , the transistor is said to be in the off state (non-conducting state). In this

    state, no current flows between the collector and the emitter, so 0CI = . The outV voltage will be the same as the CCV voltage, because no current flows between CCV and CV .

    v When 0.6 V 0.7 VBEV < and 0.2 VCEV > , the transistor is in the linear operation state. In

    the linear operation state, the collector current ( CI ) is linearly related to the base current ( BI ) by the following relationship:

    C BI Ib= . (9)

    v When 0.7 VBEV , the transistor is in the saturation state. In this state, current flows between the collector and the emitter, and CEV has a value of 0.2 V . outV in this case will be same as CEV , and the output voltage will switch from CCV to 0.2 V when the transistor switches from the off state to the saturation state.

    In the common emitter circuit, the transistor is normally designed to operate in either the off state or the on (saturation) state, but not in the linear state. The question is then what is the minimum inV voltage needed to cause the transistor to saturate? By referencing figure (see figure below) and using KVL, we get

    in B B BEV I R V= + . (10)

    Figure 22. Common emitter circuit (Jouaneh, 2013), p.43.

    and just before saturation, BI is related to CI by

  • Page 20 of 34

    or CB C FE B BII I h I Ibb

    = = = . (11)

    where CI is determined from

    ( )CC CEC

    C

    V VI

    R-

    = . (12)

    These equations can be solved to find inV to cause saturation. It is important to note that the equations here are idealistic in form. In reality, these equations may result in unreal answers. For instance, they tend to screw up when the currents and voltages are not within the bounds provided by the characteristic curves. If you apply the equations blindly, without considering the operating characteristics, you could end up with some wild results that are physically impossible. The common emitter transistor circuit can serve as semiconductor switch to turn on or off an LED, electric motor, solenoid, electric light, or some other load (represented by CR ). These loads require large currents, ranging from milliamps to many amps, to function properly. When the input voltage and current are increased enough to saturate the transistor, a large collector current flows through the load CR . The magnitude of the collector current is determined by the load resistance CR and the collector voltage ( CCV ). When the base-to-emitter voltage is below 0.6 V, the transistor is off, and no current flows through the load. Let us summarize the guidelines for designing a transistor switch: v The collector must be more positive than the base or emitter. v To be ON, the base-to-emitter voltage ( BEV ) must be at least 0.6 V. v The collector current ( CI ) is independent of base current ( BI ) when the transistor is

    saturated, as long as there is enough base current to ensure saturation. v The minimum base current ( BI ) required can be estimated by first determining the collector

    current ( CI ) and then applying ( minC

    BIIb

    ).

    v For a given input voltage, the input resistance must be chosen so that the base current ( BI ) exceeds this value by a conservative margin (e.g., 5-10 times larger).The reasons for this are that may vary among components, with temperature, and with voltage; and the load resistance may changes as current flow through it.

    v It is also important to calculate the maximum values of CI and BI to ensure that they fall within the manufacturer's specifications, and add or change series resistors if the currents are too large.

    Example: Voltage saturation calculations for the 2N3904 transistor.

    The 2N3904 transistor is a small-single transistor manufactured by many companies as a general purpose amplifier and switch. If you examine the specifications online or in a discrete transistor handbook, you can find a complete list of ratings and electrical characteristics. Here is some of the

  • Page 21 of 34

    information provided:

    v Maximum collector current (continuous)=200 mA .

    v =10 VCCV ; ( )satCEV =0.2 V; =0.7 VBEV .

    v 1 kCR = ; 5 kBR = .

    v 100FEh b= = (depending on collector current and many other things)

    and with reference to figure below:

    Figure 23. Common emitter circuit (Jouaneh, 2013), p.43.

    (a) Determine the input voltage needed to cause the transistor to saturate.

    (b) What is the output voltage ( outV ) of this circuit during the off states if 10 VCCV = ?

    (c) What is the output voltage ( outV ) of this circuit during the saturation states if 10 VCCV = ?

    Solution: (a) Because CEV (saturate) for the 2N3904 is 0.2 V , when the transistor is fully saturated the collector current is

    ( )10 0.2 9.8 mA1000C

    I-

    = = .

    Notice that CI has to be smaller than the 200 mA limit for the collector current, which is satisfied in this case. Also from the data sheet, the DC current gain ( FEh ) is about 100, BI must

    be at least 100

    CI (use Eq. CBIIb

    = ) , that means, BI just before saturation is given by

    9.8 0.098 mA100 100

    CB

    II = = = .

    Because =0.7 VBEV and 5 kBR = , the input voltage for saturation is

    0.098 5 0.7 1.19 VinV = + = . (use Eq. in B B BEV I R V= + )

  • Page 22 of 34

    To insure saturation, inV has to be greater than 1.19 V. This can be achieved easily if we let inV be 2 V for example. (b) When this transistor is off, inV has to be less than BEV when the transistor just turns on (less than 0.6 V). In this case, outV will be equal to CCV (10 V). (c) When the transistor is in saturation,

    0.2 Vout CEV V= = .

    8. Common Emitter Amplifier

  • Page 23 of 34

    9. Emitter Follower Circuit The emitter follower circuit is shown in figure below.

    Figure 24. Emitter follower circuit (Jouaneh, 2013), p.45.

    Note how the output is connected to the emitter is this case, and there is no resistor between CCV and the collector. This circuit is called the emitter follower, because the output voltage follows the input voltage with a difference of about 0.6V. Assume first that there is no resistor BR in this circuit. Then B inV V= ,

    0.6 (for 0.6 V)out E in BE in inV V V V V V= = - = - > . (13)

    and

    0 (for 0.6 V)out E inV V V= = < . (14)

  • Page 24 of 34

    Now if the resistor BR was present, we need to account for the voltage drop across this resistor and

    outV is then equal to

    0.6 (for 0.6 V)out in B B inV V I R V= - - > . (15)

    But E C BI I I= + , outEE

    VIR

    = , and C BI Ib= when the transistor is in the linear state. This gives

    ( )1out

    BE

    VIRb

    =+

    . (16)

    and

    ( )1E BI I b= + . (17)

    Eq. ( ( )1E BI I b= + ) shows the current gain of this circuit is ( )1 b+ . Substituting Eq.

    (( )1

    outB

    E

    VIRb

    =+

    ) into Eq. ( 0.6 (for 0.6 V)out in B B inV V I R V= - - > ) and solving for outV , we get

    ( )( )

    1+0.6

    1E

    out inB E

    RV V

    R Rb

    b= -

    + +. (18)

    Equation above shows that the output voltage ( outV ) is linearly related to the input voltage ( inV ) and is independent of the supply voltage ( CCV ). The output voltage ( outV ) is also in phase with the input voltage ( inV ), and voltage gain is slightly less than 1. The above three equations apply as long as the transistor is not in saturation. When the transistor saturates, outV is equal to 0.2CCV - because CEV is about 0.2 volts at saturation. Overall, the emitter follower has current gain, a feature that is just as important in applications as voltage gain. This means that this circuit requires less power from the signal source (applied to inV ) to drive a load than would otherwise be required if the load were to be powered directly by the source. By manipulating the transistor gain equation and using Ohms law, the input resistance and output resistance are :

    in FE load

    sourceout

    FE

    R h RRRh

    =

    =. (19)

  • Page 25 of 34

    Example: Analysis of a BJT circuit.

    Determine the voltages at points 1 and 2 in the circuit shown in figure below , for

    a) 0.1 VinV = and

    b) 3 VinV = .

    Let 1 kCR = ; 100 B ER R= = .and 10 VCCV = .

    Solution: (a) For 0.1 VinV = , the transistor is off, because inV has to be larger than 0.6 V to cause the transistor to start conducting. So

    1 10 VCCV V= = , since the current 0CI = .

    2 0 VV = , because 0.6 VBEV < . (b) For 3 VinV = , the transistor is either operating in the linear range or saturated. We will assume that the transistor is just at the point of being saturated, and we will check this

  • Page 26 of 34

    assumption by comparing the currents CI and BI . Applying KVL to the CCV loop gives

    CC C C CE E EV I R V I R= + + .

    Similarly, applying KVL to the inV loop gives

    in B B BE E EV I R V I R= + + .

    Noting that E C BI I I= + , and using the given values for BR , CR , ER , inV , and CCV , and assuming 0.2 VCEV = and 0.7 VBEV = at saturation, we get

    ( )1000 0.2 1001010 1000 0.2 100 10010 1100 0.2 100

    C CE E ECC

    C C B

    C C B

    C B

    R V I RVI I II I II I

    + +=+ + +=

    = + + += + +

    .

    and

    ( )100 0.7 10033 100 0.7 100 1003 100 0.7 200

    B B BE E Ein

    B C B

    B C B

    C B

    I R V I RVI I II I II I

    + +=+ + +=

    = + + += + +

    .

    Solving equations for BI and CI , we get

    8.24 mACI = , and 7.36 mABI = . For 10 mACI = , the current gain b is about 100 if the transistor is operating in the linear range. Since C BI Ib , the transistor is in saturation and the assumption is correct. This gives

    ( )1 10 8.24 1 1.76 VCC C CV V I R= - = - = . ( ) ( ) ( )2 8.24 7.36 0.1 1.56 VE E C B EV I R I I R= = + = + = .

  • Page 27 of 34

    10. Emitter Follower (or Common collector) Amplifier

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    11. Open Collector Output Many sensors used in mechatronics applications such as proximity sensors, have electronic circuits that use an internal BJT as an interface. The output of the sensor electronic circuit drives the base of the transistor. These circuits are normally known as open collector output voltage circuits. To get an output from these sensors, an appropriate pull-up resistor or load, and the supply voltage needs to be applied to the terminals of the sensor. Figure below shows a typical wiring for such a sensor. In this example, a positive voltage needs to be applied to terminal 1 and a pull-up resistor needs to be connected between terminals 1 and 2. When the proximity sensor is OFF, the transistor is not in saturation, and there will be no voltage drop across the load resistor, since the collector terminal 2 is open with respect to the emitter terminal 3. The output in this case will be pulled up by the load resistor to the value of the external supply voltage.

    Figure 25. Typical circuit for an npn type non-contact, capacitive-type proximity sensor

    (Jouaneh, 2013), p.47.

    When an object is detected by the proximity sensor, the transistor conducts and a voltage drop develops across the load resistor, resulting in the output voltage changing from the value of the supply voltage to almost zero.

  • Page 29 of 34

    12. Phototransistor, Photo Interrupter, and Opto-Isolator Instead of using a voltage source to saturate the transistor, a phototransistor (see figure below (a)) uses light that is received by a photodiode to do the same thing. Typically a phototransistor and an LED are packaged together to make optical sensors that can be used to detect the presence of objects. In these sensors, which are commonly referred to as photo interrupters (see Figure blow (b)), the LED provides a light source that is received by the phototransistor. An interruption of the light received by the phototransistor causes the phototransistor to change state, thus indicating the presence of an object in the path between the LED and the phototransistor.

    Figure 26. (a) Phototransistor; and (b) photo interrupter (Jouaneh, 2013), p.48.

    An opto-isolator or an optocoupler combines two elements (a light-emitting device such as a diode and a light-sensitive device) similar to a photo interrupter but in an enclosed package. An opto-isolator is also designed for a different purpose, which is to provide an optical coupling between the input and the output sides. The light emitter on the input side takes a voltage signal and converts it into a light signal. On the output side, the light-sensitive device detects the light from the emitter and converts it back to a voltage signal. The light-sensitive device could be a phototransistor, a photodiode, or a thyristor. This optical coupling provides electrical noise isolation between the input and the output sides. To take advantage of this isolation, a separate power supply should be used for the input and output sides. Opto-isolators are used to prevent voltage spikes on one side of the device to damage or affect components on the other side. Opto-isolators are available with isolation of 5 kV or more between the input and output sides.

  • Page 30 of 34

    13. Important Things to Know about BJTs

  • Page 31 of 34

    References Boysen, E., & Kybett, H. (2012). Complete electronics self-teaching guide with projects. 10475

    Crosspoint Boulevard Indianapolis, IN 46256: John Wiley & Sons, Inc., ISBN 978-1-118-21732-0.

    Callister, W. D., & Rethwisch, D. G. (2010). Materials science and engineering: an introduction (8th ed.). River Street, Hoboken, NJ: John Wiley & Sons. Inc., ISBN 978-0-470-41997-7.

    Jouaneh, M. (2013). Fundamentals of mechatronics. Stamford, CT, USA: Cengage Learning, ISBN 978-1-111-56901-3.

    Razavi, B. (2014). Fundamentals of microelectronics. River Street, Hoboken, NJ, USA: John Wiley & Sons, Inc., ISBN 978-1-118-15632-2.

    Scherz, P., & Monk, S. (2013). Practical electronics for inventors. New York Chicago San Francisco Lisbon: McGraw-Hill, ISBN 978-0-07-177134-4.

    Serway, R. A., & Jewett, J. W. (2014). Physics for scientists and engineers with modern physics. Boston, MA, USA: Brooks/Cole CENAGE Learning, ISBN 978-1-133-95405-7.

  • Page 32 of 34

    Additional Readings 1. Transistor

  • Page 33 of 34

    2. Pinouts for Bipolar Transistors

    3. Darlington Transistor

  • Page 34 of 34