ECE414 Diode Models 1 M H MillerDISCRETE BJT AMPLIFIER REVIEWThese notes assume prior familiarity with the semiconductor diode, the BJT, anddiscrete amplifier circuitry on the level of an introductory electronics course (ECE311).BJT device modeling is reviewed qualitatively, and the use of these modelsincircuit analysis is illustrated.BJT Large Signal ModelIt is convenient for many purposes to formulate the description of BJT characteristics for circuitapplications using as descriptive variables the base current, the collector current, and the collector-emitter voltage (and indirectly the emitter junction voltage).This leads to the simplified large-signalBJT model drawn below.The idealized diodes model the emitter and collector junctions respectively,and the controlled current source models the transistor action.It should be noted that this model is notvalid for inverted operation, i.e., with the collector junction forward-biased andthe emitter junction reverse-biased. In practice optimizing a junction foroperation as an emitter concomitantly endows it with a low reverse-breakdownvoltage, while optimizing it as a collector makes it a poor emitter of carriersinto the base.Because of this degradation inverted operation is veryuncommon, and components to accommodate modeling such operation areomitted to avoid unnecessary clutter.The diodes in this model are idealized diodes, i.e., when conducting theforward-bias voltage is zero, and the diode current is zero whatever the reversebias.The fixed voltage source added in series with the emitter diode accountsfor a finite emitter junction bias.There are two diodes, and so four possible combinationsof diode states.However as noted one combination,inverted operation with the emitter off and collectoron, is not permitted.Normal forward operationcorresponds to the emitter diode on and the collectordiode off.Saturated operation corresponds to theemitter and collector diodes both on.And cutoffcorresponds to the emitter diode off; the collector diodeis necessarily off; in this case. The simplifiedcharacteristics, a representative characteristic isillustrated, do not account for a number of second-orderconsiderations, e.g., thermal effects, junction breakdown, and the Early effect.Nevertheless if appliedproperly they are quite useful in a great many circumstancesIllustrative Large-Signal BJT CalculationConsider the NPN single-stage CE amplifier configuration drawn on the left in the figure below.Thetwo resistors R1 and R2 provide means to supply base current to the BJT base.The emitter resistor REprovides degenerative feedback to smooth emitter current perturbations, and the collector resistor RC isused to fix the collector voltage at a desired value.ECE414 Diode Models 2 M H MillerApplication of the approximate model to the analysis of the circuit is illustrated in subsequent parts ofthe figure.The first step (not all steps actually require an explicit redrawing) is to substitute theidealized model for the BJT (represented by the canonical NPN icon.); this is the second circuit in thefigure.At this point the analysis no longer pertains directly to the actual circuit but rather to anapproximation using the model.The next step is to assume the BJT operating state.It is an assumption because simply desiring aspecific operating condition does not by itself necessarily make it so.Ultimately this assumption mustbe validated for the specific circuit parameters chosen; occasionally there is unanticipated surprise forthe unwary.For the present purpose the intention is to bias the BJT to operate in the normal mode, i.e.,collector junction reverse-biased and emitter junction forward-biased.The assumption that this will beso is reflected by the (implied) diode states in the third figure.Whether it actually will be so remains tobe seen.The fourth diagram applies the commonly used simplification of replacing the R1 and R2 biasing circuitby their Thevenin equivalent representation..KCL requires IE = IB + IC = (+1) IB, and applying KVL around the base-emitter loop provides (withmodest algebraic effort) the equation.This equation is an approximate representation of the circuit performance based on the use of anapproximate model.Nevertheless there is much useful information in this expression that is neitherreadily obvious from the circuit diagram nor readily extracted from more precise computer numericalcomputations.For example the base-emitter loop equation isolates the influence of the transistor on the emitter currentin the VBE term in the numerator and the term involving in the denominator.To limit the variabilityof the emitter current because of temperature sensitivity or parameter tolerances of the BJT we canminimize the respective relative size of these terms.For example VBE has a nominal value of 0.7 voltat room temperature, and a nominal temperature coefficient of -2 millivolt/C.Over a 100Ctemperature range (mild Michigan summer to winter change) this amounts to a total junction voltagevariation of about 0.2 millivolt.To minimize the effect of this uncertainty one makes the variation(uncertainty) in VBE > RB/(+1); use the smallest value of expected.Here also a nominal factor of 10 is areasonable initial equivalent to ' >>'.Suppose we design (this is a more or less arbitrary specification here) for a nominal emitter current of 2milliampere.('Nominal current' is specified because with resistor and other device tolerances an exactcurrent specification generally requires an adjustable element and experimental setting of the current.Itis usually less costly to modify the design specifications suitably.)Suppose we design for a nominal VBB of about 2.5 volt.This design choice is not a 'rule of thumb' noris it simply a guess.The intent is to make VBB - VBE much greater than the uncertainty in VBE; thisuncertainty we take as about 0.2 volt as suggested above.With VBE 0.7 volt and VBB 2.5 volt thedifference of 1.8 volt is arguably 'much greater' than 0.2volt.Note again that this choice is notimmutable.If, ultimately, performance is not satisfactory we can revise the design in a second iteration.You might (indeed should) ask, why not make the base voltage larger to start with?An answer lies inwhat appears to be a general metaphysical rule such that if a parameter is chosen to improve operation inone aspect it will inevitably degrade performance in another aspect.In the present case for example notethat for unsaturated operation as assumed the collector voltage must be greater than the base voltage.But the collector voltage must also be less than the supply voltage.Hence a higher base voltage eitherwill diminish the allowable range of variation of the collector voltage or force use of a larger powersupply voltage.The options are not necessarily precluded; they simply represent design considerations.Since the discussion here is primarily illustrative we elect for initial trial use the nominal 2.5-volt choice.The second condition RE >> RB/(+1) can be interpreted as meaning the voltage drop across RB ismuch less than that across RE. (To see this multiply both terms by IE.)We can then estimate a value forRE by observing that the 2.5 - 0.7 = 1.8 volt is (more or less) the voltage drop across the emitter resistor.To provide for 2 milliampere choose RE = 900.This is not a standard resistance value and in generalfabricating special resistor sizes is impractical; the closest 10% values are 820 and 1 k.The firstvalue makes the current estimate a bit larger than 2 milliampere, and the second value makes it a bitsmaller.Nothing in the specifications or application (here anyway) makes one choice preferable to theother.For this illustration we choose arbitrarily to use 820; once again note that if necessary we canrevise this choice later on.With a nominal minimum estimate of 100 (2N3904) choose RB