2The BJT – Bipolar Junction Transistor Note: Normally Emitter layer is heavily doped, Base layer is lightly doped and Collector layer has Moderate doping.The Two Types of BJT Transistors:npnpnpnpnpnpECECCCCross SectionCross SectionBBBBSchematic SymbolSchematic SymbolEECollector doping is usually ~ 109Base doping is slightly higher ~ 1010 – 1011Emitter doping is much higher ~ 1017
3BJT Relationships - Equations IEICIEIC-VCE++VEC-ECEC--++VBEVBCIBVEBVCBIB--++BBn p nIE = IB + ICVCE = -VBC + VBEp n pIE = IB + ICVEC = VEB - VCBNote: The equations seen above are for the transistor, not the circuit.
4Bulk-recombination Current I co-Inc+VCB-p-- Electrons+ Holes+IpeInen+VBE-Bulk-recombination CurrentFigure : Current flow (components) for an n-p-n BJT in the active region.NOTE: Most of the current is due to electrons moving from the emitter through base to the collector. Base current consists of holes crossing from the base into the emitter and of holes that recombine with electrons in the base.
5Physical StructureConsists of 3 alternating layers of n- and p-type semiconductor called emitter (E), base (B) and collector (C).Majority of current enters collector, crosses base region and exits through emitter. A small current also enters base terminal, crosses base-emitter junction and exits through emitter.Carrier transport in the active base region directly beneath the heavily doped (n+) emitter dominates i-v characteristics of BJT.
6Ic C - - - - - - - - - - - - - - - - - n VCB + _ B p + + IB VBE _ n E nRecombinationVCB+_Electrons+ HolesBp++IB-VBE-_-nEIE
7For CB Transistor IE= Ine+ Ipe Ic= Inc- Ico And Ic= - αIE + ICo CB Current Gain, α ═ (Ic- Ico) .(IE- 0)For CE Trans., IC = βIb + (1+β) Icowhere β ═ α ,1- α is CE GainBulk-recombination currentICOIncIpeIneFigure: An npn transistor with variable biasing sources (common-emitter configuration).
8Collector-Current Curves Common-EmitterCircuit DiagramCollector-Current CurvesVCEICIC+_Active RegionVCCIBIBRegion of OperationDescriptionActiveSmall base current controls a large collector currentSaturationVCE(sat) ~ 0.2V, VCE increases with ICCutoffAchieved by reducing IB to 0, Ideally, IC will also be equal to 0.VCESaturation RegionCutoff RegionIB = 0
9BJT’s have three regions of operation: 1) Active - BJT acts like an amplifier (most common use)2) Saturation - BJT acts like a short circuit3) Cutoff - BJT acts like an open circuitBJT is used as a switch by switchingbetween these two regions.When analyzing a DC BJT circuit, the BJT is replaced by one of the DC circuit models shown below.DC Models for a BJT:
10DC and DC = Common-emitter current gain = Common-base current gain = IC = ICIB IEThe relationships between the two parameters are: = = Note: and are sometimes referred to as dc and dc because the relationships being dealt with in the BJT are DC.
11Output characteristics: npn BJT (typical) Note: The PE review text sometimes uses dc instead of dc. They are related as follows:Find the approximate values of bdc and adc from the graph.Input characteristics: npn BJT (typical)The input characteristics look like the characteristics of a forward-biased diode. Note that VBE varies only slightly, so we often ignore these characteristics and assume:Common approximation: VBE = Vo = 0.65 to 0.7VNote: Two key specifications for the BJT are Bdc and Vo (or assume Vo is about 0.7 V)
14Various Regions (Modes) of Operation of BJT Active:Most important mode of operationCentral to amplifier operationThe region where current curves are practically flatSaturation:Barrier potential of the junctions cancel each other out causing a virtual short (behaves as on state Switch)Cutoff:Current reduced to zeroIdeal transistor behaves like an open switch* Note: There is also a mode of operation called inverse active mode, but it is rarely used.
15BJT Trans-conductance Curve For Typical NPN Transistor 1 Collector Current:IC = IES eVBE/VTTransconductance:(slope of the curve)gm = IC / VBEIES = The reverse saturation currentof the B-E Junction.VT = kT/q = 26 mV T=300oK) = the emission coefficient and isusually ~1IC8 mA6 mA4 mA2 mAVBE0.7 V
16Three Possible Configurations of BJT Biasing the transistor refers to applying voltages to the transistor to achieve certain operating conditions.1. Common-Base Configuration (CB) : input = VEB & IEoutput = VCB & IC2. Common-Emitter Configuration (CE): input = VBE & IBoutput= VCE & IC3. Common-Collector Configuration (CC) :input = VBC & IB(Also known as Emitter follower) output = VEC & IE
17Circuit Diagram: NPN Transistor Common-Base BJT Configuration+_ICIEIBVCBVBEECBVCECircuit Diagram: NPN TransistorThe Table Below lists assumptions that can be made for the attributes of the common-base BJT circuit in the different regions of operation. Given for a Silicon NPN transistor.Region of OperationICVCEVBEVCBC-B BiasE-B BiasActiveIB=VBE+VCE~0.7V 0VRev.Fwd.SaturationMax~0V-0.7V<VCE<0Cutoff~0 0VNone/Rev.
18Common-Base (CB) Characteristics Vc- Ic (output) Characteristic Curves Although the Common-Base configuration is not the most common configuration, it is often helpful in the understanding operation of BJTVc- Ic (output) Characteristic CurvesICmABreakdown Reg.6Active RegionIE4Saturation RegionIE=2mA2IE=1mACutoffIE = 0VCB0.8V2V4V6V8V
19Common-Collector BJT Characteristics Emitter-Current Curves The Common-Collector biasing circuit is basically equivalent to the common-emitter biased circuit except instead of looking at IC as a function of VCE and IB we are looking at IE.Also, since ~ 1, and = IC/IE that means IC~IEIEActive RegionIBVCESaturation RegionCutoff RegionIB = 0
20n p n Transistor: Forward Active Mode Currents Base current is given byIC=IB=is forward common-emitter current gainEmitter current is given byVBEIE=Forward Collector current isIco is reverse saturation currentis forward common- base current gainIn this forward active operation region,VT = kT/q =25 mV at room temperature
21Various Biasing Circuits used for BJT Fixed Bias CircuitCollector to Base Bias CircuitPotential Divider Bias Circuit
22The Thermal Stability of Operating Point SIco The Thermal Stability Factor : SIcoSIco = ∂Ic∂IcoThis equation signifies that Ic Changes SIco times as fast as IcoDifferentiating the equation of Collector Current IC & rearranging the terms we can writeSIco ═ 1+β1- β (∂Ib/∂IC)It may be noted that Lower is the value of SIco better is the stabilityVbe, β
23The Thermal Stability Factor : SIco The Fixed Bias CircuitThe Thermal Stability Factor : SIcoSIco = ∂Ic∂IcoGeneral Equation of SIco Comes out to beSIco ═ β1- β (∂Ib/∂IC)Vbe, βRCRbRCApplying KVL through Base Circuit we can write, Ib Rb+ Vbe= VccDiff w. r. t. IC, we get (∂Ib / ∂Ic) = 0SIco= (1+β) is very largeIndicating high un-stabilityIb
24The Collector to Base Bias Circuit The General Equation for Thermal Stability Factor,SIco = ∂Ic∂IcoComes out to beSIco ═ β1- β (∂Ib/∂IC)Vbe, βIcApplying KVL through base circuitwe can write (Ib+ IC) RC + Ib Rb+ Vbe= VccDiff. w. r. t. IC we get(∂Ib / ∂Ic) = - RC / (Rb + RC)Therefore, SIco ═ (1+ β)1+ [βRC/(RC+ Rb)]Which is less than (1+β), signifying better thermal stabilityIb+VBEIE-
25The Potential Devider Bias Circuit The General Equation for Thermal Stability Factor, SIco ═ β1- β (∂Ib/∂IC)ICApplying KVL through input base circuitwe can write IbRTh + IE RE+ Vbe= VThTherefore, IbRTh + (IC+ Ib) RE+ VBE= VThDiff. w. r. t. IC & rearranging we get(∂Ib / ∂Ic) = - RE / (RTh + RE)Therefore,This shows that SIco is inversely proportional to RE andIt is less than (1+β), signifying better thermal stabilityIbICThevenin Equivalent CktICIbRth = R1*R2 & Vth = Vcc R2R1+R R1+R2Self-bias ResistorThevenins Equivalent Voltage
26A Practical C E Amplifier Circuit Input Signal Source
27BJT Amplifier (continued) If changes in operating currents and voltages are small enough, then IC and VCE waveforms are undistorted replicas of the input signal.A small voltage change at the base causes a large voltage change at the collector. The voltage gain is given by:The minus sign indicates a 1800 phase shift between input and output signals.An 8 mV peak change in vBE gives a 5 mA change in iB and a 0.5 mA change in iC.The 0.5 mA change in iC gives a 1.65 V change in vCE .
28A Practical BJT Amplifier using Coupling and Bypass Capacitors In a practical amplifier design, C1 and C3 are large coupling capacitors or dc blocking capacitors, their reactance (XC = |ZC| = 1/wC) at signal frequency is negligible. They are effective open circuits for the circuit when DC bias is considered.C2 is a bypass capacitor. It provides a low impedance path for ac current from emitter to ground. It effectively removes RE (required for good Q-point stability) from the circuit when ac signals are considered.AC coupling through capacitors is used to inject an ac input signal and extract the ac output signal without disturbing the DC Q-pointCapacitors provide negligible impedance at frequencies of interest and provide open circuits at dc.
29D C Equivalent for the BJT Amplifier (Step1) DC Equivalent CircuitAll capacitors in the original amplifier circuit are replaced by open circuits, disconnecting vI, RI, and R3 from the circuit and leaving RE intact. The the transistor Q will be replaced by its DC model.
30A C Equivalent for the BJT Amplifier (Step 2) RoR1IIR2=RBRinCoupling capacitor CC and Emitter bypass capacitor CE are replaced by short circuits.DC voltage supply is replaced with short circuits, which in this case is connected to ground.
31A C Equivalent for the BJT Amplifier (continued) All externally connected capacitors are assumed as short circuited elements for ac signalBy combining parallel resistors into equivalent RB and R, the equivalent ACcircuit above is constructed. Here, the transistor will be replaced by itsequivalent small-signal AC model (to be developed).
32A C Analysis of CE Amplifier 1) Determine DC operating point andcalculate small signal parameters2) Draw the AC equivalent circuit of Amp.• DC Voltage sources are shorted to ground• DC Current sources are open circuited• Large capacitors are short circuits• Large inductors are open circuits3) Use a Thevenin circuit (sometimes aNorton) where necessary. Ideally thebase should be a single resistor + a singlesource. Do not confuse this with the DCThevenin you did in step 1.4) Replace transistor with small signal model5) Simplify the circuit as much as necessary.Steps to Analyze a Transistor Amplifier6) Calculate the small signal parameters and gain etc.Step 1Step2Step3Step4Step5π-model used
33Hybrid-Pi Model for the BJT Transconductance:Input resistance: RinThe hybrid-pi small-signal model is the intrinsic low-frequency representation of the BJT.The small-signal parameters are controlled by the Q-point and are independent of the geometry of the BJT.Output resistance:Where, VA is Early Voltage(VA=100V for npn)
34Hybrid Parameter Model IiIoLinear Two port DeviceVoVi
35h-Parametersh11 = hi = Input Resistance h12 = hr = Reverse Transfer Voltage Ratio h21 = hf = Forward Transfer Current Ratio h22 = ho = Output Admittance
36Three Small signal Models of CE Transistor The Mid-frequency small-signal models
37An a c Equivalent Circuit BJT Mid-frequency Analysis using the hybrid-p model:A common emitter (CE) amplifierThe mid-frequency circuit is drawn as follows:the coupling capacitors (Ci and Co) and thebypass capacitor (CE) are short circuitsshort the DC supply voltage (superposition)replace the BJT with the hybrid-p modelThe resulting mid-frequency circuit is shown below.An a c Equivalent Circuitro
38Details of Small-Signal Analysis for Gain Av (Using Π-model) RsRsFrom input circuit
39C-E Amplifier Input Resistance The input resistance, the total resistance looking into the amplifier at coupling capacitor C1, represents the total resistance presented to the AC source.
40C-E Amplifier Output Resistance The output resistance is the total equivalent resistance looking into the output of the amplifier at coupling capacitor C3. The input source is set to 0 and a test source is applied at the output.But vbe=0.since ro is usually >> RC.
41High-Frequency Response – BJT Amplifiers Capacitances that will affect the high-frequency response:• Cbe, Cbc, Cce – internal capacitances• Cwi, Cwo – wiring capacitances• CS, CC – coupling capacitors• CE – bypass capacitor
42Frequency Response of Amplifiers The voltage gain of an amplifier is typically flat over the mid-frequency range, but drops drastically for low or high frequencies. A typical frequency response is shown below.For a CE BJT: (shown on lower right)low-frequency drop-off is due to CE, Ci and Cohigh-frequency drop-off is due to device capacitances Cp and Cm (combined to form Ctotal)Each capacitor forms a break point (simple pole or zero) with a break frequency of the form f=1/(2pREqC), where REq is the resistance seen by the capacitorCE usually yields the highest low-frequency breakwhich establishes fLow.
43Amplifier Power Dissipation Static power dissipation in amplifiers is determined from their DC equivalent circuits.Total power dissipated in C-B and E-B junctions is:whereTotal power supplied is:The difference is the power dissipated by the bias resistors.
46An Emitter Follower (CC) Amplifier Figure Emitter follower.Very high input ResistanceVery low out put ResistanceUnity Voltage gain with no phase shiftHigh current gainCan be used for impedance matching or a circuit for providing electrical isolation
49Capacitor Selection for the CE Amplifier The key objective in design is to make the capacitive reactancemuch smaller at the operating frequency f than the associatedresistance that must be coupled or bypassed.
50Summary of Two-Port Parameters for CE/CS, CB/CG, CC/CD
51A Small Signal h-parameter Model of C E - Transistor Vce*h12
52Small-signal Current Gain and Amplification Factor of the BJT The amplification factor is given by:For VCE << VA,mF represents the maximum voltage gain an individual BJT can provide, independent of the operating point.bo > bF for iC < IM, and bo < bF for iC > IM, however, bo and bF are usually assumed to be about equal.
53A Simple MOSFET Amplifier The MOSFET is biased in the saturation region by dc voltage sources VGS and VDS = 10 V. The DC Q-point is set at (VDS, IDS) = (4.8 V, 1.56 mA) with VGS = 3.5 V.Total gate-source voltage is:A 1 V p-p change in vGS gives a 1.25 mA p-p change in iDS and a 4 V p-p changein vDS. Notice the characteristic non-linear I/O relationship compared to the BJT.
54Eber-Moll BJT Model IE IC E C RIC RIE IF IR IB B The Eber-Moll Model for BJTs is fairly complex, but it is valid in all regions of BJT operation. The circuit diagram below shows all the components of the Eber-Moll Model:IEICECRICRIEIFIRIBB
55Eber-Moll BJT Model IC = FIF – IR IB = IE - IC IE = IF - RIR R = Common-base current gain (in forward active mode)F = Common-base current gain (in inverse active mode)IES = Reverse-Saturation Current of B-E JunctionICS = Reverse-Saturation Current of B-C JunctionIC = FIF – IR IB = IE - ICIE = IF - RIRIF = IES [exp(qVBE/kT) – 1] IR = IC [exp (qVBC/kT) – 1] If IES & ICS are not given, they can be determined using variousBJT parameters.
56Small Signal BJT Equivalent Circuit The small-signal model can be used when the BJT is in the active region. The small-signal active-region model for a CB circuit is shown below:iBiCBCriBr = ( + 1) * VTIEiEE@ = 1 and T = 25Cr = ( + 1) * 0.026IERecall: = IC / IB
57The Early Effect (Early Voltage) Orange = Actual IC (IC’) Note: Common-Emitter ConfigurationIB-VAVCEGreen = Ideal ICOrange = Actual IC (IC’)IC’ = IC VCE + 1VA
58Early Effect ExampleGiven: The common-emitter circuit below with IB = 25A, VCC = 15V, = 100 and VA = 80.Find: a) The ideal collector currentb) The actual collector currentCircuit DiagramVCEIC= 100 = IC/IBa)IC = 100 * IB = 100 * (25x10-6 A)IC = 2.5 mA+_VCCIBb) IC’ = IC VCE + 1 = 2.5x = 2.96 mAVAIC’ = 2.96 mA
59Breakdown Voltage The maximum voltage that the BJT can withstand. BVCEO = The breakdown voltage for a common-emitter biased circuit. This breakdown voltage usually ranges from ~ Volts.BVCBO = The breakdown voltage for a common-base biased circuit. This breakdown voltage is usually much higher than BVCEO and has a minimum value of ~60 Volts.Breakdown Voltage is Determined By:The Base WidthMaterial Being UsedDoping LevelsBiasing Voltage
60Potential-Divider Bias Circuit with Emitter Feedback Most popular biasing circuit.Problem: bdc can vary over a wide range for BJT’s (even with the same part number)Solution: Adding the feedback resistor RE. How large should RE be? Let’s see.Substituting the active region model into the circuit to the left and analyzing the circuit yields the following well known equation:ICEO has little effect and is often neglected yielding the simpler relationship:Voltage divider biasing circuit with emitter feedbackReplacing the input circuit by a Thevenin equivalent circuit yields:Test for stability: For a stable Q-point w.r.t. variations in bdc choose:Why? Because then
61PE-Electrical Review Course - Class 4 (Transistors) Find the Q-point for the biasing circuit shown below.The BJT has the following specifications:bdc = 100, rsat = 100 W (Vo not specified, so assume Vo = 0.7 V)Example :Example :Repeat Example 3 if RC is changed from 1k to 2.2k.
62PE-Electrical Review Course - Class 4 (Transistors) Determine the Q-point for the biasing circuit shown.The BJT has the following specifications:bdc varies from 50 to 400, Vo = 0.7 V, ICBO = 10 nASolution:Case 1: bdc = 50ExampleCase 2: bdc = Similar to Case 1 above. Results are: IC = mA, VCE = 6.14 V Summary:
63BJT Amplifier Configurations and Relationships: Using the hybrid-p model.VCCCEBR12siv+_LoCommon Collector (CC) Amplifier (also called “emitter-follower”)Note: The biasing circuit is the same for each amplifier.