Lecture 4 BJT Small Signal AnalysisJ g y
Present by : Thawatchai ThongleamPresent by : Thawatchai ThongleamFaculty of Science and TechnologyN kh P h R j bh U i iNakhon Pathom Rajabhat University
BJT Small Signal Analysis
OutlineBJT as AmplifierBJT as AmplifierSmall Signal Model
The π-ModelThe π Model The T-Model
Small Signal Analysis g yCommon Emitter (CE) AmplifierCommon Base (CB) Amplifier( ) pCommon Collector or Emitter FollowerBJT Digital LogicJ g g
Introduction Amplifier types
Voltage AmplifiersHigh input resistanceLow output resistanceR
oR
vA oviv p
i
ov v
vA =
iR ivovA oi
Current Amplifiersiv
Low input resistanceHigh output resistance
R RiA viv g p
i
oi i
iA =
iR oRiisiA oviv
i
Transconductance AmplifiersHigh input resistanceHigh output resistanceHigh output resistance
oiA =
iR oRimvG oviv
Transresistance Amplifiersi
G vA =
Low input resistanceLow output resistance
oR
iR Low output resistance
oR
vA =
iR imiR oviv
iR i
Introductionใชว้ธิีการ superposition วเิคราะห์วงจรขยายวเิคราะห์การไบอสัแรงดนักระแสตรงวเคราะหการไบอสแรงดนกระแสตรง
T i t lifi (b) Th i it f ( ) ith thTransistor as an amplifier. (b) The circuit of (a) with the signal source vbe eliminated for dc (bias) analysis.
Transfer characteristic of amplifier circuitการไบอสัแรงดนักระแสตรงหมายถึงออกแบบแรงดนักระแสตรงที่เหมาะสมใหก้บัวงจรขยายเพื่อขยายสญัญาณโดยไม่ผดิเพี้ยนญญ
ภาพที่ 4.26 (a) Basic common-emitter amplifier circuit. (b) Transfer characteristic of the circuit in (a).
Equivalence amplifier circuit
CC
1 C
C
1 C
BC1
2
Bi
o
E
2
Figure 5 27 Circuit whose operation is to be analyzed graphicallyFigure 5.27 Circuit whose operation is to be analyzed graphically.
Small Signal Model of the BJT
The amplifier circuit of Fig. 5.48(a) with the dc sources (VBE and VCC) eliminated (short sources (VBE and VCC) eliminated (short circuited). Thus only the signal components are present Note that this is a representation are present. Note that this is a representation of the signal operation of the BJT and not an actual amplifier circuitactual amplifier circuit.
ภาพที่ 4.50
The Hybrid- π Model ∞=or
BJT as a voltage-controlled BJT as a current-BJT as a voltage controlled current source (a transconductance amplifier)
BJT as a currentcontrolled current source (a current amplifier)(a transconductance amplifier) (a current amplifier).
The Hybrid- π Model ∞≠or
BJT as a voltage-controlled BJT as a current-BJT as a voltage controlled current source (a transconductance amplifier)
BJT as a currentcontrolled current source (a current amplifier)(a transconductance amplifier) (a current amplifier).
Small Signal Analysis
Linear operation of the i ll i ltransistor: small-signal
•vbe triangular waveform is superimposed on dc voltage VBE.
•Collector signal current ic, also of triangular waveform,
i d h dsuperimposed on the dc current IC.
•Ic = gm vbe, where gm is the slope of the ic - vBE curve at the bias point Qbias point Q.
Small Signal Analysis Signal Waveforms
Small Signal Analysis
Ω=== 8.10)99.0/3.2(
25mA
mVIVr
E
Te
VmAmVmA
VIg C
m /9225
3.2===
mVVT 25
Ω==β
= k091100r Ω===π k09.192g
rm
Ex 4.1 ใหเ้ขียนวงจรเทียบเคียงของทรานซิสเตอร์และหาค่า gm , roใ ป ี่และ rπ ของวงจรในรูปที 4. VA = 100
ΩΩ F5μ=
IC
IΩΩ F5μ=
IC
I100=β
F5μ
IB100=β
F5μ
IB
μμ
Single Stage BJT Amplifiers
Common Emitter (CE) AmplifierC B (CB) A lifiCommon Base (CB) AmplifierCommon Collector or Emitter Follower
Measurement of input and output impedances.
Fi M f ( ) i d (b) i dFigure Measurement of (a) input and (b) output impedances.
BJT small signal characteristic
Figure Concept of impedance seen at a node.
Common Emitter (CE) Amplifier
R
CCV
IB C
C
BR ov
1C
2C
iv
CR CI
BI o
vgm
obe
CRBRiB
E
1iv o
Ei
Find Av
ORi
πvvi = (1)outm
out
inv RG
VVA −==
( )Como Rrvgv //π−= (2)out
shortm V
IG =inV
CE
thus( )Comi
ov Rrg
vvA //−== (3)
∞≅orAssume Co RR ≅ (7)iv
o
Thus Riv
π= r//RR Bi
i(5)Cmi
ov Rg
vvA −=≡
oCo r//RR = π≅ rR i (8)(6)oCo (6)
แรงดนัเอาตพ์ตุของวงจรขยายแบบอิมิเตอร์ร่วมกลบัเฟสกบัแรงดนัอินพตุ 180 องศาุ ุ
Common Emitter (CE) Amplifier with RE
πvgm
B CCR
CCV
CI
πr orπgm
ovπvCRBR
ivB
C
BR ov
1C
2C
ivBI
EORiR
ERE
ER EI
(1) (3)outmout
inv RG
VVA −==
( )( )Cbemo
v R1rIRvg
vvA
+β+−==
(2)
out
shortm V
IG =
( )( )Ebi R1rIv +β+π
inV
Find Ro
Short vi and open gmvbe
r rπvgm xI
v
B C
πr orπvCRBR
Vx
EOR
ER E
Co RR ≅
VSmall Signal Analysis (CE)
1R CR
CCV
CIvg
B C1R CR
BC
1C 2CBIiv
ovπr or
πvgm
ovπvCR
2Riv 1R
2R ER
E
3C
EORiR
thus
πvvi =Find Av
( )Como
v RrgvA //−==(1) (3)πi
( )Como Rrvgv //π−=
( )Comi
v gv
(2)
( )
Small Signal Analysis (CE)
oCo rRR //= (4)∞≅orAssume
Co RR ≅ (5)
vthus
Cmi
ov Rg
vvA −=≡ (6)
πrRRRi //// 21=Thus Ri
(7)πi 21
Common Emitter (CE) Amplifier
CE grounds emitter, also ll d “b ” itcalled “bypass” capacitor
Small Signal Analysis
Replace BJT with hybrid π equivalent.
( )Comi
ov Rrg
vvA //−==outmv RGA =
mm gG −=
RR //i RrvR //==
Coout RrR //= Bi
in Rri
R //π==
Ex4.3 Find Av, Ri and Ro on amplifier circuit VA = 100
ΩΩ F5
ICΩΩ F5
ICΩ
100β
Ω F5μ=
IB
Ω
100β
Ω F5μ=
IB100=β
F5μ100=β
F5μ
Ex4.4 Find Av, Ri and Ro on amplifier circuit VA = 100
CC
B2
C ΩΩ F5μ=
BC
1
2 F5μ
80=βEF5μ
80=β
E 3ΩF10μ
Ex4.5 Find Av, Ri and Ro on amplifier circuit at VBE = 0.7 and β 100β=100 VA = 100
Ex4.6 Find Av, Ri and Ro on amplifier circuit VA = 100
CC
1 C ΩΩ
C
o
100=βB
C1 2
Bi
2 E
E
Ω Ω3
Common Base (CB) Amplifier
CI
CCV
πvgm
B C
1R CR
C3C2C
BI
C
ovπr or
πgm
ovπv
E
CR21 // RR
B
E
3C BI
sR1CE
outRivER
ev
2R ER sv
inR
Small Signal Analysis (CB)
Thus Ri and Ro
Ein Rg
R //1= (7)
mg
RR Cout RR = (8)
แรงดนัเอาตพ์ตุของวงจรขยายแบบเบสร่วมมีเฟสเดียวกบัแรงดนัอินพตุ
Ex4.7 Amplifier circuit at IC = 2 mA and VC = +5 V VA = 100Fi d R R A R d RFind RC , RE , Av, Ri and Ro
CCV = + 12 V
ΩC
CC
1R CR
C
ΩΩ
C2C o
470 uFB
E
3C B470 uF
470 uFsR1C
2R ERΩ 500Ωs
1 Vp
470 uF
1 kHz
Ex4.8 Amplifier circuit at IC = 2 mA and VC = +5 V VA = 100Fi d R R A R d RFind RC , RE , Av, Ri and Ro
100=β
Ex4.9 Find Av, Ri and Ro on amplifier circuit at VE = -0.7 and β 50β=50 VA = 100
Common Base (CB) Amplifier
The common-base amplifier. (a) Circuit. (b) Equivalent circuit obtained by replacing the BJT with its T modelcircuit obtained by replacing the BJT with its T model.
Small Signal Analysis (CB) Ex 4.10 จากวงจรขยายเบสร่วมโดยใชท้รานซิสเตอร์ชนิด PNP มี β = 50 ให้ัหาอตัราขยายของวงจร VA = 100
Common Collector Amplifier or Voltage Follower
B CCCV
πr orπvgm
πvBRvBR
CI
Eiv
o
BC
E ov
1C
2C
ivBI
iRER
ibR e ovE ov
ER EI
1≅vA
Find Ro with short vi
Thus RxI
π= r//RR Eo
Thus Ro
ERπrx
x
πEo
Thus R
Bibi R//RR =
Thus Ri
วงจร Emitter-Follower ถกนาํไปใชเ้ป็นวงจรภาคเอาตพ์ตของวงจรขยายที่วงจร Emitter Follower ถกูนาไปใชเปนวงจรภาคเอาตพตุของวงจรขยายทตอ้งการขบัโหลดที่มีค่าความตา้นทานตํ่ามาก
Common Collector Amplifier or Voltage FollowerCC
B C
1R πr orπvgm
πv2R
iv 1R
BC
E
1CBIi E
iR RoI
v
ER2R
E
2CEI
o
iRER
eI ov
EI
Emitter-Follower
Th ll t itt f ll lifi ( )The common-collector or emitter-follower amplifier. (a)Circuit. (b) Equivalent circuit obtained by replacing the BJT with its T model.with its T model.
( ) Th i i d h h i i ll l i h R(c) The circuit redrawn to show that ro is in parallel with RL.
(d) Circuit for determining Ro.
Ex4.11 Find Av, Ri and Ro on amplifier circuit VA = 100
CC
RCI
100 k
BC
BR
1CiBI
100 kΩ
E o2C
R I RER EI1 k Ω
LR 1 k Ω
Ex4.12 Find Av, Ri and Ro on amplifier circuit VA = 100
EEV = -5 V
2C
ER 3.3 kΩ
i BE
o
1C
2C
R100=β
BR
1 kΩC
LR100 kΩ 1 kΩ
CCV = +5 V
Ex4.13 Find Av, Ri and Ro on amplifier circuit VA = 100
Ex4.14 Find Av, Ri and Ro on amplifier circuit VA = 100 Ex4.15 Find Av, Ri and Ro on amplifier circuit
เอกสารอา้งอิง (Reference)1. Adel S. Sedra, Kenneth C. Smith “Microelectronic Circuit”2 P l R G d R b G M “A l i d D i f I d 2. Pual R. Gray and Robert G. Mayer “Analysis and Design of Integrated
Circuit” 3. Behzad Razavi “Fundamentals of Microelectronics” 4 รศ สกัรียา ชิตวงศ ์“วศิวกรรมอิเลก็ทรอนิกส์”4. รศ.สกรยา ชตวงศ “วศวกรรมอเลกทรอนกส”
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