ece 255 l17 bjt transistor amplifiersv2 - nanohub.org
TRANSCRIPT
![Page 1: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/1.jpg)
1
ECE 255: L17
BJT Transistor Amplifiers (Sedra and Smith, 7th Ed., Sec. 7.1, 7.2.2)
Mark Lundstrom School of ECE
Purdue University West Lafayette, IN USA
Spring 2019 Purdue University
Lundstrom: 2019
![Page 2: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/2.jpg)
Announcements
2
1) LTspice Project 2 is posted. The due date for it is Wed. Feb. 27th by 5:00PM electronically. You should find your assigned your beta value in your grade book.
2) HW6 will be posted today
3) Exam 2 in on Tuesday, March 5, 6:30-7:30 PM PHYS 112
Lundstrom: 2019
![Page 3: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/3.jpg)
Outline
3
1) Voltage transfer characteristic (VTC) 2) Small signal model for BJT 3) Small signal analysis
Lundstrom: 2019
![Page 4: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/4.jpg)
Voltage Transfer Characteristic
4
+V
OUT=VCC − ICRC
−
β = 100
VCC = 10 V
RC = 5 kΩIC
RBB = 430 kΩ
VIN+−
VBE ON( ) = 0.7 V
What is VOUT vs. VIN?
Lundstrom: 2019
![Page 5: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/5.jpg)
VTC
5
VIN
VOUT
VCC
≈ 0.3V
≈ 0.7 V
cutoff active saturation
VOUT
VCC = 10 V
RC = 5 kΩIC
RBB = 430 kΩ
VIN+−
Lundstrom: 2019
![Page 6: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/6.jpg)
Biasing in the active region
6
VIN
VOUT
VCC
≈ 0.3V
≈ 0.7 V
cutoff active saturation
Q : IC ,VCE( )
VOUT =VCC − IC RC
VOUT =VCC − ISeVIN VT( )RC
Lundstrom: 2019
![Page 7: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/7.jpg)
Bias Circuit
7
+V
CE
−
β = 100
VCC = 10 V
RC = 5 kΩIC
RBB = 430 kΩ
VBB = 5 V +−
IB = ? mA
IC = ? mA
VCE = ? V
VBE ON( ) = 0.7 V Lundstrom: 2019
![Page 8: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/8.jpg)
Bias Circuit
8
+V
CE
−
β = 100
VCC = 10 V
RC = 5 kΩIC
RBB = 430 kΩ
VBB = 5 V +−
IB = 0.01mA
IC = 1.0 mA
VCE = 5.0 V
VBE ON( ) = 0.7 V Lundstrom: 2019
![Page 9: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/9.jpg)
Biasing
9
VIN
VOUTVCC = 10 V
≈ 0.3V
cutoff active saturation
Q : IC = 1mA,VCE = 5.0 V( )
VO = 5 V
VBB = 5.0 V
Lundstrom: 2019
![Page 10: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/10.jpg)
Add ac small signal
10
+υO =V
O+υo sinωt
−
β = 100
VCC = 10 V
RC = 5 kΩiC = IC + ic
RBB = 430 kΩ
VBB = 5 V+−
υi sinωt
VBE ON( ) = 0.7 V
“Common emitter amplifier”
Lundstrom: 2019
![Page 11: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/11.jpg)
Qualitative
11
VI
VO
VCCAV = δVO
δVI≈ dVOdVI
AV < 0
voltage gain
υ I =VBB +υiυ I =VBB −υi
VO
VO −δVO
VO +δVO
(for this circuit)
2δVI
2δVO
![Page 12: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/12.jpg)
Qualitative
12
VI
VO
VCC
≈ 0.3V
VO =VCC − IC RC
VO =VCC − ISeVBE VT( )RC
dVO
dVBE
= −ISeVBE VT( )
VT
RC = −IC
VT
RC
gm ≡
dIC
dVBE
=IC
VT(transconductance)
Aυbe=υo
υbe
= −gmRC
Lundstrom: 2019
![Page 13: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/13.jpg)
Voltage gain of CE amplifier
13
+υOUT =VO
+υo
−
β = 100
VCC = 10 V
RC = 5 kΩiC = IC + ic
RBB = 430 kΩ
VBB = 5 V +−
υi
VBE ON( ) = 0.7 V
+υbe
−
Aυbe
=υo
υbe
= −gmRC
Aυi
=υo
υi
= ?
Lundstrom: 2019
![Page 14: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/14.jpg)
Analysis by superposition
14
+υOUT =VO
+υo
−
β = 100
VCC = 10 V
RC = 5 kΩiC = IC + ic
RBB = 430 kΩ
VBB = 5 V +−
υi
1) DC first 2) Then AC
VBE ON( ) = 0.7 V Lundstrom: 2019
![Page 15: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/15.jpg)
1) DC analysis
15
+V
O= 5 V
−
β = 100
VCC = 10 V
RC = 5 kΩIC = 1mA
RBB = 430 kΩ
VBB = 5 V +−
VBE ON( ) = 0.7 V Lundstrom: 2019
![Page 16: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/16.jpg)
2) AC analysis
16
+υo
−
RC = 5 kΩic
RBB = 430 kΩυi
We need an ac small signal model for the BJT
Lundstrom: 2019
![Page 17: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/17.jpg)
Recall: DC currents
17
N P N
IC = β IB =α IE
IB = IC β
IE =β +1β
IC = ICα
What is the a.c. small signal model?
Lundstrom: 2019
![Page 18: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/18.jpg)
ac collector current
18
N P N
IC + ic
IB + ib
IC = ISeVBE VT → IC + ic = ISe
VBE+υbe( ) VT
IC + ic = ISeVBE VT eυbe VT
IC + ic = ISeVBE VT 1+υbe VT( )
ic = ISeVBE VT υbe VT( ) = IC υbe VT( )
ic =ICVT
υbe = gmυbe Ohm’s Law
Lundstrom: 2019
![Page 19: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/19.jpg)
Summary: s.s. collector current
19
N P N
ic
ib ic = gmυbe
gm = ICVT
+υbe
−
“transconductance”
Note that the ac model parameter, gm, depends on the dc bias current, IC. Lundstrom: 2019
![Page 20: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/20.jpg)
s.s. base current
20
N P N
ic
ib
ic = gmυbe
gm = ICVT
ib =icβ= gm
βυbe =
υbe
β gm= υbe
rπ
ib =υbe
rπ
gmrπ = β
+υbe
−
Lundstrom: 2019
![Page 21: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/21.jpg)
s.s. eqv. circuit model: gm form
21
icib
B
E
C
gm = IC VT gmrπ = β
+υbe
−E
C B
ib ic
rπ gmυπ
+υπ
−
“hybrid pi model”
![Page 22: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/22.jpg)
s.s. eqv. circuit model: beta form
22
gm = ICVT
gmrπ = βE
C B ib ic
rπ gmυπ
+υπ
−
gm = β rπ
ic =βrπυπ = βib
βib
ic = gmυπ
VCCS
CCCS
Lundstrom: 2019
![Page 23: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/23.jpg)
s.s. eqv. circuit model: vce dependence
23
E
C B ib ic
rπ gmυπ
+υπ
−
This model says that the collector current does not depend on the collector-emitter voltage.
Lundstrom: 2019
![Page 24: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/24.jpg)
Output resistance
24 E
VCE
IC
IC = ISeqVBE kBT 1+
υCE
VA
⎛
⎝⎜⎞
⎠⎟
dIC
dVCE
= ISeqVBE kBT 1VA
⎛
⎝⎜⎞
⎠⎟=
′IC
VA
ic =
υce
r0
ro ≈
VA
IC
VA = “Early Voltage”
dIC
dVCE
≈icυceVBE1, IB1
![Page 25: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/25.jpg)
Hybrid pi model
25
gm = ICVT
gmrπ = βE
C B
ib ic
rπ gmυπ
+υπ
−
ro
+υce
−
ro =VA ICLundstrom: 2019
![Page 26: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/26.jpg)
Small signal circuit
26
+υo
−
RC = 5 kΩiC = IC + ic
RBB = 430 kΩυi
We now have an ac small signal model for the BJT
Lundstrom: 2019
![Page 27: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/27.jpg)
Simple s.s. model
27
gm = ICVT
gmrπ = β
E
C B ib ic
rπ+υπ
−
gmυπ
Lundstrom: 2019
![Page 28: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/28.jpg)
ac analysis
28
+υo
−
RC
ic
RBB
υi
C B ib
rπ+υπ
−
gmυπ
E
![Page 29: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/29.jpg)
Same circuit
29
+υo
− RC
ic RBBυs
C B
ib rπ+υπ
−
gmυπ
E
Lundstrom: 2019
![Page 30: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/30.jpg)
ac analysis
30
υo = −gmυπRC
υπ =rπ
rπ+ RBB
υs
υo = −rπ
rπ+ RBB
⎛
⎝⎜
⎞
⎠⎟ gmRCυs
υo
υs
= Aυs= −
rπ
rπ+ RBB
⎛
⎝⎜
⎞
⎠⎟ gmRC
β = 100
RC = 5 kΩIC = 1mA
RBB = 430 kΩ
gm = ICVT
= 1mA0.026 V
= 38.5 mS
gmrπ = β
rπ = β gm = 100 0.039 = 2.6 kΩ
Aυs= −1.2
![Page 31: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/31.jpg)
Hybrid pi model with output resistance
31
gm = ICVT
gmrπ = βE
C B
ib ic
rπ gmυπ
+υπ
−
ro
+υce
−
ro =VA ICLundstrom: 2019
![Page 32: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/32.jpg)
Circuit with output resistance
32
+υo
− RC
ic RBBυi
C B
ib rπ+υπ
−
gmυπ
E
ro
Lundstrom: 2019
![Page 33: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/33.jpg)
Transistor parameters
33
N P N
ic
ib
+υbe
−
β = 100
VBE ON( ) = 0.7 V
VA = 100 V
ro =VAIC
= 100 V1mA
= 100 kΩ
Lundstrom: 2019
![Page 34: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/34.jpg)
2) AC analysis with output resistance
34
υo
υi
= A = −rπ
rπ+ RBB
⎛
⎝⎜
⎞
⎠⎟ gmRC
Av = −1.2→ Av = −1.1
υo
υi
= A = −rπ
rπ+ RBB
⎛
⎝⎜
⎞
⎠⎟ gmRC || r0
5 kΩ ||100 kΩ = 4.76 kΩ
(without ro)
(with ro)
Lundstrom: 2019
![Page 35: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/35.jpg)
Hybrid pi model of BJT
35
gm = ICVT
gmrπ = βE
C B
ib ic
rπ gmυπ
+υπ
−
ro
+υce
−
ro =VA ICLundstrom: 2019
Question: What does the small signal model for a PNP transistor like?
![Page 36: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/36.jpg)
Summary
36 Lundstrom: 2019
The small signal model of a BJT consists of two resistors and one voltage-controlled current course. The values of the ac model parameters are determined by the dc bias current.
The DC bias circuit places the operating point in the portion of the Voltage Transfer Characteristics where the output voltage changes rapidly with input voltage.
Circuit analysis consists of two steps: 1) dc analysis to determine the OP, and 2) ac small signal analysis using the ac circuit model.
![Page 37: ECE 255 L17 BJT Transistor AmplifiersV2 - nanoHUB.org](https://reader031.vdocuments.mx/reader031/viewer/2022012018/61dae21c75446315b2066de9/html5/thumbnails/37.jpg)
Transistor Amplifiers
Lundstrom: 2019 37
1) Voltage transfer characteristic (VTC) 2) Small signal model for BJT 3) Small signal analysis