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Lecture 27
OUTLINE
The BJT (cont’d)
• Small-signal model
• Cutoff frequency
• Transient (switching) response
Reading: Pierret 12; Hu 8.8-8.9
Small-Signal Model
Common-emitter
configuration,
forward-active mode:
I C F I F 0 e qVBE / kT
B
C
+
“hybrid pi”
BJT small signal model:
C
vbe
E
dI C
IC
d
qVBE / kT
gm
F I F 0e
dVBE dVBE
kT / q
EE130/230M Spring 2013
gm vbe
E
Transconductance:
r
Lecture 27, Slide 2
Small-Signal Model (cont.)
gm
1
dI B
1 dI C
r dVBE dc dVBE dc
r
dc
gm
C C J , BE C D , BE C D , BE
CJ, BE
A s
Wdep, BE
CD,BE
dQF
dVBE
QF
forward transit time F
IC
C D , BE
EE130/230M Spring 2013
where QF is the magnitude of
minority-carrier charge stored in
the base and emitter regions
d F I C
F gm
dVBE
Lecture 27, Slide 3
Example
A BJT is biased at IC = 1 mA and VCE = 3V. dc = 90, F = 5ps, T = 300K.
Find (a) gm , (b) r , (c) C .
Solution:
(a)
g m I C /( kT / q)
1 mA
mA
39
39 mS (milli siemens)
26 mV
V
(b) r = dc / gm = 90/0.039 = 2.3 kW
(c) C F g m 5 10 12 0.039 1.9 10 14 F 19 fF (femto farad)
EE130/230M Spring 2013
Lecture 27, Slide 4
Cutoff Frequency, fT
B
ib
ib
vbe
input admittance 1 / r jwC
+
C
ic g m vbe
(w )
C
vbe
r
gm vbe
E
ic
gm
gm
1 / r jwC g m / dc jw F g m C J , BE
ib
1
1 / dc jw F C J , BE kT / qI C
The cutoff frequency is defined to be the frequency (f = w/2)
at which the short-circuit a.c. current gain equals 1:
ac 1 at fT
EE130/230M Spring 2013
1
2 F CJ , BE kT / qI C
Lecture 27, Slide 5
E
For the full BJT
equivalent circuit:
1
fT
2 F CJ , BE CJ , BC kT / qI C CJ , BC re rc
fT is commonly used
as a metric for the
speed of a BJT.
Si/SiGe HBT by IBM
To maximize fT:
• increase IC
• minimize CJ,BE, CJ,BC
• minimize re, rc
• minimize F
EE130/230M Spring 2013
Lecture 27, Slide 6
Base Widening at High IC: Kirk Effect
For a NPN BJT:
J C qnvsat dep,C qN C qn qN C
JC
vsat
• At very high current densities (>0.5mA/mm2), the density of mobile charge passing
through the collector depletion region exceeds the ionized dopant charge density:
increasing IC
The base width (W) is effectively increased (referred to as “base push out”)
F increases and hence fT decreases.
•This effect can be avoided by increasing NC increased CJ,BC , decreased VCE0
EE130/230M Spring 2013
Lecture 27, Slide 7
Summary: BJT Small Signal Model
Hybrid pi model for the common-emitter configuration,
forward-active mode:
B
C
+
C
vbe
r
gm vbe
E
E
r
dc
gm
gm
C C J , BE F g m
EE130/230M Spring 2013
Lecture 27, Slide 8
IC
kT / q
BJT Switching - Qualitative
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Lecture 27, Slide 9
Turn-on Transient Response
dQB
QB
I BB
dt
B
where IBB=VS/RS
•The general solution is:
QB (t ) I BB B Aet / B
•Initial condition: QB(0)=0
since transistor is in cutoff
QB (t ) I BB B (1 e
t / B
)
QB (t ) I BB B 1 e t / B
0 t tr
t
iC (t ) t
VCC
t t r
RL
EE130/230M Spring 2013
Lecture 27, Slide 10
1
t r B ln
VCC / RL
1 I
BB B
Turn-off Transient Response
dQB
Q
I BB B
dt
B
• The general solution is:
QB (t ) I BB B Aet / B
• Initial condition: QB(0)=IBBB
QB (t ) I BB B 1 et / B
1
t sd B ln
I CC t
I
BB B
I CC 0 t t sd
iC (t )
t / B
Q
(
t
)
I
1
e
B BB B
t t sd
t
t
EE130/230M Spring 2013
Lecture 27, Slide 11
Reducing B for Faster Turn-Off
• The speed at which a BJT is turned off is dependent on the
amount of excess minority-carrier charge stored in the base,
QB, and also the recombination lifetime, B.
– By reducing B, the carrier removal rate is increased
Example: Add recombination centers (Au atoms) in the base
EE130/230M Spring 2013
Lecture 27, Slide 12
Schottky-Clamped BJT
• When the BJT enters the saturation mode, the Schottky
diode begins to conduct and “clamps” the C-B junction
voltage at a relatively low positive value.
reduced stored charge in quasi-neutral base
EE130/230M Spring 2013
Lecture 27, Slide 13