Post on 25-Sep-2020
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 1
Outline of Chapter 5• 1- Introduction to The Bipolar Junction Transistor• 2- Active Mode Operation of BJT• 3- DC Analysis of Active Mode BJT Circuits• 4- BJT as an Amplifier• 5- BJT Small Signal Models• 6- CEA, CEA with RE, CBA, & CCA • 7- Integrated Circuit Amplifiers
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 2
Small Signal Model• Apply small signal
at base: vs(t)=vbe(t)• Results in signal
current, ic(t), at collector
• Can we generate a small signal model based on what we know so far
)()( tvgti bemc =
Cbemc
Ccc
RtvgtvRitv
)()()(0−==−
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 3
Small Signal Model: vbe controls ic
• In response to signal input between base and emitter (vbe), signal current flows in collector (ic)
• Can describe using hybrid-π small signal model
gmvbe+-
vbe
B C
E
C
B
Evbe
ic
)()( tvgti bemc = Hybrid-π small signal model
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 4
Output Resistance and Small Signal Model
• For constant VBE and small VCE, BJT in saturation:
ICC
IB
B
IEE
VCE
VBE
+VCE
_
Linear dependence on IC vs. VCE for constant VBEdefined as the Early Effect
Active Mode; Early Effect
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 5
Modeling the Early Effect• Extrapolated curves
intersect at common point (-VA, 0)
• VA is the Early voltage– typically 50 to 100V
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛=
A
CE
T
BESC V
VVVII 1expIC
VCE
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 6
BJT Small Signal Output Resistance
C
A
constvCE
Co I
VVIr
BE
=⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂∂
≡
−
=
1
.
• Derivation of ro in active mode is a small signal approximation that provides expression for BJT output resistance in the active mode:
IC
VCE
VBE
C
Ao I
Vr =
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 7
BJT Small Signal Model With Output Resistance ro
• The model is updated to include the output resistance, ro , between C & E terminals.
• The resistance is in parallel with the current source
gmvbe+-
vbe
B C
E
ro
C
Ao I
Vr =T
Cm V
Ig =
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 8
Small Signal: vbe proportional to ib
• Since there is both a voltage and a current at the base node, there must be an equivalent resistance (V=IR)
• Small signal base current: ib
• Small signal base emitter voltage: vbe
• Define small signal input resistance at base as vbe/ib= rπ
bbe irv ⋅= π
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 9
Derive an Expression for BJT Small Signal Base Resistance – rπ
• Define expression for rπ:
• Make use of linearity:
• Take derivative and simplify:
⎟⎟⎠
⎞⎜⎜⎝
⎛==
T
BESCB V
VIII expββ
1−
⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂∂
≡=OPBE
B
b
be
VIr
iv
π
mC
T
OPBE
C
OPBE
B
gIV
VI
VIr ββ
βπ =⋅
=⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂∂
=⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂∂
=−− 11
1
B
T
m IV
gr ==
βπ
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 10
Hybrid-π Small Signal Models
πrvi be
b =
βib
B C
E
rorπibgmvbe+
-vbe
B C
E
rorπ
( ) bbmbem iirgvg βπ ==
B
T
m IV
gr ==
βπ
VCCS based model CCCS based model
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 11
Transistor View: Inclusion of ro and rπ
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 12
Small-Signal: vbe proportional to ie
eebe irv ⋅=
• Since there is both a voltage and a current at the emitter node, there must be an equivalent resistance (V=IR)
• Small signal emitter current: ie• Small signal base emitter
voltage: vbe
• Define small signal input resistance at emitter as vbe/ie= re
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 13
Derive an Expression for BJT Small Signal Emitter Resistance – re
• Define expression for re:
• Make use of linearity:
• Take derivative and simplify:
⎟⎟⎠
⎞⎜⎜⎝
⎛==
T
BESCE V
VIII expαα
1−
⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂∂
≡=OPBE
Ee
e
be
VIr
iv
mC
T
OPBE
C
OPBE
Ee gI
VVI
VIr αα
α=
⋅=
⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂∂
=⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂∂
=−− 11
1
E
T
me I
Vg
r ==α
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 14
T-Models
gmvbe
+
-vbe
B
C
E
ro
re
αie
B
C
E
ro
reie
VCCS based model CCCS based model
e
bee r
vi = ( ) eeembem iirgvg α==E
T
me I
Vg
r ==α
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 15
Hybrid-π Small Signal Model – Summary
T
Cm V
Ig =C
Ao I
Vr =B
T
IVr =π
• Useful to use model when:– emitter terminal at signal ground– input applied at base
gmvbevbe
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 16
– input applied at base or emitter
T Small Signal Model – Summary
• Useful to use model when:
– emitter terminal not at signal ground
T
Cm V
Ig =C
Ao I
Vr =E
Te I
Vr =
e
beebe
eebbe
rriiriir
ririv
)1()1(;)/(
+=+==
==
ββ
π
π
π
• Note:
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 17
PNP Small Signal Model• Small-signal model for
pnp’s identical to npn• Re-orient the model to
reflect direction of current flow and voltage polarity
• Common mistakes:– Get location of B, E,
and C terminals wrong– DC current flows one way,
signal current flows other way
Note: Vbe = -Veb
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 18
Example: Calculate Common Emitter Voltage Gain
VA
m mg 4.42= Ω= kro 8.70Ω= kr 36.2π
Use Hybrid-π model, and assume DC operating point is such that the following small signal parameters apply:
Ω= kRC 2
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 19
Small Signal Example
X
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 20
Small Signal Example
Cobemout Rrvgv ⋅−=
VVRrgvv
vvA Com
be
out
s
outV /5.82−=⋅−===
bes vv =
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 21
Small Signal Analysis – Comments• Analysis procedure:
– Solve for DC operating point
– Calculate small-signal parameters, gm, rπ, re, ro
– Construct small-signal equivalent circuit
– Compute voltage and current gains, input and output resistances.
• What to do about ro?– Often, including ro
complicates circuit analysis
– Omitting ro from small signal model results in acceptable accuracy
– Sometimes, ro must be included
• The often used rule of thumb: if neither end of ro is at a signal ground, you can ignore it
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 22
Small Signal Approximation
• Small signal analysis requires the use of “small”signals to be valid; how small is “small enough”?
• BJT based on pn junction, thus vbe constraint follows that for diode
• For linear approximation to be valid:
• Works for vbe less than approximately 10mV in amplitude
1<<⋅ T
d
Vnv
1<<T
be
Vv
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 23
What is the Limit on vs in Order to Remain in Small Signal Approximation?
bes vv =• For this circuit, since vs = vbe, vs must remain less than 10 mV in order for small signal model to be valid• What modifications can be made to increase allowable magnitude of vs?
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 24
Outline of Chapter 5
• 1- Introduction to The Bipolar Junction Transistor• 2- Active Mode Operation of BJT• 3- DC Analysis of Active Mode BJT Circuits• 4- BJT as an Amplifier• 5- BJT Small Signal Models• 6- CEA, CEA with RE, CBA, & CCA• 7- Integrated Circuit Amplifiers
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 25
The Common Emitter Amplifier (CEA)• Input at base; output at collector• The emitter has a small-signal
ground and is “common” to both input and output.
• By-pass (red) capacitors and coupling (green) capacitors are used to DC-bias transistor and couple signals.
• Use Hybrid-π model with the output resistance, ro.
01
01
=∞=
∞==
ωω
ω
whenCj
CwhenCj
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 26
CEA DC Analysis – Confirm Active• DC Analysis
– Thevenin:
– Analysis:
mAII EC 82.11
=+
=ββ
VkIV COUT 18.3)1(5 =Ω−=
( ) ( )
18755000//3000
25.153
3553
55
==
=⎟⎠⎞
⎜⎝⎛
+−+⎟
⎠⎞
⎜⎝⎛
+=
EQ
EQ
Rkk
kkk
kV
VkIV EE 515.05)3( =−Ω=
VVV EB 215.17.0 =+=
mAk
RV
I
II
kIRIV
EQ
EQE
EB
EEQBEQ
84.1)3(
1
57.0)1/(
05)3(7.0
=Ω+
+
+−=
+=
=+Ω−−−
β
β
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 27
CEA Voltage Gain
inbe vv = ( )Ω−= krvgv obemout 1
( )Ω−== krgvvA om
in
outVO 1
Ω==
Ω==
==
54945
4.1359
0728.0
C
AO
B
T
T
Cm
IVr
IVr
VA
VIg
π
Voltage gain analysis
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 28
Rin Rout
CEA Input/Output Resistance
Input Resistance:
Ω==
≡
786|| EQIN
in
inIN
RrRivR
π Ω=Ω= 9821krR oOUT
Output resistance: set vin = 0; thus vbe = 0; leads to gmvbe = 0 and thus open circuited; note one node of rotied to ground
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 29
CEA Summary
( )Comin
outVO Rrg
vvA −==
πrRIN =
CoOUT RrR =
• Large gain parameters
• RIN & ROUT both moderate
• RIN & ROUT not ideal for any amplifier configuration
• In practice, not usually used by itself for gain
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 30
CEA with RE
• There is NO small-signal ground in the emitter
• Since there is neither collector nor emitter at signal ground– Use T small-
signal model– Neglect ro
RE=3kΩ
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 31
CEA with RE - Voltage Gain Analysis
• Draw small-signal T-model equivalent circuit.
• Neglect rO
• Voltage gain
inEe
ebe v
Rrrv+
=
Cbemout Rvgv −=
Ee
eCm
in
outVO Rr
rRgvvA
+−==
RC
vin
gmvbe
+
-vbe re
vout
RE
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 32
RIN: the β+1 Reflection Rule
• The β+1 rule takes advantage of the relationship between iEand iB
b
Eeb
b
xbe
in
inIN i
Ririi
vvivR +
=+
=≡ π
• Rule generally applicable only when ro neglected
ib
VXie
EIN RrR )1( ++= βπ
be ii )1( += β
vin
vout
When looking into the base, the input resistance is the base resistance plus (β+1) times total resistance in the emitter
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 33
The β+1 Reflection Rule in Reverse: Looking Into the Emitter
ib
VX
ve
e
Bbee
e
xeb
in
inIN i
Ririi
vvivR
−−−
=−+
=≡
)1( ++=
βB
eINRrRbe ii )1( += β
Veb
-
+
+-
• RB looks (β+1) smaller from emitter perspective
• When looking into the emitter, the input resistance is the emitter resistance PLUS whatever is in the base divided by (β+1)
xebinxebin vvvvvv =−+= ;
vin
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 34
CEA with RE– Input/Output Resistance• Neglect rO
• Input Resistance• Using the β+1 reflection
rule:
• Output resistance: set vin = 0; thus vbe = 0; leads to gmvbe = 0 and thus open circuited; by inspection:
Ω= kROUT 1
Rout( )( )[ ]EeEQIN RrRR ++= 1|| β
Rin
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 35
The CEA With RE – Summary
COUT RR =
moderate
moderate
• Moderate gain due to REwhich reduces gain
• Large RIN good for voltage and transconductanceamplifier configuration
• Moderate ROUT a problem, but fixable
Ee
eCm
in
outVO Rr
rRgvvA
+−==
( )( )EeIN RrR ++= 1β large
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 36
The Common Base Amplifier (CBA)• The input is ve(t)• The output is vc(t)• The base has a small-
signal ground and is “common” to both input and output.
• By-pass capacitors and coupling capacitors are used to DC-bias transistor and couple signals.
• Use T model without the output resistance, ro.
by-pass
coupling
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 37
CBA – Voltage Gain Analysis
inbe vv −=
• Draw small-signal T-model equivalent circuit.
• Neglect rO
• Circuit analysis - voltage gain
)1( Ω−= kvgv bemout
)1( Ω== kgvvA m
in
outVO
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 38
CBA – Short Circuit Current Gain Analysis• Draw small-signal T-model
equivalent circuit.• Neglect rO
• Circuit analysis - current gain
eout ii α−=
⎟⎟⎠
⎞⎜⎜⎝
⎛+
==Ee
E
in
outIS Rr
RiiA α
VX
+
_
_
VX
ineX iii +=
inEe
Ee i
RrRi ⎟⎟
⎠
⎞⎜⎜⎝
⎛+
−=
iX
EXeeX Ririv =−=
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 39
CBA – Input/Output resistance
Ω= kROUT 1
Rout
• Input Resistance
• Output resistance• With vIN = -vbe = 0
EeIN RrR ||=
Rin
LOW input resistance can be useful !!
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 40
The Common Collector Amplifier (CCA)• The input is vb(t)• The output is ve(t)• The collector has a small-
signal ground and is “common” to both input and output.
• By-pass capacitors and coupling capacitors are used to DC-bias transistor and couple signals.
• Use T model with the output resistance, ro.
by-pass
coupling
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 41
CCA – Voltage-Gain Analysis
⎟⎟⎠
⎞⎜⎜⎝
⎛+ΩΩ
=eo
oinout rkr
krvv4//
4//
+
- -+
Since re small, Almost vout=vin
Voltage Division:
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 42
The CCA – Current-Gain Analysis
⎟⎟⎠
⎞⎜⎜⎝
⎛++Ω
Ω+==
)1(88)1(
ββ
ein
outIS rk
kiiA
)1/(;
βα
+=−−==+
exin
xinbeeb
iiiiiiiii
eexin rikiv =Ω= )8(
eout ii =
iX
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 43
CCA - Input/Output Resistance• Input Resistance; by
inspection using β+1 rule:
RIN
HIGH INPUT RESISTANCE
• Output Resistance, vin= 0
EoeOUT RrrR ////=
ROUTLOW OUTPUT RESISTANCE
( )( ){ }EoeIN RrrkR //1//8 ++Ω= β
Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I
BJTs 44
CCA Operation – Voltage Buffer• Good voltage buffer
– The VOLTAGE gain is almost unity, and the DC component is only reduced by 0.7V
– Large short circuit current gain
– High input resistance (which reduces loading to the circuits before)
– Low output resistance (which reduces the loading of circuits after)