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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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DeII
Dp
p
An
niS NL
D
NL
DAqnI 2
VD (V)
I D (
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.
T
Cm
T
BES
Tm
T
BES
BEBE
Cm
V
Ig
V
VI
Vg
V
VI
dV
d
dV
dIg
exp1
exp
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 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.
375
75.31
m
T
Cm
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 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
C
A
T
BES
A
C
CEo I
V
VV
I
V
I
Vr
exp
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 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.
)400( mVVRIV BECCCC