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Chapter 3 Bipolar Junction Transistor (BJT) SJTU Zhou Lingling 1 Outline • • • • • • • • Introduction Operation in the Active Mode Analysis of Transistor Circuits at DC The transistor as an Amplifier Graphical Analysis Biasing the BJT for Discrete-Circuit Design Configuration for Basic Single Stage BJT Amplifier High frequency Model SJTU Zhou Lingling 2 Introduction • • • • Physical Structure Circuit Symbols for BJTs Modes of Operation Basic Characteristic SJTU Zhou Lingling 3 Physical Structure A simplified structure of the npn transistor. SJTU Zhou Lingling 4 Physical Structure A dual of the npn is called pnp type. This is the simplified structure of the pnp transistor. SJTU Zhou Lingling 5 Circuit Symbols for BJTs The emitter is distinguished by the arrowhead. SJTU Zhou Lingling 6 Modes of Operation Modes EBJ CBJ Cutoff Reverse Reverse Saturation Forward Forward Active Forward Reverse Amplifier Reverse active Reverse Forward Performance degradation SJTU Zhou Lingling Application Switching application in digital circuits 7 Basic Characteristics • Far more useful than two terminal devices (such as diodes) • The voltage between two terminals can control the current flowing in the third terminal. We can say that the collector current can be controlled by the voltage across EB junction. • Much popular application is to be an amplifier SJTU Zhou Lingling 8 Operation in the Active Mode • Current flow • Current equation • Graphical representation of transistor’s characteristics SJTU Zhou Lingling 9 Current Flow Current flow in an npn transistor biased to operate in the active mode. SJTU Zhou Lingling 10 Collector Current • Collector current is the drift current. • Carriers are successful excess minority carriers. • The magnitude of collector current is almost independent of voltage across CB junction. • This current can be calculated by the gradient of the profile of electron concentration in base region. SJTU Zhou Lingling 11 Base Current • Base current consists of two components. Diffusion current Recombination current • Recombination current is dominant. • The value of base current is very small. SJTU Zhou Lingling 12 Emitter Current • • • • Emitter current consists of two components. Both of them are diffusion currents. Heavily doped in emitter region. Diffusion current produced by the majority in emitter region is dominant. SJTU Zhou Lingling 13 Profiles of Minority-Carrier Concentrations SJTU Zhou Lingling 14 Current Equation • Collector current iC I n I s e • Base current Is iB iC • Emitter current vBE VT vBE VT e I s vBE VT iE e iC SJTU Zhou Lingling 15 Explanation for Saturation Current • Saturation current is also called current scale. • Expression for saturation current: Is AE qDn n p 0 AE qDn ni W N AW 2 • Has strong function with temperature due to intrinsic carrier concentration. • Its value is usually in the range of 10-12A to 10-18A. SJTU Zhou Lingling 16 Explanation for Common-Emitter Current Gain • Expression for common –emitter current gain: Dp N A W 1 W 2 =1 Dn N D LP 2 Dn b • Its value is highly influenced by two factors. • Its value is in the range 50 to 200 for general transistor. SJTU Zhou Lingling 17 Explanation for Common-Base Current Gain • Expression for common –base current gain: = 1+ • Its value is less than but very close to unity. • Small changes in α correspond to very large changes in β. SJTU Zhou Lingling 18 Recapitulation • Collector current has the exponential relationship with forward-biased voltage vBE as long as the CB junction remains reversebiased. • To behave as an ideal constant current source. • Emitter current is approximately equal to collector current. SJTU Zhou Lingling 19 Graphical Representation of Transistor’s Characteristics • Characteristic curve relates to a certain configuration. • Input curve is much similar to that of the diode, only output curves are shown here. • Three regions are shown in output curves. • Early Effect is shown in output curve of CE configuration. SJTU Zhou Lingling 20 Output Curves for CB Configuration SJTU Zhou Lingling 21 Output Curves for CB Configuration • Active region EBJ is forward-biased, CBJ is reverse-biased; Equal distance between neighbouring output curves; Almost horizontal, but slightly positive slope. • Saturation region EBJ and CBJ are not only forward-biased but also turned on; Collector current is diffusion current not drift current. Turn on voltage for CBJ is smaller than that of EBJ. • Breakdown region EBJ forward-biased, CBJ reverse-biased; Great voltage value give rise to CBJ breakdown; Collector current increases dramatically. SJTU Zhou Lingling 22 Output Curves for CE Configuration (a) Conceptual circuit for measuring the iC –vCE characteristics of the BJT. (b) The iC –vCE characteristics of a practical BJT. SJTU Zhou Lingling 23 The Early Effect • Curves in active region are more sloped than those in CB configuration. • Early voltage. • Effective base width and base width modulation. SJTU Zhou Lingling 24 The Early Effect(cont’d) • Assuming current scale remains constant, collector current is modified by this term: vBE vCE iC I s e (1 ) VA • Narrow base width, small value of Early voltage, strong effect of base width modulation, strong linear dependence of Ci on vCE . SJTU VT Zhou Lingling 25 Analysis of Transistor Circuit at DC • Equivalent Circuit Models • Analysis Steps • Examples SJTU Zhou Lingling 26 Equivalent Circuit Models Large-signal equivalent-circuit models of the npn BJT operating in the forward active mode. In practical DC analysis, constant voltage drop model is popular used. SJTU Zhou Lingling 27 DC Analysis Steps a. Using simple constant-voltage drop model, assuming vBE 0.7V irrespective of the exact value of currents. b. Assuming the device operates at the active region, we can apply the relationship between IB, IC, and IE, to determine the voltage VCE or VCB. c. Check the value of VCE or VCB, if i. VC>VB (or VCE>0.2V), the assumption is correct. ii. VC<VB (or VCE<0.2V), the assumption is incorrect. It means the BJT is operating in saturation region. Thus we shall assume VCE=VCE(sat) to obtain IC. Here the common emitter current gain is defined as forced=IC/IB, we will find forced< . SJTU Zhou Lingling , 28 Examples • Example 5.4 shows the order of the analysis steps indicated by the circled numbers. • Example 5.5 shows the analysis of BJT operating saturation mode. • Example 5.6 shows the transistor operating in cutoff mode. SJTU Zhou Lingling 29 Examples(cont’d) • Example 5.7 shows the analysis for pnp type circuit. It indicates the the current is affected by illspecified parameter β. As a rule, one should strive to design the circuit such that its performance is as insensitive to the value of β as possible. • Example 5.8 is the bad design due to the currents critically depending on the value of β. • Example 5.9 is similar to the example 5.5 except the transistor is pnp type. SJTU Zhou Lingling 30 Examples(cont’d) • Example 5.10 shows the application of Thévenin’s theorem in calculating emitter current and so on. This circuit is the good design for the emitter is almost independent of β and temperature. • Example 5.11 shows the DC analysis for two stage amplifier. • Example 5.12 shows the analysis of the power amplifier composed of the complimentary transistors. SJTU Zhou Lingling 31 The Transistor as an Amplifier • Conceptual Circuits • Small-signal equivalent circuit models • Application of the small-signal equivalent circuit models • Augmenting the hybrid π model. SJTU Zhou Lingling 32 Conceptual Circuit (a) Conceptual circuit to illustrate the operation of the transistor as an amplifier. (b) The circuit of (a) with the signal source vbe eliminated for dc (bias) analysis. SJTU Zhou Lingling 33 Conceptual Circuit(cont’d) With the dc sources (VBE and VCC) eliminated (short circuited), thus only the signal components are present. Note that this is a representation of the signal operation of the BJT and not an actual amplifier circuit. SJTU Zhou Lingling 34 Small-Signal Circuit Models • Transconductance • Input resistance at base • Input resistance at emitter • Hybrid π and T model SJTU Zhou Lingling 35 Transconductance • Expression gm I CQ VT • Physical meaning gm is the slope of the iC–vBE curve at the bias point Q. • At room temperature, g m 40ms SJTU Zhou Lingling 36 Input Resistance at Base and Emitter • Input resistance at base r vbe V T ib I BQ gm • Input resistance at emitter vbe VT re ie I EQ gm • Relationship between these two resistances r (1 )re SJTU Zhou Lingling 37 The Hybrid- Model • The equivalent circuit in (a) represents the BJT as a voltage-controlled current source (a transconductance amplifier), • The equivalent circuit in (b) represents the BJT as a current-controlled current source (a current amplifier). SJTU Zhou Lingling 38 The T Model • These models explicitly show the emitter resistance re rather than the base resistance r featured in the hybrid- model. SJTU Zhou Lingling 39 Augmenting the Hybrid- Model Expression for the output resistance. i ro C v CE v BE const. 1 VA ' IC Output resistance represents the Early Effect(or base width modulation) SJTU Zhou Lingling 40 Models for pnp Type • Models derived from npn type transistor apply equally well to pnp transistor with no changes of polarities. Because the small signal can not change the bias conditions, small signal models are independent of polarities. • No matter what the configuration is, model is unique. Which one to be selected is only determined by the simplest analysis. SJTU Zhou Lingling 41 Graphical Analysis a. Graphical construction for the determination of the dc base current in the circuit. b. Load line intersects with the input characteristic curve. SJTU Zhou Lingling 42 Graphical Analysis(cont’d) Graphical construction for determining the dc collector current IC and the collector-to-emitter voltage VCE in the circuit. SJTU Zhou Lingling 43 Small Signal Analysis Graphical determination of the signal components vbe, ib, ic, and vce when a signal component vi is superimposed on the dc voltage VBB SJTU Zhou Lingling 44 Effect of Bias-Point Location on Allowable Signal Swing SJTU a. Load-line A results in bias point QA with a corresponding VCE which is too close to VCC and thus limits the positive swing of vCE. b. At the other extreme, load-line B results in an operating point too close to the saturation region, thus limiting the negative swing of vCE. Zhou Lingling 45 Biasing in BJT Amplifier Circuit • Biasing with voltage Classical discrete circuit bias arrangement Single power supply Two-power-supply With feedback resistor • Biasing with current source SJTU Zhou Lingling 46 Classical Discrete Circuit Bias Arrangement by fixing VBE by fixing IB. SJTU Zhou Lingling 47 Classical Discrete Circuit Bias Arrangement • Both result in wide variations in IC and hence in VCE and therefore are considered to be “bad.” • Neither scheme is recommended. SJTU Zhou Lingling 48 Classical Biasing for BJTs Using a Single Power Supply Circuit with the voltage divider supplying the base replaced with its Thévenin equivalent. Stabilizing the DC emitter current is obtained by considering the negative feedback action provided by RE SJTU Zhou Lingling 49 Classical Biasing for BJTs Using a Single Power Supply • Two constraints VBB VBE RB RE 1 • Rules of thumb VBB 13 VCC I C RC 13 VCC VCB 13 VCC I RB! I RB 2 (0.1I E , I E ) SJTU Zhou Lingling 50 Two-Power-Supply Version • Resistor RB can be eliminated in common base configuration. • Resistor RB is needed only if the signal is to be capacitively coupled to the base. • Two constraints should apply. SJTU Zhou Lingling 51 Biasing with Feedback Resistor Resistor RB provides negative feedback. IE is insensitive to β provided that RC RB (1 ) The value of RB determines the allowable signal swing at the collector. SJTU Zhou Lingling 52 Biasing Using Current Source (a) Q1 and Q2 are required to be identical and have high β. (b) Short circuit between Q1’s base and collector terminals. (c) Current source isn’t ideal due to finite output resistor of Q2 SJTU Zhou Lingling 53 Application of the Small-Signal Models a. Determine the DC operating point of BJT and in particular the DC collector current IC(ICQ). b. Calculate the values of the small-signal model parameters, such as gm=IC/VT, r=/gm=VT/IB, re=/gm=VT/IE. c. Draw ac circuit path. d. Replace the BJT with one of its small-signal models. The model selected may be more convenient than the others in circuits analysis. e. Determine the required quantities. SJTU Zhou Lingling 54 Basic Single-Stage BJT Amplifier • Characteristic parameters • Basic structure • Configuration Common-Emitter amplifier Emitter directly connects to ground Emitter connects to ground by resistor RE Common-base amplifier Common-collector amplifier(emitter follower) SJTU Zhou Lingling 55 Characteristic Parameters of Amplifier This is the two-port network of amplifier. Voltage signal source. Output signal is obtained from the load resistor. SJTU Zhou Lingling 56 Definitions • Input resistance with no load v Ri i ii R L • Input resistance Rin vi ii • Open-circuit voltage gain Avo vo vi RL • Voltage gain A vo v vi SJTU Zhou Lingling 57 Definitions(cont’d) • Short-circuit current gain Ais io ii RL 0 • Current gain Ai io ii • Short-circuit transconductance io Gm vi RL 0 SJTU Zhou Lingling 58 Definitions(cont’d) • Open-circuit overall voltage gain v0 Gvo vsig RL • Overall voltage gain v0 Gv vsig SJTU Zhou Lingling 59 Definitions(cont’d) Output resistance of amplifier proper vx Ro ix Output resistance Rout vi 0 SJTU Zhou Lingling vx ix vsig 0 60 Definitions(cont’d) Voltage amplifier Voltage amplifier Transconductance amplifier SJTU Zhou Lingling 61 Relationships • Voltage divided coefficient vi Rin vsig Rin Rsig RL Av Avo RL Ro Gv Rin RL Avo Rin Rsig RL Ro Ri Gvo Avo Ri Rsig RL Gv Gvo RL Rout Avo Gm Ro SJTU Zhou Lingling 62 Basic Structure Basic structure of the circuit used to realize single-stage, discrete-circuit BJT amplifier configurations. SJTU Zhou Lingling 63 Common-Emitter Amplifier SJTU Zhou Lingling 64 Common-Emitter Amplifier Equivalent circuit obtained by replacing the transistor with its hybrid- model. SJTU Zhou Lingling 65 Characteristics of CE Amplifier • Input resistance • Voltage gain Rin r Av g m (ro // RC // RL ) • Overall voltage gain Gv • Output resistance ( RC // RL // ro ) r Rsig Rout RC • Short-circuit current gain Ais SJTU Zhou Lingling 66 Summary of CE amplifier • • • • • • Large voltage gain Inverting amplifier Large current gain Input resistance is relatively low. Output resistance is relatively high. Frequency response is rather poor. SJTU Zhou Lingling 67 The Common-Emitter Amplifier with a Resistance in the Emitter SJTU Zhou Lingling 68 The Common-Emitter Amplifier with a Resistance in the Emitter SJTU Zhou Lingling 69 Characteristics of the CE Amplifier with a Resistance in the Emitter • Input resistance Rin RB //(1 )(re Re ) • Voltage gain RC // RL Av re Re • Overall voltage gain Gv • Output resistance ( RC // RL ) Rsig (1 )( re Re ) Rout RC • Short-circuit current gain SJTU Ais Zhou Lingling 70 Summary of CE Amplifier with RE • The input resistance Rin is increased by the factor (1+gmRe) • The voltage gain from base to collector is reduced by the factor (1+gmRe). • For the same nonlinear distortion, the input signal vi can be increased by the factor (1+gmRe). • The overall voltage gain is less dependent on the value of β. SJTU Zhou Lingling 71 Summary of CE Amplifier with RE • The reduction in gain is the price for obtaining the other performance improvements. • Resistor RE introduces the negative feedback into the amplifier. • The high frequency response is significant improved. SJTU Zhou Lingling 72 Common-Base Amplifier SJTU Zhou Lingling 73 Common-Base Amplifier SJTU Zhou Lingling 74 Characteristics of CB Amplifier • Input resistance Rin re • Voltage gain Av g m ( RC // RL ) • Overall voltage gain Gv • Output resistance ( RC // RL ) Rsig re Rout RC • Short-circuit current gain Ais SJTU Zhou Lingling 75 Summary of the CB Amplifier • • • • • • • Very low input resistance High output resistance Short-circuit current gain is nearly unity High voltage gain Noninverting amplifier Current buffer Excellent high-frequency performance SJTU Zhou Lingling 76 The Common-Collector Amplifier or Emitter-Follower SJTU Zhou Lingling 77 The Common-Collector Amplifier or Emitter-Follower SJTU Zhou Lingling 78 The Common-Collector Amplifier or Emitter-Follower SJTU Zhou Lingling 79 Characteristics of CC Amplifier • Input resistance Rib (1 )(re ro // RL ) • Voltage gain (1 )( r // R ) Av o L (1 )( re ro // RL ) • Overall voltage gain RB // Rib (1 )(ro // RL ) Gv RB // Rib Rsig (1 )(re ro // RL ) • Output resistance Rout re RB // Rsig 1 • Short-circuit current gain Ais (1 ) SJTU Zhou Lingling 80 Summary for CC Amplifier or Emitter-Follower • High input resistance • Low output resistance • Voltage gain is smaller than but very close to unity • Large current gain • The last or output stage of cascade amplifier • Frequency response is excellent well SJTU Zhou Lingling 81 Summary and Comparisons • The CE configuration is the best suited for realizing the amplifier gain. • Including RE provides performance improvements at the expense of gain reduction. • The CB configuration only has the typical application in amplifier. Much superior high-frequency response. • The emitter follower can be used as a voltage buffer and exists in output stage of a multistage amplifier. SJTU Zhou Lingling 82 Internal Capacitances of the BJT and High Frequency Model • Internal capacitance The base-charging or diffusion capacitance Junction capacitances The base-emitter junction capacitance The collector-base junction capacitance • High frequency small signal model • Cutoff frequency and unity-gain frequency SJTU Zhou Lingling 83 The Base-Charging or Diffusion Capacitance • • Diffusion capacitance almost entirely exists in forward-biased pn junction Expression of the small-signal diffusion capacitance IC Cde F g m F VT • Proportional to the biased current SJTU Zhou Lingling 84 Junction Capacitances • The Base-Emitter Junction Capacitance C je • C je0 2C je0 VBE m (1 ) Voe The collector-base junction capacitance C 0 C V (1 CB ) m Voc SJTU Zhou Lingling 85 The High-Frequency Hybrid- Model • Two capacitances Cπ and Cμ , where C Cde C je • One resistance rx . Accurate value is obtained form high frequency measurement. SJTU Zhou Lingling 86 The Cutoff and Unity-Gain Frequency • • Circuit for deriving an expression for h fe ( s ) IC IB vCE 0 According to the definition, output port is short circuit SJTU Zhou Lingling 87 The Cutoff and Unity-Gain Frequency(cont’d) • Expression of the short-circuit current transfer function h fe ( s) 0 1 s(C C )r • Characteristic is similar to the one of firstorder low-pass filter SJTU Zhou Lingling 88 The Cutoff and Unity-Gain Frequency (cont’d) 1 (C C )r gm T 0 C C SJTU Zhou Lingling 89