EE105 Fall 2007 Lecture 5, Slide 1 Prof. Liu, UC Berkeley

Lecture 5

OUTLINE• BJT (cont’d)– Transconductance– Small-signal model– The Early effect– BJT operation in saturation mode

Reading: Chapter 4.4.3-4.5

ANNOUNCEMENTS• HW1 will be considered as extra credit.• HW3 is posted, due Tuesday 9/18

EE105 Fall 2007 Lecture 5, Slide 2 Prof. Liu, UC Berkeley

Notes 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

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A)

EE105 Fall 2007 Lecture 5, Slide 3 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.

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Cm

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EE105 Fall 2007 Lecture 5, Slide 4 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 5 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 6 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 7 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 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 Berkeley

Small-Signal Model: VBE Change

EE105 Fall 2007 Lecture 5, Slide 9 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 10 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.

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gr

VI

g

EE105 Fall 2007 Lecture 5, Slide 11 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 small-signal analysis.

EE105 Fall 2007 Lecture 5, Slide 12 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 quasi-neutral base width decreases, so that collector current increases.

EE105 Fall 2007 Lecture 5, Slide 13 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 14 Prof. Liu, UC Berkeley

Early Effect Representation

EE105 Fall 2007 Lecture 5, Slide 15 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 16 Prof. Liu, UC Berkeley

Early Effect and Small-Signal Model

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EE105 Fall 2007 Lecture 5, Slide 17 Prof. Liu, UC Berkeley

Summary of BJT Concepts

EE105 Fall 2007 Lecture 5, Slide 18 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 19 Prof. Liu, UC Berkeley

Large-Signal Model for Saturation Mode

EE105 Fall 2007 Lecture 5, Slide 20 Prof. Liu, UC Berkeley

BJT Output Characteristics • The operating speed of the BJT also drops in saturation.

EE105 Fall 2007 Lecture 5, Slide 21 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.

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EE105 Fall 2007 Lecture 5, Slide 22 Prof. Liu, UC Berkeley

Deep Saturation• In deep saturation, the BJT does not behave as a

voltage-controlled current source.• VCE is ~constant.