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ECE 342 – Jose Schutt‐Aine 1 Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois [email protected] ECE 342 Electronic Circuits Lecture 22 Transistor Capacitances
ECE 342 – Jose Schutt‐Aine 1
Jose E. Schutt-AineElectrical & Computer Engineering
University of [email protected]
ECE 342Electronic Circuits
Lecture 22Transistor Capacitances
ECE 342 – Jose Schutt‐Aine 2
Model for general Amplifying Element
Cc1 and Cc2 are coupling capacitors (large) F
Cin and Cout are parasitic capacitors (small) pF
ECE 342 – Jose Schutt‐Aine 3
Midband Frequencies
- Coupling capacitors are short circuits
- Parasitic capacitors are open circuits
out in LMB
in g in out L
v R RA Av R R R R
ECE 342 – Jose Schutt‐Aine 4
Low Frequency Model- Coupling capacitors are present- Parasitic capacitors are open circuits
1
1
1
1 1 ( )in in in c in
abc g in
g inc
v R v j C Rvj C R RR R
j C
1
1
( )1 ( )
c g ininab in
g in c g in
j C R RRv vR R j C R R
ECE 342 – Jose Schutt‐Aine 5
Low Frequency Model
1 221
1 122l l
L out cg in c
define f and fR R CR R C
1
1
/1 /
in lab in
g in l
R jf fv vR R jf f
2
2
/,1 /
lLout ab
L out l
jf fRSimilarly v AvR R jf f
ECE 342 – Jose Schutt‐Aine 6
1 2
1 2
/ /1 / 1 /
out in l lL
in g in L out l l
v R jf f jf fROverall gain Av R R R R jf f jf f
1 2
1 2
/ /1 / 1 /
out l lMB
in l l
v jf f jf fAv jf f jf f
Low Frequency Model
ECE 342 – Jose Schutt‐Aine 7
Rout = 3 k, Rg=200 , Rin=12 k, RL=10 kCc1 = 5 F and Cc2 = 1 F
1 6
1 2.612 (12,200 5 10 )lf Hz
Example
2 6
1 12.22 (13,000 10 )lf Hz
ECE 342 – Jose Schutt‐Aine 8
High Frequency Model- Assume coupling capacitors are short- Account for parasitic capacitors
1th g inR R R
1in in
thg in
v RVR R
Potential Theveninequivalent for input as seen by Cin
ECE 342 – Jose Schutt‐Aine 9
1
11
in inab
g in in th
v RvR R j C R
11 1
1 11 / 2
in inab h
g in h th in
v Rv where fR R jf f R C
2
11
ab Lout
out L out th
Av RLikewise vR R j C R
2th out Lwith R R R
22 2
1 11 / 2
ab Lout h
L out h th out
Av Rv where fR R jf f R C
High Frequency Model
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1 2
1 11 / 1 /
o in L
i in g L out h h
v R RAv R R R R jf f jf f
1 2
1 11 / 1 /
oMB
i h h
v Av jf f jf f
Overall gain is:
or
High Frequency
ECE 342 – Jose Schutt‐Aine 11
Example: Rout = 3 k, Rg=200 , Rin=12 k, RL=10 kCin = 200 pF and Cout= 40 pF
1 10
1 4.052 2 10 (12,200 200)hf MHz
2 12
1 1.722 40 10 (10,000 3,000)hf MHz
64.05 10log 5.52 512.2
decades
Summary: low-frequency < 12.2 Hz, High frequency > 1.72 MHz
Example
ECE 342 – Jose Schutt‐Aine 12
Triode region:
Saturation region:
Cutoff:
12gs gd oxC C WLC
23gs oxC WLC 0gdC
0gd gsC C
gb oxC WLC
MOSFET - Gate Capacitance Effect
ECE 342 – Jose Schutt‐Aine 13
ov ov oxC WL COverlap capacitance (gate-to-source):
1
sbosb
SB
o
CCVV
1
dbodb
DB
o
CCVV
Body
CSB
CGS CGD CGB
CDB
RG
Gate
DrainSourceRS
MOSFET – Junction Capacitances
ECE 342 – Jose Schutt‐Aine 14
22 Dm n ox eff n ox D
eff
W W Ig C V C IL L V
MOSFET High-Frequency Model
2 2mb m mF sb
g g gV
1/ds A DD
r V II
23gs ox ov oxC WLC WL C
gd ov oxC WL C
1
sbosb
SB
o
CCVV
1
dbodb
DB
o
CCVV
ECE 342 – Jose Schutt‐Aine 15
nde
BE
dQCdv
BJT Capacitances
Base: Diffusion Capacitance: Cde (small signal)
where Qn is minority carrier charge in base
C Fde F F m
BE T
diC gdv V
where F is the forward transit time (time spent crossing base)
ECE 342 – Jose Schutt‐Aine 16
Base-emitter junction capacitance:
1
jeoje m
BE
oe
CC
VV
Cjeo is Cje at 0 V. Voe is EBJ built in voltage ~ 0.9 V
BJT Capacitances
ECE 342 – Jose Schutt‐Aine 17
BJT CapacitancesIn hybrid pi model, Cde+Cje=C
Collector-base junction capacitance
1
om
CB
oe
CC
VV
Co is C at 0 V. Voc is CBJ built in voltage ~ 0.9 V
C is around a few tens of pFC is around a few pF
ECE 342 – Jose Schutt‐Aine 18
High-Frequency Hybrid- Model
, ,ACm o
T C m
VIg r rV I g
, ,2
mde je de F m
T
gC C C C C C gf
, 0.3 0.5
1
jcom
CB
oe
CC m
VV
2
mT
gfC C
ECE 342 – Jose Schutt‐Aine 19
CS - Three Frequency Bands
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CE - Three Frequency Bands
ECE 342 – Jose Schutt‐Aine 21
o m gs gd gsI g V sC V
Unity-Gain Frequency fTfT is defined as the frequency at which the short-circuit current gain of the common source configuration becomes unity
(neglect sCgdVgs since Cgd is small)
o m gsI g V i
gsgs gd
IVs C C
o m
i gs gd
I gI s C C
s jDefine:
ECE 342 – Jose Schutt‐Aine 22
For s=j, magnitude of current gain becomes unity at
2m m
T Tgs gd gs gd
g gfC C C C
fT ~ 100 MHz for 5-m CMOS, fT ~ several GHz for 0.13m CMOS
Calculating fT
ECE 342 – Jose Schutt‐Aine 23
C mI g sC v
BJT - Short-Circuit Current Gain
1BIv
sC sCr
ECE 342 – Jose Schutt‐Aine 24
Define hfe as short-circuit current gain
1mC
feB
g sCIhI s C C
r
1C m
feB
I g rhI s C C r
at freq. of interestmg sC
BJT - Short-Circuit Current Gain
ECE 342 – Jose Schutt‐Aine 25
BJT - Short-Circuit Current Gain
1o
fehs C C r
Define hfe has a single pole (or STC) response. Unity gain bandwidth is for:
1 11 2
m mfe
T
g r gh ors C C r f C C
In some cases, if C is known, then
ECE 342 – Jose Schutt‐Aine 26
2m
Tgf
C C
From which we get
2m m
T T
g gC Cf
, m m
T T
g gThus C C C C
BJT - Short-Circuit Current Gain
