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Lecture 5 ANNOUNCEMENTS • HW1 will be considered as extra credit. • HW3 is posted, due Tuesday 9/18 OUTLINE • BJT (cont’d) – – – – Transconductance Small-signal model The Early effect BJT operation in saturation mode Reading: Chapter 4.4.3-4.5 EE105 Fall 2007 Lecture 5, Slide 1 Prof. Liu, UC Berkeley Transconductance, 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. dIC d VBE IS exp gm ≡ ≅ dVBE dVBE VT 1 VBE gm = IS exp VT VT IC gm = VT EE105 Fall 2007 Lecture 5, Slide 2 Prof. Liu, UC Berkeley Visualization 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 3 Prof. Liu, UC Berkeley Transconductance 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 4 Prof. Liu, UC Berkeley Transconductance 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 5 Prof. Liu, UC Berkeley Derivation 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 change in current. – 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 6 Prof. Liu, UC Berkeley Small-Signal Model: VBE Change EE105 Fall 2007 Lecture 5, Slide 7 Prof. Liu, UC Berkeley Small-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 8 Prof. Liu, UC Berkeley Small-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. IC 1 gm = = VT 3 .75 Ω rπ = EE105 Fall 2007 β gm = 375 Ω Lecture 5, Slide 9 Prof. Liu, UC Berkeley Small-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 smallsignal analysis. EE105 Fall 2007 Lecture 5, Slide 10 Prof. Liu, UC Berkeley The 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 quasineutral base width decreases, so that collector current increases. EE105 Fall 2007 Lecture 5, Slide 11 Prof. Liu, UC Berkeley Early 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 12 Prof. Liu, UC Berkeley Early Effect Representation EE105 Fall 2007 Lecture 5, Slide 13 Prof. Liu, UC Berkeley Early 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 14 Prof. Liu, UC Berkeley Early Effect and Small-Signal Model ∆VCE VA VA ro ≡ = ≈ VBE I C ∆I C I S exp VT EE105 Fall 2007 Lecture 5, Slide 15 Prof. Liu, UC Berkeley Summary of BJT Concepts EE105 Fall 2007 Lecture 5, Slide 16 Prof. Liu, UC Berkeley BJT 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 17 Prof. Liu, UC Berkeley Large-Signal Model for Saturation Mode EE105 Fall 2007 Lecture 5, Slide 18 Prof. Liu, UC Berkeley BJT Output Characteristics • The operating speed of the BJT also drops in saturation. EE105 Fall 2007 Lecture 5, Slide 19 Prof. Liu, UC Berkeley Example: 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. V CC ≥ I C R C + (V BE − 400 mV ) EE105 Fall 2007 Lecture 5, Slide 20 Prof. Liu, UC Berkeley Deep Saturation • In deep saturation, the BJT does not behave as a voltage-controlled current source. • VCE is ~constant. EE105 Fall 2007 Lecture 5, Slide 21 Prof. Liu, UC Berkeley