bjt small-signal models - itesobjt small-signal models dr. josé ernesto rayas sánchez february 19,...
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![Page 1: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/1.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
1
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BJT Small-Signal Models
Dr. José Ernesto Rayas Sánchez
Some figures of this presentation were taken from the instructional resources of the following textbook:
A. S. Sedra and K. C. Smith, Microelectronic Circuits. New York, NY: Oxford University Press, 2003.
2Dr. J. E. Rayas Sánchez
Outline
DC Bias + small-signal excitation
Load lines
Amplification process in BJTs
Small-signal models
DC and small-signal analysis: example
N-port networks
Z, Y and H-parameters
Manufacturing data sheets
![Page 2: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/2.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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3Dr. J. E. Rayas Sánchez
DC Bias + Small-Signal Excitation
If vi = 0 (bias only):0=−− BEBBBB vRiV
B
BEBBB R
vVi −= Input Load Line
4Dr. J. E. Rayas Sánchez
DC Bias + Small-Signal Excitation (cont)
If vi = 0 (bias only):0=−− CECCCC vRiV
C
CECCC R
vVi −= Load Line
![Page 3: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/3.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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5Dr. J. E. Rayas Sánchez
DC Bias + Small-Signal Excitation (cont)
If vi ≠ 0
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DC Bias + Small-Signal Excitation (cont)
If vi ≠ 0
A small variation of vBE can produce a large variation in vCE
Amplification
![Page 4: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/4.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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7Dr. J. E. Rayas Sánchez
BJT Small-Signal Models: T Model using β
Neglecting output resistance, ro
Considering ro
re
ib
B C
E
ib
re = /gm 1/gmgm = ICQ / VT
re
ib
B C
E
ib
re = /gm 1/gmgm = ICQ / VT
ro
ro = VA/ICQ
re
ib
B C
E
ib
re = /gm 1/gmgm = ICQ / VT
8Dr. J. E. Rayas Sánchez
BJT Small-Signal Models: T Model using α
Neglecting output resistance, ro
Considering ro
re
ie
B C
E
iere = /gm 1/gmgm = ICQ / VT
re
iB C
E
ire = /gm 1/gmgm = ICQ / VT
ro
ro = VA/ICQ
![Page 5: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/5.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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9Dr. J. E. Rayas Sánchez
BJT Small-Signal Models: Hybrid π Model
Neglecting output resistance, ro
Considering ro
rgmv r
B C
E
v
gm = ICQ / VT
r gm
ro = VA/ICQ
10Dr. J. E. Rayas Sánchez
DC and Small-Signal Analysis – Example
100=β1=η
Bias point calculation (DC analysis)
mA023.0KΩ100
V7.0V3 =−=BI
V1.3)KΩ3(mA3.2V10 =−=CEVmA3.2100 == BC II
1-mΩ92mV25mA3.2 ===
T
CQm V
Ig
η
KΩ087.1mΩ92100
1 === −mg
r βπ
![Page 6: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/6.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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11Dr. J. E. Rayas Sánchez
DC and Small-Signal Analysis – Example (cont)
100=β1=η
Small-signal equivalent circuit (neglecting ro):
1-mΩ92=mgKΩ087.1=πr
12Dr. J. E. Rayas Sánchez
DC and Small-Signal Analysis – Example (cont)
Small-signal analysis
µA914.71.087KΩ100KΩV8.0 =
+=
+=
πrRvi
BB
ib
7.914 µA
![Page 7: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/7.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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13Dr. J. E. Rayas Sánchez
DC and Small-Signal Analysis – Example (cont)
Small-signal analysis
µA914.7=bimV6.8)µA(1.087KΩ914.7 === πriv bbe
14Dr. J. E. Rayas Sánchez
DC and Small-Signal Analysis – Example (cont)
Small-signal analysis
mV6.8=bevV374.2)mV6.8(276mV6.8)KΩ3)(mΩ92( 1 −=−=−=−= −
beCmo vRgv2.374 V
V8.0V374.2−==
i
ov v
vA
V/V96.2−=vA
![Page 8: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/8.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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15Dr. J. E. Rayas Sánchez
N-Ports Networks (Linear Circuits)
(R. Ludwig and P. Bretchko, RF Circuit Design, Prentice Hall, 2000)
16Dr. J. E. Rayas Sánchez
Impedance Matrix Representation (Z)
Each element of matrix Z is given by
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
NV
VV
M2
1
V
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
NI
II
M2
1
I
ZIV =
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
NNNN
N
N
ZZZ
ZZZZZZ
K
M
K
K
21
22221
11211
Z
jkIj
iij
kIVZ
≠=
=for 0
![Page 9: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/9.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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17Dr. J. E. Rayas Sánchez
Admittance Matrix Representation (Y)
Each element of matrix Y is given by
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
NV
VV
M2
1
V
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
NI
II
M2
1
I
YVI =
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
NNNN
N
N
YYY
YYYYYY
K
M
K
K
21
22221
11211
Y
jkVj
iij
kVIY
≠=
=for 0
18Dr. J. E. Rayas Sánchez
Z-Parameters for 2-Port Networks
⎥⎦
⎤⎢⎣
⎡=
2
1
VV
V ⎥⎦
⎤⎢⎣
⎡=
2
1
II
I
ZIV =
⎥⎦
⎤⎢⎣
⎡=
2221
1211
ZZZZ
Z
Equivalent circuit:
![Page 10: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/10.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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19Dr. J. E. Rayas Sánchez
Y-Parameters for 2-Port Networks
⎥⎦
⎤⎢⎣
⎡=
2
1
VV
V ⎥⎦
⎤⎢⎣
⎡=
2
1
II
I
YVI =
⎥⎦
⎤⎢⎣
⎡=
2221
1211
YYYY
Y
Equivalent circuit:
20Dr. J. E. Rayas Sánchez
H-Parameters (Hybrid) for 2-Port Networks
⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡
2
1
2
1
VI
IV
H
⎥⎦
⎤⎢⎣
⎡=
2221
1211
HHHH
H
Equivalent circuit:
![Page 11: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/11.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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21Dr. J. E. Rayas Sánchez
H-Parameters for a BJT
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡
2
1
2221
1211
2
1
VI
HHHH
IV
Equivalent circuit:
ib
ic
vcevbe
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡
ce
b
oefe
reie
c
eb
vi
hhhh
iv
Equivalent circuit at low freq.:
22Dr. J. E. Rayas Sánchez
BJT Manufacturing Data Sheets
![Page 12: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/12.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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23Dr. J. E. Rayas Sánchez
BJT Manufacturing Data Sheets (cont)
24Dr. J. E. Rayas Sánchez
BJT Manufacturing Data Sheets (cont)
![Page 13: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/13.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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25Dr. J. E. Rayas Sánchez
BJT Manufacturing Data Sheets (cont)
26Dr. J. E. Rayas Sánchez
BJT Manufacturing Data Sheets (cont)
![Page 14: BJT Small-Signal Models - ITESOBJT Small-Signal Models Dr. José Ernesto Rayas Sánchez February 19, 2007 1 1 BJT Small-Signal Models Dr. José Ernesto Rayas Sánchez Some figures](https://reader031.vdocuments.us/reader031/viewer/2022011815/5e5cb0a836807308725172fd/html5/thumbnails/14.jpg)
BJT Small-Signal ModelsDr. José Ernesto Rayas Sánchez
February 19, 2007
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27Dr. J. E. Rayas Sánchez
BJT Manufacturing Data Sheets (cont)
28Dr. J. E. Rayas Sánchez
Getting π Parameters from H-Parameters
Hybrid π Model: Hybrid-Parameters Model:hie
hrevce hfeibhoe vcevbe
icib
iehr ≈π
iefem hhg /≈
oeo hr /1= oeCQA hIV /=