Bipolar Junction TransistorsMurray ThompsonSept. 5, 1999Contents1 Introduction 12 A Reassurance 13 Summary of Bipolar Transistor “theory” so far 24 Transistor Model 55 Various Simple Amplifiers 66 A Useful form of the Common Emitter Amplifier 207 A More Useful Form of the Common Emitter Amplifier 21——-1 IntroductionThese notes follow those on pn junctions, in which the basic components ofnpn transistors were discussed.2 A ReassuranceAt this point, some students, who prefer to have precise calculations andexact theory, may start to become concerned about these sloppy methods,1bad approximations and imprecise calculations. We can reassure them. Inspite of these rough methods, the general concept of negative feedback (tobe introduced later) will allow us to use these imperfect circuits yet gainextremely linearcircuits, extremely precise amplifications and precision measurements of ourinput signals.First we must consider these imperfect amplifiers. The later feedback andprecision circuits would be useless without them!3 Summary of Bipolar Transistor “theory” sofar1. The fraction of the electrons leaving the emitter and going to the col-lector instead of the base is normally calledIcollectorIemitter= α.More strictly, in case of non-linear behaviour, we defineα =dIcollectordIemitter2. The ratio of the collector current to the base current is normally calledβ. Thus, β =IcollectorIbaseFrom this we can getβ =α1−α.More strictly, in case of non-linear behaviour, we defineα =dIcollectordIemitter3. Hence (1 − α)β = αα =β1+β4. By arranging the geometry so that the base region is very thin, most ofthe electrons entering from the emitter into the base will be fall over theedge down the steep electric potential fall of the base-collector junctionbefore they meet and recombine with holes in the base.Thus, by making the base be very thin so that the emitter-base junctionand the collector-base junction are very close, and doping the collector-base junction so that it is very thin (with a high electric field~E = −dVdx,the fraction α of the electrons leaving the emitter and going to the2collector instead of the base can be made close to 1.0 and β =α1−αcanbe made large. This can make the transistor more useful.While a transistor with a large β, such as β = 100, can be used tomake amplifiers with a high gain, the thin base and collector-base junc-tion have a general defect. This defect is that the thin collector-basejunction will have high electric fields~E and avalanche breakdown mayoccur.5. So long as the collector-base voltage is greater than about 2 or 3 volts,very few of the electrons which fall over the collector-base junction canbounce back.Thus, So long as the collector-base voltage is greater than about 2 or3 volts, the fraction α of electrons passing through both junctions isonly slightly dependent upon the collector-base voltage.A typical set of Icollectorand VCollector−Emittercurves for equispaced basecurrents are shown below.Although the following curves are not usually shown in specifications,the following shows ICollectorand IBasecurves for equispaced collectorvoltages.36. Thus α and particularly β are useful parameters because they are nearlyconstant for any given bipolar junction transistor over a range of work-ing voltages and currents.The β may vary from one transistor to another due to manufacturingvariations and due to changing temperature. Note that ICin the fol-lowing graph has a logarithmic horizontal scale and covers a very widerage.Even though β does not change much with voltage and current, inany given transistor, the variation in β due to temperature and man-ufacturing is significant. The variation due to manufacturing, can beminimized by selecting transistors with particular values of β.7. In most practical circuits, we try to make the action be independent of β.This can be done in a variety of ways but will require that β be largeso that β >> 1 and we can approximate functions like β + 1 as β.8. The transistor is said to be in saturation if the collector voltage is toolow.49. Any transistor has maximum ratings for(a) The maximum power giving a maximum product of IC maxandVCE max.(b) A maximum current into the collector IC maxthrough its connect-ing wire and weld.(c) A maximum voltage on the collector-base junction VCE maxabovewhich the junction may break down.4 Transistor ModelBy inspecting the transistor ICollector, VCEand β curves above, we can makea model of the actions within a transistor. Like some other models, thereproduction is imperfect but will allow us to make systems where the actionis nearly independent of β.We want a 3-terminal model which we can use to “replace the transistor”when want to make calculations. In this model we assume51. The base-emitter junction is kept forward biased (“turned on”) by asmall but sufficient base-emitter current to keep the base emitter volt-age near 0.7 volt.2. The Base-Collector voltage is sufficient for the transistor to have aβ > 10A common convention is to use lower case r for each of the internal resis-tances to distinguish them from the normal external resistors we attach tothe emitter, base and collector.We will call the join of the 3 lines as the point “join”.We replace the base to emitter junction with a small 0.7 volt battery witha small (perhaps negligible resistor rb.The current through the base is called Ib.From the previous discussion of p,n junctions, we know that the emitterhas the dynamic junction impedance (which may also be negligible) of aboutre= 2 ohm +0.026 voltIbase.We insert a “Current Generator” in the collector to cause a current IC= βIb.5 Various Simple AmplifiersWe will now consider four general circuits corresponding to the 3 permuta-tions of 1 terminal being “shared” between the circuitry of the input andoutput attached circuitry – the permutation of the common emitter is usedtwice. Each amplifier amplifies an input DC voltage which may change.By using an additional “coupling capacitor”, each can amplify only the ACcomponent of the input voltage.61. Grounded Emitter AmplifierThe simple transistor model suggests how an amplifier might be made.We call this a grounded emitter amplifier.Variations ∆Vinputin the base input voltage will cause variations inthe emitter current through rb. The transistor can be replaced forcalculation purposes by the transistor model as in the next diagram.If, as usual, reis small,