Student Biographies - Virginia Commonwealth University

Student Biographies - Virginia Commonwealth University

Bipolar Junction Transistors Physical Structure and Modes of Operation Emitter (E) Metal contact n-type p-type n-type Emitter region Base region Collecter region Emitter-base junction (EBJ) Mode Base (B) EBJ Cutoff Reverse Active Forward Saturation Forward REP 02/13/20 ENGR224 Collecter (C)

Collecter-base junction (CBJ) CBJ Reverse Reverse Forward Page BJT 4.1-1 Bipolar Junction Transistors Operation of the npn Transistor in the Active Mode p n E Injected electrons iE Diffusing electrons Injected holes (iB1) REP 02/13/20 ENGR224 C iC iB iE V BE Collected electrons iB v BE

iE n B vCB iC iC VCB Page BJT 4.1-2 Bipolar Junction Transistors Current Flow Only diffusion-current components are considered Profiles of minority-carrier concentrations in the base and in the emitter of an npn transistor operating in the active mode; vBE > 0 and vCB 0. EBJ depletion region Carrier concentration Emitter (n) Base (p) CBJ depletion region Collector (n) v BE n p (0) n p 0 e VT dn p x

I n AE qDn dx n p 0 AE qDn W Electron concentration np (ideal) Hole concentration pn0 np(0) pn(0) np (with recombination) Distance (x) Effective base width W REP 02/13/20 ENGR224 Page BJT 4.1-3 Bipolar Junction Transistors The Collector Current Most of the diffusing electrons will reach the boundary of the collector-base depletion region These successful electrons will be swept across the CBJ depletion region into the collector By convention, the direction of iC is opposite to that of electron flow

iC I n and n p 0 n p 0 e vBE iC I S e vBE VT VT saturation current IS AE qDn ni2 N AW n p 0 ni2 N A I S AE qDn n p 0 W REP 02/13/20 ENGR224 Page BJT 4.1-4 Bipolar Junction Transistors The Base Current Two components of base current, iB1 and iB2. iB1 AE qD p ni2 N D Lp Hole diffusivity in the emitter e v BE VT Hole diffusion length in the emitter iB 2 Qn

b minority-carrier lifetime Doping concentration of the emitter 1 Qn AE q n p 0 W 2 AE qWni2 vBE VT Qn e 2N A iB 2 1 AE qWni2 vBE VT e 2 bNA REP 02/13/20 ENGR224 Dp N A W 1 W 2 v e BE iB I S D N L n D p 2 Dn b i iB C I iB S vBE e VT VT

Dp N A W 1 W 2 1 Dn N D L p 2 Dn b common-emitter current gain Page BJT 4.1-5 Bipolar Junction Transistors The Emitter Current common-base current gain iE iC iB 1 iC 1 vBE VT iE IS iC iE iE REP 02/13/20 ENGR224 1 iE I S e vBE VT 1 Page BJT 4.1-6

Bipolar Junction Transistors First Order Equivalent Circuit Models The externally controlled signals for this model are the three currents shown outside the gray box. The voltage VBE, exists internally as a result of the currents and can be externally measured. We can force a current and measure a voltage. The diode in the model is designated as D E since the current flowing through the diode is the same as the emitter current. The collector current is dependent on the base-emitter voltage V BE. The model is a non-linear voltage controlled current source Voltage Controlled Current Source Model C B C The externally controlled signals for this model are two currents and the voltage VBE shown outside the gray box. The current iE exists internally as a result of the voltage VBE and can be externally measured. The collector current is dependent on the emitter current iE. iC

iE iB B DE vBE iC iB ISe DE vBE iE E iE Current Controlled Current Source E REP 02/13/20 ENGR224 VBE VT Page BJT 4.1-7 Bipolar Junction Transistors Equivalent Circuit Models, contd In this version of the model the diode conducts the BASE current which is beta times smaller.

In one version the dependent current source is voltage controlled (v BE), in the other version the dependent current source is current controlled (). iB B iC iC v BE C DB IS I S e vBE VT B iB v BE C DB IS I B iE iE E Note connection point is now on the opposite side of the diode

Voltage Controlled Current Source Model REP 02/13/20 ENGR224 E Current Controlled Current Source Page BJT 4.1-8 Bipolar Junction Transistors Two Port Model of the Common-Base Configuration iC B iB ISe vBE C B VBE VT iin DE iE E C B The base lead is common to both ports E E B

Two port Network E C B B If we switch the leads within the network the common base aspect is more apparent iE B iC C iout B Two-Port representation of a BJT Transistor symbol in a common-base configuration REP 02/13/20 ENGR224 iin iE iout ic Ai iout iC iin iE The common-base current gain is Page BJT 4.1-9 Bipolar Junction Transistors Two Port Model of the Common-Emitter Configuration iC B

iB v BE C DB IS B I B E Two port Network C E The emitter lead is common to both ports iE E iC is out of phase with iB iin B iB E iC C iout iin iB E

Two-Port representation of a BJT Transistor symbol in a common-emitter configuration REP 02/13/20 ENGR224 iout iC i i Ai out C iin iB The common-emitter current gain is Page BJT 4.1-10 Bipolar Junction Transistors Operation of the pnp Transistor in the Active Mode n p E Injected holes iE Diffusing holes Injected electrons (iB1) REP 02/13/20 ENGR224 C iC iB iE VEB Collected holes

iB vEB iE p B vBC iC iC VBC Page BJT 4.1-11 Bipolar Junction Transistors Equivalent pnp Circuit Models E iE B iB E vEB DE iE IS ISe iC

vEB VEB VT B DB IS I S e vEB VT C iB iC C REP 02/13/20 ENGR224 Page BJT 4.1-12 Bipolar Junction Transistors Circuit Symbols and Conventions - npn C C VCB iC B B iB V BE

E iE E npn BJT REP 02/13/20 ENGR224 Voltage polarities and current flow in a transistor biased in the active mode. Page BJT 4.1-13 Bipolar Junction Transistors Circuit Symbols and Conventions - pnp E E VEB iE B B iB VBC C iC C pnp BJT REP 02/13/20 ENGR224 Voltage polarities and current flow in a transistor biased in the active mode. Page BJT 4.1-14

Bipolar Junction Transistors Example 4.1 The transistor in the circuit below has = 100 and exhibits a vBE of 0.7V at iC = 1 mA. Design the circuit so that a current of 2 mA flows through the collector and a voltage of +5V appears at the collector. 15V 5V 10V RC 5k 2mA 2mA since V BE 0.7V at iC 1mA, 15V 15V RC I C 2mA RC VC 5V RE 15V RE 15V 2 V BE 0.7 VT ln 0.717V 1 and V E V BE 0.717V VE VBE I E I C I B for 100, 100 101 0.99 thus I E

RE V E 15 IE REP 02/13/20 ENGR224 IC 2 2.02mA 0.99 .0717 15 7.07k 2.02 Page BJT 4.1-15 Bipolar Junction Transistors Graphical Representation of Transistor Characteristics Similar to diodes, except we talk about the voltage across one junction V BE and the current through the other terminal i C. For most of the conditions we will encounter in working with BJTs the ideality factor, n will be considered to be 1. iC iC I S evBE VT iC I 0 0.5 0.7 iC-vBE characteristics 0

0.5 0.7 vBE V REP 02/13/20 ENGR224 0 T1>T2>T3 vBE V vBE I iB S I iE S T1 T2 T3 0.5 0.7 Effect of temperature on iC-vBE characteristic. At a constant current, vBE changes by 2mV/oC. vBE V Page BJT 4.1-16 Bipolar Junction Transistors iC versus vCB Characteristics npn transistor in active mode vCB iC saturation iC mA iE

iE 4 mA 4 3 3 mA 2 1 2 mA 1 mA iE 0 1 2 3 -Vnp = forward bias saturation Current controlled current source vCB V +Vnp = reverse bias iC mA iB 4 iC vs vCE iB 3 See next page iB 2 iB1 0 1 2 3 REP 02/13/20 ENGR224 vCE V Page BJT 4.1-17 Bipolar Junction Transistors iC=vCE Characteristics

The Early Voltage (typically 50 -100 Volts), also known as the Base-Width Modulation parameter. As the base-collector junction reverse bias is increased the depletion layer expands and consumes some of the base narrowing it and causing an increase in the collector current. iC I S e vBE VT vCE 1 VA Saturatio n region iC i rO C vCE v BE constant V rO A IC Active region vBE . . .

vBE . . . vBE . . . iC vBE 1 vBE . . . vCE VA REP 02/13/20 ENGR224 0 vCE Page BJT 4.1-18 Bipolar Junction Transistors Example 4.2 We wish to analyze this circuit to determine all node voltages and branch currents. We will assume that is specified to be 100. 10V RC 4.7 k 4V 10 V RC 4.7k 4V RE 3.3k

REP 02/13/20 ENGR224 RE 3.3k Page BJT 4.1-19 Bipolar Junction Transistors Example 4.2, contd We dont know whether the transistor is in the active mode or not. A simple approach would be to assume that the device is in the active mode, and then check our results at the end 1 VE 4 VBE 4 0.7 3.3 V 10V 3 IC 4V 4.7 k VC 4 5 IB 3.3 k VE 1 IE 2 V 0 3.3 IE E 1 mA RE 3.3 2 100

0.99 1 1013 I C 0.99 1 0.99 mA I C I E , 4 VC 10 I C RC 10 0.99 4.7 5.3 V I 1 IB E 0.01 mA 1 101 REP 02/13/20 ENGR224 5 Page BJT 4.1-20 Bipolar Junction Transistors Example 4.3 We wish to analyze the circuit shown below to determine the voltages at all nodes and the currents through all branches. Note that this circuit is identical to the previous circuit except that the voltage at the base is now +6 V. Assuming active-mode: 10V 10V VE 5.6 VBE 6 0.7 5.3 V 3 IC 6V RC 4.7 k 4V

4.7 k VC IB RE 3.3k 3.3 k IE VE 1 4 IE 5.3 1.6 mA 3.3 I C I C 1.6 mA 2 VC 10 4.7 I C 10 7.52 2.48 V Collector voltage > base voltage saturation mode, not active mode REP 02/13/20 ENGR224 Page BJT 4.1-21 Bipolar Junction Transistors Example 4.4 We wish to analyze the circuit below to determine the voltages at all nodes and the currents through all branches. This circuit is identical to that considered in the previous two examples except that now the base voltage is zero. 10V 10V I C 0 mA 3

RC 4.7 k 5 I B 0 mA RE 3.3k REP 02/13/20 ENGR224 3.3 k 4.7 k VC 10 V 4 VE 0V cutoff I E 0 mA 2 1 Page BJT 4.1-22 Bipolar Junction Transistors Example 4.6 We will analyze the following circuit to determine the voltages at all nodes and currents through all branches. Assume =100. VB VBE 0.7 V 10V 10V IC 5V I C 4.3 mA RC 2 k

IB RB 100 k 5V 100 k I B 0.043 mA 2 REP 02/13/20 ENGR224 3 RC 2 k VC 1.4 V IB 1 5 VBE 5 0.7 0.043 mA RB 100 I C I B 100 0.043 4.3 mA 2 3 4 I E 4.343 mA 5 VC 10 I C RC 10 4.3 2 1.4 V 4 I E 1 I B 1010.043 4.3 mA Page BJT 4.1-23 5

Bipolar Junction Transistors Example 4.7 We want to analyze the circuit shown below to determine the voltages at all nodes and currents through all branches. Assume =100. 15 V RB1 100 k RB 2 50 k 15 V RC 5 k VBB 5 V RC 5 k RBB RE 3 k 33.3 k VBB 15 RE 3 k RB 2 50 15 5 V RB1 RB 2 100 50 RBB RB1 // RB 2 100 // 50 33.3 k VBB I B RBB VBE I E RE IB REP 02/13/20 ENGR224 IE

1 Page BJT 4.1-24 Bipolar Junction Transistors Example 4.7, contd 15 V 1.28 mA 5V 0.013 mA 1.29 IB 0.0128 mA 101 VB VBE I E RE 8.6 V 33.3 k 3.87 V 0.013 mA 1.29 mA IE 100 k 5 k 50 k VBB VBE RE RBB 1 0.103 mA 0.09 mA 0.7 1.29 3 4.57 V 3 k

assuming active - mode operation, I C I E 0.99 1.29 1.28 mA VC 15 I C RC 15 1.28 5 8.6 V REP 02/13/20 ENGR224 Page BJT 4.1-25 Bipolar Junction Transistors The BJT as an Amplifier Objectives 1. Biasing 2. DC equations 3. Transconductance 4. Input resistance looking into the base 5. Input resistance looking into the emitter 6. Voltage gain 7. Gummel plots Lesson 1. Biasing 1) For our amplifiers, the BJT must be biased in the FORWARD-ACTIVE 2) However, its a difficult challenge to establish a CONSTANT DC CURRENT 3) Our goal: A Q point insensitive to TEMPERATURE , , V BE . REP 02/13/20 ENGR224 Page BJT 4.1-26 Bipolar Junction Transistors The BJT as an Amplifier 2. DC Equations (learn em now) 1) I C I S eVBE / VT 2) I E I C /

3) I B I C / 4) VC VCC I C RC 0.99 1 100 1 3. Transconductance (remember the small-signal approximation from before?) - Valid only for vBE< 10 mV - Defined as the incremental change in output current for an incremental change in input voltage at a DC operating point.. iC gm vBE REP 02/13/20 ENGR224 iC I C Page BJT 4.1-27 Bipolar Junction Transistors The BJT as an Amplifier iC I S eVBE /VT I S e(VBE vbe ) /VT I S eVBE /VT evbe /VT I C evbe /VT ic If vbe<< VT IC Q VBE

vBE x 2 x3 (e 1 x .......) 2! 3! x Vbe vbe IC iC I C (1 ) I C I C iC vbe g m vbe VT VT VT Note that iC = IC at vBE = VBE, so... v BE / VT gm ISe vBE REP 02/13/20 ENGR224 iC I C IC VT Page BJT 4.1-28 Bipolar Junction Transistors The BJT as an Amplifier Input Resistance looking into the Base ( highlight this in your text & on this page!) Defined as the incremental change input voltage for an incremental change in base current at a DC operating point vBE r iB iC I C

vBE iB iC I C VT IC Other important relationships ( be prepared to use any of these!) r REP 02/13/20 ENGR224 gm VT r IB Page BJT 4.1-29 Bipolar Junction Transistors The BJT as an Amplifier Input Resistance looking into the Emitter (hightlight this in your text & on this page) Define as the incremental change in input voltage for an incremental change in emitter current at DC operating point.. vBE re i E iC I C 1 i C 1 I C

1 VT IC Other important relationship ( be prepared to use either of them!) VT re IE REP 02/13/20 ENGR224 1 re gm gm Page BJT 4.1-30 Bipolar Junction Transistors The BJT as an Amplifier Relationship between r and re - The same input resistance . . . just viewed from two different places ! VT r IB VT re IE REP 02/13/20 ENGR224 r ( 1)re I E ( 1) I B r re 1

Page BJT 4.1-31 Bipolar Junction Transistors The BJT as an Amplifier Lets look at Voltage Gain again A BJT senses vbe This is a and causes a proportional current gm vbe VOLTAGE - CONTROLED CURRENT SOURCE So . . . How do we obtain an output voltage so that we get a voltage gain? Out of phase with the input REP 02/13/20 ENGR224 Page BJT 4.1-32 Bipolar Junction Transistors Voltage Gain vC VCC iC RC VCC I C iC RC VCC I C RC iC RC VC iC RC Signal voltage: vC iC RC g m vbe RC g m RC vbe REP 02/13/20 ENGR224 Voltage gain: vc Voltage gain g m RC vbe Page BJT 4.1-33

Bipolar Junction Transistors Small-signal equivalent circuit models Every current and voltage in the amplifier circuit is composed of two components: a dc component and a signal component. The dc components are determined from the dc circuit below on the left. By eliminating the dc voltages, we are left with the signal components (on the right). The resulting circuit is equivalent to the transistor as far as small-signal operation is concerned. IC IB vbe V BE + - RC RC vCE VCC IE Amplifier circuit with dc sources REP 02/13/20 ENGR224 ib vbe r vbe + -

vbe ic g m vbe vce v ie be re Amplifier circuit with dc sources eliminated Page BJT 4.1-34 Bipolar Junction Transistors The Hybrid- Model current-controlled current source voltage-controlled current source ic g m vbe and ib vbe r g m vbe g m ib r v v ie be g m vbe be 1 g m r r r vbe 1 vbe r g m r ib g m vbe ib r

1 ie vbe re ib B ic v BE ic C r B v BE g m vbe C ib I B r g m I C VT ie E REP 02/13/20 ENGR224 ie

r g m E Page BJT 4.1-35 Bipolar Junction Transistors The T Model These models explicitly show the emitter resistance r e rather than the base resistance rp featured in the hybrid- model. ib C ic g m vbe ib B v BE re ie E voltage-controlled current source REP 02/13/20 ENGR224 ib vbe v g m vbe be 1 g m re re re vbe v 1 be

re re 1 1 vbe v be 1 re r g m vbe g m ie re g m re ie g m vbe ie C ic ie ib B v BE ie re E current-controlled current source Page BJT 4.1-36 Bipolar Junction Transistors Application of the Small-Signal Equivalent Circuits

The availability of the small-signal BJT circuit models makes the analysis of transistor amplifier circuits a systematic process consisting of the following steps: Determine the dc operating point of the BJT and in particular the dc collector current IC. Calculate the values of the small-signal model parameters: gm IC V 1 , r , and re T VT gm I E gm Eliminate the dc sources by replacing each dc voltage source with a short circuit and each dc current source with an open circuit. Replace the BJT with one of its small-signal equivalent circuit models. Although any one of the models can be used, one might be more convenient than the others for the particular circuit being analyzed. This point will be made clearer later in this chapter. Analyze the resulting circuit to determine the required quantities (e.g., voltage gain, input resistance). REP 02/13/20 ENGR224 Page BJT 4.1-37 Bipolar Junction Transistors Example 4.9 We wish to analyze the transistor amplifier shown below to determine its voltage gain. Assume = 100. VCC 10V 2 10V 2.3 mA RC 3 k

R BB 100 k vi 3V 1 Assume vi 0 to find the dc base current IB 100 k VBB VBE RBB 3 0.7 IB 0.023 mA 100 REP 02/13/20 ENGR224 2 3.1 V 3 0.023 mA + - VBB 3 V 1 3 k 0 .7 V 2.323 mA The dc collector current will be I C I B 100 0.023 2.3 mA

The dc voltage at the collector will be 3 VC VCC I C RC VC 10 2.3 3 3.1V Page BJT 4.1-38 Bipolar Junction Transistors Example 4.9, contd Having determined the operating point, we now proceed to determine the small-signal model parameters RBB 100 k vi + - B r v BE C g m vbe RC 3 k E re VT 25 mV 10.8 I E 2.3 0.99 mA gm

r I C 2.3 mA 92 mA / V VT 25 mV 100 1.09 k gm 92 REP 02/13/20 ENGR224 vbe vi vi r r RBB 1.09 0.011 vi 101.09 Voltage gain : vo 3.04 V / V vi vo g m vbe RC vo 92 0.011 vi 3 3.04vi Page BJT 4.1-39 Bipolar Junction Transistors A note about Output Signal Swing

The collector voltage (and vo) can have a maximum value of zero volts before the transistor goes from forward active mode to saturation mode since the base is grounded. When no input (ac) voltage is applied the output (collector) was found to be at a DC level of -5.4V. If we desire a symmetric output signal (about the -5.4V DC level) the signal would have to go to -5.4 - 5.4 or -10.8 Volts (this is a large output signal swing). This causes a problem, since our lower voltage supply is only -10V. In order to avoid possibly producing a distorted output signal the input signal range must be limited so that the output is not clipped as shown below. Limiting the input signal to smaller values to limit clipping is not the same as using a small signal to invoke the linear approximation as indicated in the next bullet item. Another important point to be made about the output signal is that it is shown to be linear in the figure below but in fact the i C-vbe characteristic is not linear for a large output signal swing. t 0 vC V -5.4 -10 REP 02/13/20 ENGR224 clipping Page BJT 4.1-40 Bipolar Junction Transistors Modifying the Hybrid- Model to Include the Early Effect The Early effect causes the collector current to depend on vBE as well as vCE. The dependence on vCE is modeled by assigning a finite output resistance to the controlled current-source. By including ro in the equivalent circuit shown below, the gain will be somewhat reduced. voltage-controlled current source B

current-controlled current source C v r g m v B ib C r ro ib 1 E i V ro C A vCE vbe 0 I C E vo g m vbe RC // ro REP 02/13/20 ENGR224 Page BJT 4.1-41 ro

Bipolar Junction Transistors Summary of the BJT Small-Signal Model Parameters Keep these at your fingertips (I.e. formula sheet for an exam or homework or in lab) See Table 4.3 Model parameters in terms of DC bias currents Model parameters in terms of the transconductance, gm Model parameters in terms of re Relationships between the common-emitter current gain and the common-base gain I gm C VT V V re T T IE IC V V r T T IB IC V ro A IC gm

r gm re r 1 re re 1 REP 02/13/20 ENGR224 1 gm gm 1 1 r re 1 1 1 Page BJT 4.1-42 Bipolar Junction Transistors Graphical Analysis iC vi iB

vBE REP 02/13/20 ENGR224 vCE Page BJT 4.1-43 Bipolar Junction Transistors Graphical Analysis (cont.) vCE VCC iC RC VCC 1 iC vCE RC RC REP 02/13/20 ENGR224 Page BJT 4.1-44 Bipolar Junction Transistors Graphical Analysis (cont.) REP 02/13/20 ENGR224 Page BJT 4.1-45 Bipolar Junction Transistors Graphical Analysis (cont.) REP 02/13/20 ENGR224 Page BJT 4.1-46 Bipolar Junction Transistors Single Power Supply

Biasing the BJT involves establishing a constant dc current in the emitter which is calculable, predictable, and insensitive to temperature variations and to (for transistors of the same type). The bias point should allow for maximum output signal swing. To design for a stable IE, the design constraints (shown below) must be satisfied. VCC VCC R1 V BB VCC RC RC R BB IC IE R2 RE R2 V BB VCC R R 2 1 RR RBB 1 2 R1 R2 IE V BB V BE R E R B 1

RE Design constraints: Circuit topology for biasing a BJT amplifier REP 02/13/20 ENGR224 VBB VBE and RE Page BJT 4.1-47 RB 1 Bipolar Junction Transistors Single Power Supply, contd From the previous page, our design constraints are as follows: VBB VBE and RE RB 1 When biasing the BJT, we must make sure of the following: VBB must not be too large, or it will lower the sum of voltages across R C and VCB RC should be large enough to obtain high voltage gain and large signal swing VCB (or VCE) should be large enough to provide a large signal swing Rules of thumb: 1 VBB VCC 3

1 VCB (or VCE ) VCC 3 1 I C RC VCC 3 Wed like for RB to be small, which is achieved by low values of R1 and R2. This could result in higher current drain from the power supply, hence lower input resistance (if the input signal is coupled to the base). This means that we want to make the base voltage independent of and solely determined by the voltage divider. In order to achieve this, another rule of thumb is practiced: select R 1 and R2 such that their current is in the range of I E to 0.1I E REP 02/13/20 ENGR224 Page BJT 4.1-48 Bipolar Junction Transistors Example 4.12 We wish to design the bias network of the amplifier shown below to establish a current I E = 1mA using a power supply VCC = +12 V. VCC VCC neglecting base current: for voltage divider current = 0.1IE R1 RC R1 R2 12 120 k 0.1I E

R2 VCC 4 V R1 R2 R2 RE Thus R2 40 k and R1 80 k for nonzero base current: IE V B 4 V VE 4 V BE 3.3 V I R E E 3.3 k VE REP 02/13/20 ENGR224 V BB V BE 3.3 0.93 mA R E RB 1 3.3 0.267 for voltage divider current = IE R1 8k and R2 4k IE 3.3 1 mA 3.3 0.0266 Page BJT 4.1-49 Bipolar Junction Transistors Example 4.12, contd Depending on what the emitter current is, we can have two designs: Design 1: the voltage divider current = 0.1I E, and Design 2: the voltage divider current = I E Design 1

R1 80 k and R2 40 k IE VBB VBE 3.3 0.93 mA R E R B 1 3.3 0.267 12 VC RC IC RC 12 8 4.34k 0.99 0.93 REP 02/13/20 ENGR224 Design 2 R1 8k and R2 4k IE 3.3 1 mA 3.3 0.0266 12 VC RC IC RC 12 8 4.04k 0.99 1 Page BJT 4.1-50 Bipolar Junction Transistors Biasing Using Two Power Supplies

A somewhat simpler bias arrangement is possible if two power supplies are available. If the transistor is to be used with the base grounded, then R B can be eliminated altogether. If the input signal is to be coupled to the base, then R B is needed. VCC IE RC I IB E 1 V EE V BE R E R B 1 Design constraints: VBB VBE and RE RB 1 IE RB RE V EE REP 02/13/20 ENGR224 Page BJT 4.1-51 Bipolar Junction Transistors An Alternative Biasing Arrangement VCC I E RC I B RB VBE VCC

VCC I E RC RC VC VBE I B RB IB RB V BE IC IE IE IE RB VBE 1 VCC VBE RC RB 1 select RB 1 RC VCB I B RB I E REP 02/13/20 ENGR224 RB 1 Page BJT 4.1-52 Bipolar Junction Transistors Biasing Using a Current Source The BJT can be biased using a current source The advantage is that the emitter current is independent of the values and RB Current-source biasing leads to significant design simplification VCC

VCC I REF I R RC IC RB I IC Q1 VBE V Q2 I REF VCC V EE V BE R VEE VCC V EE VBE R since Q1 and Q2 have the same VBE I I REF REP 02/13/20 ENGR224 Page BJT 4.1-53 Bipolar Junction Transistors Common-Emitter Amplifier Circuit

REP 02/13/20 ENGR224 AC Hybrid -based model Page BJT 4.1-54 Bipolar Junction Transistors Common-Emitter Amplifier (cont.) Input Resistance: Current Gain: Ri r Voltage Gain: v r vs Rs r vo g m v Rc ro vo g m Rc ro v Rc ro vo Av vs Rs r REP 02/13/20 ENGR224 Ai io ib Ai g m v ro v ro RC

r ro ro RC Output Resistance: Ro RC ro Page BJT 4.1-55 Bipolar Junction Transistors Exercise 4.31 For a CE amplifier, let I=1 mA, RC=5k, =100, VA=100V, and Rs=5k. Find Ri, Av, Ai, and Ro: I C I 1mA gm IC r V ro A VT gm IC 1mA 100 .25mV 40mA / V 40mA / V 100V 1mA 2.5k 100k

Rc ro 1005k 100k vo Av vs Rs r 5k 2.5k 63.5V / V ro 100k Ai 100 ro RC 100k 5k 95.2 A / A Ro RC ro 5k 100k 4.76k Ri r 2.5k What is Av if a 5k load resistor is added to the circuit: Av load Av noload REP 02/13/20 ENGR224 RL 5k 63.5 32.5V / V RL Ro 5k 4.76k Page BJT 4.1-56 Bipolar Junction Transistors Common-Emitter Amplifier with an Emitter Resistor REP 02/13/20 ENGR224 Page BJT 4.1-57 Bipolar Junction Transistors Common-Emitter Amplifier with an Emitter Resistor (cont.)

Input Resistance: Voltage Gain: vb ie re Re vo ie Rc ie ib 1 ie 1 vb Ri 1 re Re ib vo Rc vb re Re Ri (with R e included) 1 re Re 1 re Ri (without R e ) vb Ri vs Ri Rs Re 1 1 g m Re re REP 02/13/20 ENGR224 vo Rc vb re Re Av since 1

vo Rc vs Rs 1 re Re Page BJT 4.1-58 Bipolar Junction Transistors Common-Emitter Amplifier with an Emitter Resistor (cont.) Characteristics of CE amplifier with resistance Re: v r 1 e vb re Re 1 g m Re Input resistance is increased by the factor of (1+gmRe) Output Resistance: An input signal of (1+gmRe) times larger can be applied to the input without inducing nonlinear distortion The voltage gain is reduced The voltage gain is less dependent on the value of The high frequency response is significantly improved Ro Rc Current Gain: io

Ai ib REP 02/13/20 ENGR224 Page BJT 4.1-59 Bipolar Junction Transistors Exercise 4.32 For a CE amplifier with Re, let I=1 mA, RC=5k, =100, and Rs=5k. Find Re such that the amplifier has an input resistence of 4 times that of the source. Find A v, Ai, and Ro: V 25mV re T 25 IE 1mA Ro Rc 5k Ri 20k 1 re Re 100 1 25 Re Re 173 Rc 100(5k) Rs 1 re Re 5k 100 1 25 173 500k 20V / V 25k Av Ai 100 A / A REP 02/13/20 ENGR224 Page BJT 4.1-60 Bipolar Junction Transistors Exercise 4.32 For the same CE amplifier, find the maximum v s without Re and with Re if v is to be limited to 5mV:

100 .9901 v (max) with Re v (max) without Re 1 g m Re 1 101 3 5 mV 1 39 . 064 X 10 *173 .9901 gm 39.604 X 10 3 40mV re 25 R Ri vs (max) v (max) s Ri 100 r 2525 3 5k 20k g m 39.604 X 10 40mV 20k r v (max) 5mV vs (max) 50mV R r

s 2525 vs (max) 5000 2525 vs (max) 14.9mV REP 02/13/20 ENGR224 Page BJT 4.1-61 Bipolar Junction Transistors Common-Base Amplifier REP 02/13/20 ENGR224 Page BJT 4.1-62 Bipolar Junction Transistors Common-Base Amplifier (cont.) Input Resistance: Ri re Voltage Gain: Current Gain: io ie Ai ib ie vo ie Rc vs ie Rs re Av Output Resistance: Ro Rc

vo Rc vs Rs re REP 02/13/20 ENGR224 Page BJT 4.1-63 Bipolar Junction Transistors Exercise 4.33 For a CB amplifier with Re, let I=1 mA, RC=5k, =100, and Rs=5k. Find RiAv, Ai, and Ro: V 25mV Ri re T 25 IE 1mA 100 .9901 1 101 Rc 0.9901(5k) Av Rs re 5k 25 0.985V / V Ai 0.99 A / A Ro Rc 5k Note that RiAv, Ai are much lower than the CE amplifier using the same components although the voltage gain of the CB amplifier can be almost equivalent if R s is low. REP 02/13/20 ENGR224

Page BJT 4.1-64 Bipolar Junction Transistors Common-Collector Amplifier - Emitter Follower REP 02/13/20 ENGR224 Page BJT 4.1-65 Bipolar Junction Transistors Common-Collector Amplifier - Emitter Follower (cont.) REP 02/13/20 ENGR224 Page BJT 4.1-66 Bipolar Junction Transistors Common-Collector Amplifier - Emitter Follower (cont.) Input Resistance: Ri 1 re ro RL if re RL ro Ri 1 RL Current Gain: io ro Ai 1 ib ro RL REP 02/13/20 ENGR224 Voltage Gain: 1 re ro RL vb vs Rs 1 re ro RL ro RL vo

vb re ro RL 1 RL ro vo Av vs Rs 1 re RL ro RL ro vo Av Rs vs re RL ro 1 Page BJT 4.1-67 Bipolar Junction Transistors Common-Collector Amplifier - Emitter Follower (cont.) Output Resistance: v x ie re 1 ie Rs vx ie re 1 Rs vx ix ie ro vx vx ix ro re 1 Rs REP 02/13/20 ENGR224 since Ro vx ix 1 ix 1 1

Ro v x ro re 1 Rs Thus Ro is the parallel equivalent of ro and re 1 Rs Rs Ro ro re 1 Page BJT 4.1-68 Bipolar Junction Transistors Common-Collector Amplifier - Emitter Follower (cont.) Output Resistance (cont.): when ro is large Ro re Rs 1 Voltage Gain revisited: Open-circuit voltage gain: Av RL Av Av REP 02/13/20 ENGR224 ro Rs re ro

1 RL RL RL Ro Page BJT 4.1-69 Bipolar Junction Transistors Exercise 4.34 For an emitter follower with a load resistence, R L=1k, let I=5 mA, =100, VA=100V, and vb v o vo Rs=10k. Find Ri , v , v , v , Ro , Av RL , and Ai : s b s V 25mV re T 5 IE 5mA 100 .9901 1 101 V V 100V r0 A A 20.2 K I C I E .99015mA Ri 1 re ro RL vb Ri 96.7 k

0.906V / V vs Rs Ri 10k 96.7k r R 20k 1k 0.995V / V vo o L vb re ro RL 5 20k 1k vo vo vb 0.995 0.906 0.901V / V vv vb vs 100 1 5 20.2k 1k 96.74k REP 02/13/20 ENGR224 Page BJT 4.1-70 Bipolar Junction Transistors Exercise 4.34 (cont.) For an emitter follower with a load resistence, R L=1k, let I=5 mA, =100, VA=100V, and vb v o vo Rs=10k. Find Ri , v , v , v , Ro , Av RL , and Ai : s b s R Ro ro re s 20k 1 103.5 Av ro Rs re ro

1 0.995V / V RL Ai 1 10k 5 100 1 20k 10k 5 20k 101 ro 20k 101 r0 RL 20k 1k 96.2 A / A REP 02/13/20 ENGR224 Page BJT 4.1-71 Bipolar Junction Transistors The BJT as a switch-cutoff and saturation The BJT has 4 modes of operation: Cutoff Forward Active Saturation Inverse Active

So far, we have studied the forward active mode in great detail. Now we will look at the BJT in cutoff mode and at the BJT in saturation mode. These two extreme modes of operation are very useful if the transistor is used as a switch, such as in digital logic circuits. Mode EBJ Cutoff Reverse Forward Active Forward Saturation Forward Inverse Active Reverse REP 02/13/20 ENGR224 CBJ Reverse Reverse Forward Forward Page BJT 4.1-72 Bipolar Junction Transistors Cutoff Region Consider the circuit shown below. If voltage source v I is goes lesss than about 0.5V, the Emitter-Base Junction will conduct negligible current (reverse-biased). The CBJ is also reverse-biased since VCC is positive. The device will be in the cutoff mode. It follows that: i E 0 i C 0 i B 0 vC VCC VCC

iC RC RB vI REP 02/13/20 ENGR224 + - vC iB Page BJT 4.1-73 Bipolar Junction Transistors Active Region To turn the transistor on, vI must be increased to above 0.7V. This gives base current: The collector current is given by iB v I which VBEapplies only v 0.7 I if the device is in active mode. At this point, we dont know for sure, therefore we assume active mode and calculate the collector current from RB RB i C i B vC VCC RC iC VCC Next, we check whether vCB 0.7 or not. In our case, just check whether vC 0 or not . If so, then our original assumption

is true. If not, the device is in saturation. iC RC RB vI REP 02/13/20 ENGR224 + - vC iB Page BJT 4.1-74 Bipolar Junction Transistors Saturation Region Saturation occurs when we attempt to force a current in the collector higher than the collector circuit can support while maintaining active-mode operation. VCC By setting vCB 0, we calculate V V B VCC 0.7 IC CC RC RC I IB C I Csat Maximum collector current RC MAXIMUM BASE current in forward active

RB Increasing i B above I B , the collector current will increase and the collector voltage will fall below that of the base. This will continue until the CBJ becomes forward-biased. I Csat VCC VCE RC I B ( EOS ) I Csat Constant current vI + - IB V BE vC VCEsat IB is usually higher than IB(EOS) by a factor of 2 to 10 -- overdrive factor. EOS=edge of saturation REP 02/13/20 ENGR224

forced I Csat IB This value can be set at will. Page BJT 4.1-75 Bipolar Junction Transistors Model for the Saturated BJT A simple model for the npn and pnp transistors in saturation mode is shown on the left. For quick approximate calculations one may consider V BE and VCEsat to be zero and use the three-terminal short circuit shown on the right to model a saturated transistor. C B C VCEsat 0.2 V V BE 0.7 V npn B E E E approximate model V EB 0.7 V

VECsat 0.2 V C B pnp REP 02/13/20 ENGR224 Page BJT 4.1-76 Bipolar Junction Transistors Example 4.13 We wish to analyze the circuit to determine the voltages at all nodes and currents in all branches. Assume the transistor is specified to be at least 50. Assuming saturation: 10V 10V V E 6 V BE 6 0.7 5.3 V 4 I C 6V RC 4.7 k 6V 5 RE 3.3k 4.7 k VC IB 3.3 k IE

IE VE 1 2 3 5.3 1.6 mA 3.3 1 2 VC VE VCEsat 5.3 0.2 5.5 V 10 5.5 IC 0.96 mA 4.7 3 4 I B I E I C 1.6 0.96 0.64 mA forced I C 0.96 1.5 I B 0.64 forced min , transistor is saturated REP 02/13/20 ENGR224 Page BJT 4.1-77 5 Bipolar Junction Transistors Example 4.14

The transistor shown below is specified to have in the range 50 to 150. Find the value of RB that results in saturation with an overdrive factor of at least 10. 10V VC VCEsat 0.2 V I Csat 1 k RB 5V VCEsat IB VC 10 0.2 I Csat 9.8 mA 1 To saturate the transistor with the lowest , I 9 .8 I B ( EOS ) Csat 0.196 mA min 50 For an overdrive factor of 10, I B 10 0.196 1.96 mA 5 0 .7 4 .3 1.96 R B 2.2 k RB 1.94 REP 02/13/20 ENGR224

Page BJT 4.1-78 Bipolar Junction Transistors Example 4.15 We want to analyze the circuit below to determine the voltages at all nodes and the currents through all branches. The minimum value of is specified to be 30. 5V IE IE 10 k 1 k VE V ECsat IB VB 0.1V B mA 10 VC IC IB 10 k 5V V E V B VBE VB 0.7 5 V E 5 V B 0.7 4.3 V B mA 1 1

IC VC 5 VB 0.5 5 0.1V B 0.55 mA 10 10 using I E I B I C 4.3 VB 0.1VB 0.1V B 0.55 VB 3.75 3.13 V 1.2 VC VE VECsat VB 0.7 0.2 V B 0.5 REP 02/13/20 ENGR224 Page BJT 4.1-79 Bipolar Junction Transistors Example 4.15, contd Substituting in the equations on the previous page, we obtain the following: VE 3.83 V VC 3.63 V forced I E 1.17 mA I C 0.86 mA 0.86 2.8 0.31 forced min the transistor is clearly saturated I B 0.31 mA REP 02/13/20 ENGR224

Page BJT 4.1-80 Bipolar Junction Transistors Introduction - Equation forms for use in SPICE Consider the equation for the emitter current in an ideal pnp bipolar junction transistor We can simplify the equations by collecting the terms into only a few constants, giving the coefficients different names, for example, half of the equation given above becomes; The other half of the equation is similarly reduced This allows the emitter current to be written in a much more compact form: REP 02/13/20 ENGR224 Page BJT 4.1-81 Bipolar Junction Transistors Equation forms for use in SPICE (continued) Now consider the equation for the collector current in an ideal pnp bipolar junction transistor The right half of the equation reduces to: The left half of the equation is similarly reduced This allows the collector current to be written in a much more compact form:

If we know two of the terminal currents we can find the current in the third terminal REP 02/13/20 ENGR224 Page BJT 4.1-82 Bipolar Junction Transistors The Ebers-Moll equations for an ideal PNP BJT The key results are The equivalent circuit (just another way to state the equations) IC C C P IC FIF B IR IB N IF RIR B IB IE IE REP 02/13/20 ENGR224 E

P E Page BJT 4.1-83 Bipolar Junction Transistors Use in SPICE The current sources illustrate the interaction of the two junctions due to the narrow base region IS is one of the three required SPICE parameters for a BJT in SPICE2 The reduced equations can be manipulated to show that: Only three numbers, F , R and IS are needed for the Ebers-Moll equations to be completely specified. All other parameters can be calculated from these three The equations can be applied to all regions of operation Can be extended to the nonideal case by defining coefficients in front of the exponential terms For NPN transistors the diodes, currents and voltage polarities are reversed REP 02/13/20 ENGR224 Page BJT 4.1-84 Bipolar Junction Transistors An Alternative form of the Ebers-Moll Model, the Transport Model In this model the diodes DBE and DBC have saturation currents IS/F and IS/F respectively The base current, ib can be written as

v BE v BC I S VT I V S e T 1 iB e 1 R F iT is the current component of i C which arises from the minority carrier diffusion (transport) across the base, hence the name of this model vVBE vVBC T T iT I S e 1 I S e 1 iC DBC

B The transport model is exactly equivalent to the EbersMoll model but it highlights different aspects of BJT behavior. It uses one less circuit element and one less parameter in SPICE REP 02/13/20 ENGR224 C IS/R iB iT DBE IS/F iE Page BJT 4.1-85 E Bipolar Junction Transistors Common-Base Characteristics First-Order iC-vCB Characteristics Second-Order iC-vCB Characteristics REP 02/13/20 ENGR224 Page BJT 4.1-86 Bipolar Junction Transistors Common-Emitter Characteristics Second-Order iC-vCE Characteristics (refer to lesson 17) REP 02/13/20 ENGR224 Page BJT 4.1-87 Bipolar Junction Transistors DC and ac BETA DC (spice)

More accurate than F, because its determined at Q Common-emitter current gain at DC BETAAC (spice) Input ac signal results in iB iC. Thus changes, because Since vCE is constant, ac=short-circuit current gain. Typically, ac=dc. Use ac in small-signal model. REP 02/13/20 ENGR224 Page BJT 4.1-88 Bipolar Junction Transistors Complete BJT Models Low-frequency model rx=base resistance of bulk Si 1 r= i B VC REP 02/13/20 ENGR224 Page BJT 4.1-89 Bipolar Junction Transistors Complete BJT Models High-frequency model V C C JC C JC 1 CB VJC MJC V C C D C JE g m TF C JE 1 BE VJE f 3 dB

1 2 r C C REP 02/13/20 ENGR224 MJE gm fT 2 C C Page BJT 4.1-90

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