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ECE 342 – Jose Schutt‐Aine 1
ECE 442Solid‐State Devices & Circuits
7. BJT Amplifiers
Jose E. Schutt-AineElectrical & Computer Engineering
University of [email protected]
ECE 342 – Jose Schutt‐Aine 2
• Definitions– Used to increase the amplitude of an input signal to a
desired level– This is a fundamental signal processing function– Must be linear (free of distortion) – Shape of signal
preserved
Amplifiers
( ) ( ),o iv t Av t where A is the voltage gain=
vi(t) vo(t)AMP
: ov
i
vVoltage Gain Av
=
( ) :( )
Lp
I
Load Power PPower Gain AInput Power P
=
ECE 342 – Jose Schutt‐Aine 3
Amplifiers
: p v iNote A A A=
: oi
i
iCurrent Gain Ai
=
o op
I I
v iAv i
=
20log VVoltage gain in dB A=
20log ICurrent gain in dB A=
10log PPower gain in dB A=
Expressing gain in dB (decibels)
ECE 342 – Jose Schutt‐Aine 4
Amplifiers
1 1 2 2DCP V I V I= +
100L
DC
P Power EfficiencyP
η = × =
Since output associated with the signal is larger than the input signal, power must come from DC supply
DC I L dissipatedP P P P+ = +
ECE 342 – Jose Schutt‐Aine 5
An amplifier has ±10 V power supplies and an input current of 0.1 mA (sine wave) input voltage 1 V peak-to-peak and an output voltage with a peak of 9V. The load impedance is 1 kΩ and the amp draws 9.5 mA from each power supply. Determine:
- the voltage gain- the current gain- the power gain- the power drawn from supplies- the power dissipated and η
Problem
9 91
ov
i
VAV
= = =
9ˆ 91oI mAk
= =Ω
20log 20log 9 19.1v dB vA A dB− = = =
ˆ 9 90ˆ 0.1o
ii
IAI
= = =The current gain is
ECE 342 – Jose Schutt‐Aine 6
Problem
40.5 8100.05
dv
I
PAP
= = =
20log90 39.1i dBA dB− = =
9 9 40.52 2L o rms o rmsPower at Load P V I mW− −= = = =
1 0.1 0.052 2I I rms I rmsPower at input P V I mW− −= = = =
10log810 29.1v dBA dB− = =
10 9.5 10 9.5 190dcP mW= × + × =
dissipated dc I LP P P P= + −
190 0.05 4.05 149.6dissipatedP mW= − − =
100 21.3%L
dc
PP
η = × =
ECE 342 – Jose Schutt‐Aine 7
Biasing of Amp
( ) ( )I QI IV t V v t= +
Bias will provide quiescent points for input and output about which variations will take place. Bias maintain amplifier in active region.
( ) ( )o QO oV t V v t= +
( ) ( )o v Iv t A v t=o
vI at Q
dvAdv
=
Amplifier characteristics are determined by bias point
ECE 342 – Jose Schutt‐Aine 8
Voltage Amplifier
vo i Lo
L o
A v RvR R
=+
: o vo Lv
i L o
v A RVoltage gain is Av R R= =
+
Want Ro small (as small as possible) to achieve maximum gain ideal Ro=0
ii s
i S
RInput v vR R
=+
Want Ri large ( so vi≈vs) (actually want Ri >> Rs) ideal Ri=∞
: o i Lvo
s i s L o
v R ROverall gain Av R R R R
= ⋅+ +
ECE 342 – Jose Schutt‐Aine 9
In some cases, connecting load to source leads to signal attenuation; for this case an amplifier with a high input resistance (greater than source) is needed and low output resistance. Such an amplifier is a buffer amplifier.
Voltage Amplifier
ECE 342 – Jose Schutt‐Aine 10
Voltage Amplifier
0
:o
ovo
i i
vOpen Circuit Voltage Gain Av
=
=
: iideal R = ∞0oR =
ECE 342 – Jose Schutt‐Aine 11
Current Amplifier
0
:o
ois
i i
iShort Circuit Current Gain Ai
=
=
: 0iideal R =
oR = ∞
ECE 342 – Jose Schutt‐Aine 12
Transconductance Amplifier
Short Circuit Transconductance : om
i
iGv
=
: iideal R = ∞
oR = ∞
ECE 342 – Jose Schutt‐Aine 13
Transresistance Amplifier
Open Circuit Transresistance : om
i
vRi
=
: 0iideal R =0oR =
ECE 342 – Jose Schutt‐Aine 14
Small-Signal Model
• What is a small-signal incremental model?
– Equivalent circuit that only accounts for signal level fluctuations about the DC bias operating points
– Fluctuations are assumed to be small enough so as not to drive the devices out of the proper range of operation
– Assumed to be linear
– Derives from superposition principle
ECE 342 – Jose Schutt‐Aine 15
Common Emitter ConfigurationThe emitter current IE can be approximated as:
/BE TV VE SI I e
An incremental conductance ge can be defined as
/BE TV VSE Ee
BE T T
II Ig eV V V∂
≡ = =∂
1 Te
e E
Vrg I
= =
26Usually, 26T eE
mVV mV rI
= ⇒ =
From which we get:
Emitter resistance
ECE 342 – Jose Schutt‐Aine 16
Hybrid-π Incremental Model for BJTs
rπ: input resistance looking into the baserx: parasitic series resistance looking into base – ohmic base resistancegm: BJT transconductancero=rce: output collector resistance related to the Early effect
ECE 342 – Jose Schutt‐Aine 17
Hybrid-π Parameters
tanC
C Cm
BE TI cons t
i Igv V
=
∂= =∂
:b
vr is defined as riπ
π π =
mb
g vSince i π
β=
m
then rgπβ
=
A Ace o
C B
V Vr r
I Iβ= = =
is associated with the Early effectce or r=
( )1 er rπ β= +
me
grα
=
mg rπβ =
Can show that
1 1m
e
gr rπ
+ =
ECE 342 – Jose Schutt‐Aine 18
Common Emitter (CE) Amplifier
Bias: Choose R1 & R2 to set VB VE is then set. Choose RE to set IE~IC. Quiescent point of Vout will be determined by RC. Emitter is an AC short.
ECE 342 – Jose Schutt‐Aine 19
Incremental Model for CE Amplifier
1 2BR R R=
Hybrid-π model (ignoring rx)
iin B
i
vR R ri π= =
B inSometimes R r and R rπ π
rπ
E
ro
+
-
gmvπ
vout
RCvin
C
RB
Rsig
+vπ
-
RL
B
+
vi
-
ii io
ECE 342 – Jose Schutt‐Aine 20
( )( )
B o C Lo m sig
B sig
R r r R Rv g v
R r Rπ
π
= −+
iv vπ=( )o m o C Lv g v r R Rπ= −
( )ov m o C L
i
vA g r R Rv
= = −
gain from base to collector
, sigB i
sig
v rand if R r v
r Rπ
ππ +
( )sig in sig B
iin sig B sig
v R v R rv
R R R r Rπ
π
= =+ +
CE Amplifier
ECE 342 – Jose Schutt‐Aine 21
Open-circuit voltage gain:
( )vo m o CA g r R= −
In most cases o C vo m Cr R A g R⇒ = −
( )( ) ( )B
v m o C LB sig
R rG g r R R
R r Rπ
π
= −+
( )o C Lv
sig
r R RG
r Rπ
β= −
+
and for the case where BR rπ
CE Amplifier
ECE 342 – Jose Schutt‐Aine 22
Output Impedance
out C oR R r=
,o C out CIf r R R R
Lv vo
L o
Rfrom which A AR R
⎛ ⎞= ⎜ ⎟+⎝ ⎠
It can be seen that if Rsig >> rπ, the gain will be highly dependent on β. This is not good because of β variations
( ),sig v m C L oIf R r G g R R rπ −
CE Amplifier
ECE 342 – Jose Schutt‐Aine 23
CE with External Resistors
ECE 342 – Jose Schutt‐Aine 24
( )out m L Cv g v R Rπ= −
xm
E
v vg vR r
ππ
π
= +
1E Bin m E
R Rv g R vr r ππ π
⎛ ⎞= + + +⎜ ⎟⎝ ⎠
( )1
m L C inout
E Bm E
g R R vv R Rg R
r rπ π
= −+ + +
CE with External Resistors
in x Bvv v v Rrπ
ππ
= + +
ECE 342 – Jose Schutt‐Aine 25
( ) ( )1
11
MB m L CE B
A g R RR R
r rπ π
β= −
++ +
RE and RB degrade the gain
CE with External Resistors
( ) ( )( )1
m L C m L Cout
in m E E B E B
g r R R g r R Rvv g r R R r R R r R
π π
π π πβ= − = −
+ + + + + +
( )( )1
L CMB
E B
R RA
R r Rπ
ββ
= −+ + +
ECE 342 – Jose Schutt‐Aine 26
( )( )
( )
( ) ( )
11
1 1
L CL C
MBBE B
E
R RR R
A r RR r R R ππ
ββ ββ
β β
⎛ ⎞⎜ ⎟+⎝ ⎠= − = −
+ + + + ++ +
The gain can be written as:
( )and since =
1β α
β +
( )L CMB
E e
R RA
R rα
= −+
CE with External Resistors
( )neglecting
1BR
β +
ECE 342 – Jose Schutt‐Aine 27
Given VBEON=0.6V, find the gain for the circuit shown
1.5BQV V=
Example
1 2
0.9 0.9 0.91E
E E
I mAR R k
= =+ Ω
1.5 0.6 0.9EQV V V V= − =
ECE 342 – Jose Schutt‐Aine 28
1CMB
E e
RA withR rα α= −+
26 28.80.9
Te
E
VrI
= = = Ω
0.9 12 0.9 10 3C outQI mA V V V⇒ = − × =
AC analysis: RE2 is shorted and RE=RE1=100Ω. Since β is not known, use:
10,000 77.5100 28.8MBA = − = −
+
Example (Cont’)
77.5MBA = −
ECE 342 – Jose Schutt‐Aine 29
1o m E m E
vv g v R v g Rr rπ
π ππ π
⎛ ⎞ ⎛ ⎞= + = +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
Emitter Follower
1in B b o E m B
vv v R i v v v R g Rr r
ππ π π
π π
⎛ ⎞= + + = + + +⎜ ⎟
⎝ ⎠
Incremental modelcircuit
ECE 342 – Jose Schutt‐Aine 30
Emitter follower has unity voltage gain
( )( )
11
11 1
m Em Eo
in m E BBm E
g Rg r Rrv
v g r R r RRg Rr r
ππ
π π
π π
⎛ ⎞+⎜ ⎟ +⎝ ⎠= =
+ + +⎛ ⎞+ + +⎜ ⎟
⎝ ⎠
Emitter Follower
Using mg rπ β=( )
( )1
11
Eo
in E B
Rvv R r Rπ
ββ
+=
+ + +
11 Bin E m
Rv v R gr rππ π
⎡ ⎤⎛ ⎞= + + +⎢ ⎥⎜ ⎟
⎝ ⎠⎣ ⎦
ECE 342 – Jose Schutt‐Aine 31
( )1in B Er r R Rπ β= + + +
Emitter Follower – Input Impedance
( )1 / 1//
B E minin
b
v R r R g rvri v r
π π π
π π
⎡ ⎤+ + +⎣ ⎦= =
ECE 342 – Jose Schutt‐Aine 32
Emitter Follower – Output Impedance
oB
B
vir Rπ
= −+
o o o m o oo m
E B E B B
v v v g r v vi g vR r R R r R r R
ππ
π π π
= − + = + ++ + +
[ ] ( )1 1 1( 1)m
o o o B EE B B E B
gi v v r R RR r R r R R r Rπ
π π π
β⎡ ⎤
= + + = + + +⎢ ⎥+ + +⎣ ⎦
ECE 342 – Jose Schutt‐Aine 33
Using mg rπ β=
( ) ( )( )
/ ( 1)( 1) / ( 1)
E B E Boout
o B E E B
R r R R r Rv Ri r R R R r R
π π
π π
ββ β
+ + += = =
+ + + + + +
( ) / ( 1)out E BR R r Rπ β= + +
' '( 1)( 1) 1
EMB out E
E
rRA and R Rr R
π
π
ββ β+
= =+ + +
Output Impedance (cont’)
If we neglect RB
ECE 342 – Jose Schutt‐Aine 34
Common Base Configuration
ECE 342 – Jose Schutt‐Aine 35
,i o m C m i Cv v v g v R g v Rπ π= − = − =
o Cm C
i e
v RVoltage gain g Rv r
α= = =
( ) 11o m m
i im
i g v g vCurrent gaini i
g vr
π π
ππ
β αβ
−= = = = =
+⎛ ⎞+ −⎜ ⎟
⎝ ⎠
out CR R= 1inrr π
β=
+
Common Base Configuration
ECE 342 – Jose Schutt‐Aine 36
m Cg R
CR
1rπ
β +
/( 1)ER rπ β +
( )1Er Rπ β+ +
1m Cg R−
rπ
CR
CE CB EF
Avo
Rin
Rout
BJT Topologies - Summary