# Lecture 5 ```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
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
– 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
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