EE130 Lecture 27, Slide 1 Spring 2007
Lecture #27
OUTLINE
• BJT small signal model
• BJT cutoff frequency
• BJT transient (switching) response
Reading: Finish Chapter 12
EE130 Lecture 27, Slide 2 Spring 2007
Transconductance:
vber gmvbe
C
E
B
E
C
+
Small-Signal ModelCommon-emitter configuration,forward-active mode:
kTqVFFC
EBeII /0
qkT
IeI
dV
dI
dV
dIg CkTqV
FFEB
C
EB
Cm
EB
//
0
“hybrid-pi” BJT small signal model:
EE130 Lecture 27, Slide 3 Spring 2007
Small-Signal Model (cont.)
, mFBE
CFBED
C
FF
gdV
IdC
I
Q
BE
F
dV
dQC BED,
m
dc
dc
m
BE
C
dcBE
B
gr
g
dV
dI
dV
dI
r
11
BEDBEDBEJ CCCC ,,,
BEdep
s
W
AC
,BEJ,
where QF is the magnitude of minority-carrier charge stored in the base and emitter regions
forward transit time
EE130 Lecture 27, Slide 4 Spring 2007
A BJT is biased at IC = 1 mA and VCE = 3 V. dc=90, F=5 ps, and T = 300 K. Find (a) gm , (b) r , (c) C .
Solution:
(a)
(b) r = dc / gm = 90/0.039 = 2.3 k
c)
Example: Small-Signal Model Parameters
siemens)(milliqkTIg Cm mS 39V
mA39
mV 26
mA 1)//(
ad)(femto fargC mF fF 19F109.1039.0105 1412
EE130 Lecture 27, Slide 5 Spring 2007
The cutoff frequency is defined to be the frequency (f = /2) at which the short-circuit a.c. current gain equals 1:
Cutoff Frequency, fT
CBEJFTac qIkTC
f/2
1at 1
,
CBEJFdc
BEJmFdcm
mm
b
c
bemc
bbbe
qIkTCj
Cgjg
g
Cjr
g
i
i
vgi
Cjr
iiv
//1
1
//1)(
/1admittanceinput
,
,
vber gmvbe
C
E
B
E
C
+
EE130 Lecture 27, Slide 6 Spring 2007
fT is commonly used as a metric for the speed of a BJT.
SiGe HBT by IBM
For the full BJT equivalent circuit: ceBCJCBCJBEJF
T rrCqIkTCCf
,,, /2
1
To maximize fT:
– increase IC
– minimize CJ,BE, CJ,BC
– minimize re, rc
– minimize F
EE130 Lecture 27, Slide 7 Spring 2007
• At very high current densities (>0.5mA/m2), base widening occurs, so QB increases.
F increases, fT decreases.
Top to bottom : VCE = 0.5V, 0.8V, 1.5V, 3V.
Base Widening at High IC: the Kirk Effect
Consider an npn BJT:At high current levels, the density of electrons (n IC/qAvsat) in the collector depletion region is significant, resulting in widening of the quasi-neutral base region.As W increases, the depletion width in the collector also increases, since the charge density decreases:
At very high current densities, the excess hole concentration in the collector is so high that it effectively extends the p-type base.
sat
CCCCdep Av
IqNqnqN ,
EE130 Lecture 27, Slide 8 Spring 2007
Summary: BJT Small Signal Model
vber gmvbe
C
E
B
E
C
+
Hybrid-pi model for the common-emitter configuration, forward-active mode:
m
dc
gr
mFBEJ gCC ,
qkT
Ig C
m /
EE130 Lecture 27, Slide 9 Spring 2007
BJT Switching - Qualitative
EE130 Lecture 27, Slide 10 Spring 2007
Turn-on transient• We know:
• The general solution is:
• Initial condition: QB(0)=0. since transistor is in cutoff
B
BBB
B QI
dt
dQ
BtBBBB AeItQ /)(
)1()( / BtBBBB eItQ
rL
CC
rt
tBBB
t
B
C
ttR
V
ttAeItQ
ti
B
0)(
)(
/
where IBB=VS/RS
BBB
LCCBr
IRV
t
/
1
1ln
EE130 Lecture 27, Slide 11 Spring 2007
Turn-off transient
• We know:
• The general solution is:
• Initial condition: QB(0)=IBBB
B
BBB
B QI
dt
dQ
BtBBBB AeItQ /)(
BtBBBB eItQ /1)(
sdt
eBBB
t
B
sdCC
C ttItQ
ttI
ti Bt
/1)(
0
)(
BBB
tCCBsd
II
t1
ln
EE130 Lecture 27, Slide 12 Spring 2007
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, 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 Lecture 27, Slide 13 Spring 2007
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