Transcript lecture 2:bjt small

LECTURE 1:
BASIC BJT AMPLIFIER
-AC ANALYSIS-
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 BJT
LINEAR AMPLIFIER
- BJT small signal operation
- BJT AC equivalent circuits
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 Understand
the concept of an analog signal
and the principle of linear amplifier.
 Investigate the process a single-transistor
circuit can amplify a small, time-varying
input signal.
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Signals contain some type of information.
 The electrical signals in form of time-varying
current and voltage are analog signal.
 Electronic circuit that process analog signal – analog
circuit, example linear amplifier.
 Linear amplifier – magnify an input signal and
produce an output signal whose magnitude is larger
and directly proportional to input signal.

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 Block
diagram of a compact disc player system.
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 From
figure, a dc voltage source connected to
amplifier.
 The amplifier contain transistors that must be
forward biased so that they can act as
amplifying devices.
 We want the o/p signal to be linearly
proportional to input signal
o/p of speaker is
an exact reproduction of signal from compact
disc.
 So, we need a linear amplifier.
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2


type of amplifier analysis:
dc analysis due to applied dc voltage source.
ac analysis due to time-varying signal source.
 dc
analysis is performed by ac source set to zero
~ large signal analysis.
 ac analysis is performed by dc source set to zero
~ small signal analysis.
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Transistor -- heart of an amplifier.
 Bipolar transistors is used in linear amplifier cct
because of their high gain.
 Figure (a) – cct where input signal vI contain dc and
ac signal. Figure (b) – VBB is dc voltage to bias
transistor at Q-point and vs is ac signal that is to be
amplified. Figure (c) – voltage transfer characteristic
graph.
 To become amplifier, transistor need to be biased
with dc voltage @ Q-point  transistor biased in
forward-active region.
 A time-varying (sinusoidal) signal is superimposed on
dc input voltage, VBB, o/p voltage change along the
curve producing a time-varying o/p voltage.

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Figure a
Figure b
Figure c
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


If o/p voltage directly proportional to and larger than i/p
voltage  linear amplifier cct.
If transistor is not biased (in cutoff or saturation), o/p voltage
doesn’t change with a change in i/p  cct is not an amplifier.
Summary of notation
Variable
iB, vBE
IB, VBE
ib, vbe
Ib, Vbe
Meaning
Total instantaneous values
DC values
Instantaneous ac values
Phasor values
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Fig d) Common-emitter cct
with a time-varying signal
source in series with
dc source.
Fig e) Common-emitter transistor
characteristic, dc load line and sinusoidal
variation in base current, collector current
and collector-emitter voltage.
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The graph shows collector current, iC vs c-e voltage,
vCE for different values of iB.
 Q-point is chosen where distance between iB curves
are even to get linear amplification.
 Line between VCC / RC and VCC –- dc load line.
 Signal source, vs produce ac base current
superimposed on quiescent base current.
 ac collector current produce a time-varying voltage
across RC, that induces an ac c-e voltage, vCE.
 vCE or vO will be larger than i/p to produce signal
amplification.

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 Based
on Fig. d & e
(time-varying signals linearly related &
superimposed on dc values)

iB  I BQ  ib
(1)
iC  I CQ  ic
(2)
vCE  VCEQ  vce
(3)
vBE  VBEQ  vbe
(4)
If signal source, vs = 0:
VBB  I BQ RB  VBEQ (B - E loop)
(5)
VCC  I CQ RC  VCEQ (C - E loop)
(6)
– For B-E loop, considering time varying signals:
VBB  vs  iB RB  vBE  ( I BQ  ib ) RB  (VBEQ  vbe )
Rearrange:
VBB  I BQ RB  VBEQ  ib RB  vbe  vs
(7)
(8)
Base on (5), left side of (7) is 0. So:
vs  ib RB  vbe
(9)
– For C-E loop, considering time varying signals:
VCC  iC RC  vCE  ( I CQ  ic ) RC  (VCEQ  vce )
(10)
VCC  I CQ RC  VCEQ  ic Rc  vce
(11)
– Base on (6), left side of (11) is 0. So:
ic Rc  vce  0
(12)





Signal source, vs in base cct
generate time-varying component
in base cct –- iB and vBE.
Figure f) shows the exponential
relationship between iB and vBE.
If magnitude of time-varying signal
superimposed on dc quiescent pt is
small => develop a linear r/ship
between ac vBE and ac iB.
This r/ship corresponds to the
slope of curve at Q-point.
Slope at Q-point is inversely
proportional to a small-signal
parameter, rΠ.
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
From figure above, relation between vBE and iB is:
iB 

v
. exp BE

 VT
IS



If vBE is composed of dc term with sinusoidal
component superimposed, vBE=VBEQ + vbe, then
 V BEQ  v be
iB 
. exp

VT

IS





The term [IS/β].exp (VBEQ / VT) is quiescent base
current, we can write
 v BE
i B  I BQ . exp
 VT



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The base current eq. is not linear and can’t be
written as ac current superimposed on dc quiescent
value.
 If vbe << VT, we can expand the exponential term in
a Taylor series, keeping only linear term which lead
to small signal approximation.

 v BE
i B  I BQ  1 
 VT

I BQ

  I BQ 
.v BE  I BQ  i b
VT

Where ib is the time-varying base current
 I BQ
i b  
 VT

v be


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RC
ic
vO
RB
vs
ib
+
vce
+
vbe
-
AC equivalent circuit of C-E with npn transistor
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Input loop:
vs  ib RB  vbe
 I BQ 
vbe
ib  
 VT 
Output loop:
0.026 V
ic RC  vce  0
Set all dc current and voltage
to zero – voltage become
short cct & current become
open cct.
ic  ib
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Replacing all capacitors by short circuits
Replacing all inductors by open circuits
Replacing dc voltage sources by ground
connections
Replacing dc current sources by open
circuits
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 Definition

of small signal
Small signal : ac input signal voltages and currents
are in the order of ±10 percent of Q-point voltages
and currents.
e.g. If dc current is 10 mA, the ac current (peak-topeak) < 0.1 mA.
 Figure
shows iB vs. vBE with
small-time varying signal
superimposed at Q-pt.
 Since sinusoidal signals are
small, the slope at Q-pt
treated as a constant, has
units of conductance.
 The inverse of this
conductance is smallsignal resistance, rπ
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
We can relate small-signal input base current to smallsignal input voltage by:
v be  i b r

Finding rπ from Q-point slope lead to:
v be
VT
 VT
 r 

ib
I BQ
I CQ
 rπ also
known as diffusion resistance and is a function of
Q-point parameters. VT is known as thermal voltage.
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Now, we consider the output terminal characteristic of
BJT.
 Assume o/p collector current is independent of collectoremitter voltage collector-current is a function of baseemitter voltage, so the equation:

i C 

i C
v BE
.v BE
Q  pt
From eq 5.2 in Chapter 5 Neaman,
iC
 v BE
 I S exp
 VT



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
After substitution and rearrange the above, we obtain:
I CQ
 v BE 
iC
1


. I S exp

v BE Q  pt VT
 VT  Q  pt VT

The term ICQ / VT is a conductance. Since this term
relates current in collector to a voltage in B-E circuit, it
is called transconductance and is written:
gm 

I CQ
VT
Transconductance also a function of Q-pt parameters and
directly proportional to dc bias current.
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 Using
these new parameters  develop a simplified
small-signal hybrid-π equivalent cct for npn BJT.
 Phasor components given in parentheses.
 This circuit can be inserted into ac equivalent circuit
shown previously.
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gm=ICQ/VT
r=VT/ICQ
Transconductance parameter
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
We can relate small-signal collector current to smallsignal base current for o/p of equivalent cct.
i C
ic 
.i b
i B Q  pt

Where
i C
i B

Q  pt
β is called ac common-emitter current gain.
 Thus:

i c  i b
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ib
(Ib )

Current gain parameter
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 Combine
cct.
BJT equivalent cct to ac equivalent
Small-signal hybrid-π model
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
Voltage gain, Av = ratio of o/p voltage to i/p voltage.

Small-signal B-E voltage is called the control voltage, Vbe
or V.

The dependent current source is gmV flows through RC
produce –ve C-E voltage at the output.
Vo  Vce  g mVbe RC
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
From the input portion of the circuit, using voltage
divider:
 r 
Vs
Vbe  
 r  RB 

The small-signal voltage gain is:
 r 
Vo

Av   g m RC 
Vs
 r  RB 
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Given :  = 100, VCC = 12V
VBE = 0.7V, RC = 6k, VT=0.026V,
RB = 50k and
VBB = 1.2V
Calculate the small-signal
voltage gain.
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1.
2.
3.
4.
5.
6.
I BQ 
VBB  VBE ( on)
RB
1.2  0.7

 10 A
50
I CQ  I BQ  100(10A)  1 mA
VCEQ  VCC  I CQ RC  12  (1)(6)  6V
VT
(100)(0.026)
r 

 2.6 k
I CQ
1
I CQ
1
gm 

 38.5 mA / V
VT
0.026
 r

Vo
  11.4
Av 
 g m RC 
Vs
 r  RB 
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 Given
VCC=5V, VBB=2V, RB=650kΩ, RC=15kΩ,
β=100 and VBE(on)=0.7V.
 Determine:
a) Q-points,
b) gm and r
c) voltage gain.
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Early Voltage
(VA)
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Figure above show current-voltage characteristic for
constant values of B-E voltage.
 The curves are linear with respect to C-E voltage in
forward-active mode.
 The slope is due to base-width modulation effect  Early
Effect.
 When the curves extrapolated at zero current, they meet
a point on –ve voltage axis, vce = -VA. VA --- Early voltage

with typical value in range of 50 < VA < 300V.
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


Early Effect => collector current, iC is dependent
to collector-emitter voltage, vCE (refer Chapter 5Neaman):

 v BE  
v CE 
 . 1 

i C  I S exp
VA 
 VT   

The output resistance, rO:
v CE
rO 
i C Q  pt
Substitute and rearrange both equation,

 v BE
1
 I S exp
rO
 VT

 1
.
 V A

Q  pt
I CQ
VA
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
Hence, small-signal transistor output resistance, rO
become:
VA
rO 
I CQ
 rO
is equivalent to Norton resistance  rO is parallel with
dependent current sources.
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Transconductance
parameter
ro=VA/ICQ
Current gain
parameter
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 From




Neaman textbook,
Ac equivalent circuit – pg 386
Transconductance and current gain – pg 386 &
387
Small-signal hybrid-π equivalent circuit – pg 387
Do example 6.3
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




Include 2 additional resistance,
rb and rμ.
rb  series resistance of
semiconductor material.
Since rb << rμ., rb is neglected
(short cct) at low freq.
rμ  reverse-biased diffusion
resistance of B-C junction.
Typically in megaohms and
neglected (open cct).
Normally, in hybrid-π model, we
neglect both rb and rμ.
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