Lecture 5Notes on PN JunctionsTransconductance, gmVisualization of TransconductanceTransconductance and ICTransconductance and Emitter AreaDerivation of Small-Signal ModelSmall-Signal Model: VBE ChangeSmall-Signal Model: VCE ChangeSmall-Signal Model: Example 1Small-Signal Model: Example 2The Early EffectEarly Effect: Impact on BJT I-VEarly Effect RepresentationEarly Effect and Large-Signal ModelEarly Effect and Small-Signal ModelSummary of BJT ConceptsBJT in Saturation ModeLarge-Signal Model for Saturation ModeBJT Output CharacteristicsExample: Acceptable VCC RangeDeep SaturationEE105 Fall 2007 Lecture 5, Slide 1 Prof. Liu, UC BerkeleyLecture 5OUTLINE•BJT (cont’d)–Transconductance–Small-signal model–The Early effect–BJT operation in saturation modeReading: Chapter 4.4.3-4.5ANNOUNCEMENTS•HW1 will be considered as extra credit.•HW3 is posted, due Tuesday 9/18EE105 Fall 2007 Lecture 5, Slide 2 Prof. Liu, UC BerkeleyNotes on PN Junctions•Typically, pn junctions in IC devices are formed by counter-doping. The equations provided in class (and in the textbook) can be readily applied to such diodes if–NA net acceptor doping on p-side (NA-ND)p-side–ND net donor doping on n-side (ND-NA)n-side)1( kTVqSDDeIIDppAnniSNLDNLDAq nI2VD (V)ID (A)EE105 Fall 2007 Lecture 5, Slide 3 Prof. Liu, UC BerkeleyTransconductance, gm•The transconductance (gm) of a transistor is a measure of how well it converts a voltage signal into a current signal.•It will be shown later that gm is one of the most important parameters in integrated circuit design. TCmTBESTmTBESBEBECmVIgVVIVgVVIdVddVdIgexp1expEE105 Fall 2007 Lecture 5, Slide 4 Prof. Liu, UC BerkeleyVisualization of Transconductance•gm can be visualized as the slope of the IC vs. VBE curve.•The slope (hence gm) increases with IC.EE105 Fall 2007 Lecture 5, Slide 5 Prof. Liu, UC BerkeleyTransconductance and IC •For a given VBE swing (V), the resulting current swing about IC2 is larger than it is about IC1. –This is because gm is larger when VBE = VB2.EE105 Fall 2007 Lecture 5, Slide 6 Prof. Liu, UC BerkeleyTransconductance and Emitter Area•When the BJT emitter area is increased by a factor n, IS increases by the factor n. For a fixed value of VBE, IC and hence gm increase by a factor of n.EE105 Fall 2007 Lecture 5, Slide 7 Prof. Liu, UC BerkeleyDerivation of Small-Signal Model•The BJT small-signal model is derived by perturbing the voltage difference between two terminals while fixing the voltage on the third terminal, and analyzing the resultant changes in terminal currents. –This is done for each of the three terminals as the one with fixed voltage. –We model the current change by a controlled source or resistor.EE105 Fall 2007 Lecture 5, Slide 8 Prof. Liu, UC BerkeleySmall-Signal Model: VBE ChangeEE105 Fall 2007 Lecture 5, Slide 9 Prof. Liu, UC BerkeleySmall-Signal Model: VCE Change•Ideally, VCE has no effect on the collector current. Thus, it will not contribute to the small-signal model.•It can be shown that VCB ideally has no effect on the small-signal model, either.EE105 Fall 2007 Lecture 5, Slide 10 Prof. Liu, UC BerkeleySmall-Signal Model: Example 1•The small-signal model parameters are calculated for the DC operating point, and are used to determine the change in IC due to a change in VBE.37575.31mTCmgrVIgEE105 Fall 2007 Lecture 5, Slide 11 Prof. Liu, UC BerkeleySmall-Signal Model: Example 2•In this example, a resistor is placed between the power supply and collector, to obtain an output voltage signal.•Since the power supply voltage does not vary with time, it is regarded as ground (reference potential) in small-signal analysis.EE105 Fall 2007 Lecture 5, Slide 12 Prof. Liu, UC BerkeleyThe Early Effect•In reality, the collector current depends on VCE:–For a fixed value of VBE, as VCE increases, the reverse bias on the collector-base junction increases, hence the width of the depletion region increases. Therefore, the quasi-neutral base width decreases, so that collector current increases.EE105 Fall 2007 Lecture 5, Slide 13 Prof. Liu, UC BerkeleyEarly Effect: Impact on BJT I-V•Due to the Early effect, collector current increases with increasing VCE, for a fixed value of VBE.EE105 Fall 2007 Lecture 5, Slide 14 Prof. Liu, UC BerkeleyEarly Effect RepresentationEE105 Fall 2007 Lecture 5, Slide 15 Prof. Liu, UC BerkeleyEarly Effect and Large-Signal Model•The Early effect can be accounted for, by simply multiplying the collector current by a correction factor. •The base current does not change significantly.EE105 Fall 2007 Lecture 5, Slide 16 Prof. Liu, UC BerkeleyEarly Effect and Small-Signal ModelCATBESACCEoIVVVIVIVr expEE105 Fall 2007 Lecture 5, Slide 17 Prof. Liu, UC BerkeleySummary of BJT ConceptsEE105 Fall 2007 Lecture 5, Slide 18 Prof. Liu, UC BerkeleyBJT in Saturation Mode•When the collector voltage drops below the base voltage, the collector-base junction is forward biased. Base current increases, so that the current gain (IC/IB) decreases.EE105 Fall 2007 Lecture 5, Slide 19 Prof. Liu, UC BerkeleyLarge-Signal Model for Saturation ModeEE105 Fall 2007 Lecture 5, Slide 20 Prof. Liu, UC BerkeleyBJT Output Characteristics •The operating speed of the BJT also drops in saturation.EE105 Fall 2007 Lecture 5, Slide 21 Prof. Liu, UC BerkeleyExample: Acceptable VCC Range•In order to prevent the BJT from entering very deeply into saturation, the collector voltage must not fall below the base voltage by more than 400 mV.)400( mVVRIVBECCCCEE105 Fall 2007 Lecture 5, Slide 22 Prof. Liu, UC BerkeleyDeep Saturation•In deep saturation, the BJT does not behave as a voltage-controlled current source.•VCE is
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