Transcript Document

A.1 Large Signal Operation-Transfer Charact.
Figure 6.32 Biasing the BJT amplifier at a point Q located on the active-mode segment of the VTC.
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A.1 Large Signal Operation-Transfer Charact.
O  CE  VCC  RC iC
iC  I S e BE / VT  I S e I / VT
 O  VCC  RC I S e
 I / VT
ICsat
VCC  VCEsat

RC
2
A.2 Amplifier Gain
BJT is biased at a point in active region called Quiescent point
I C  I S e BE / VT
(5.53)
VCE  VCC  RC IC
(5.54)
d O
A 
d I
 I  VBE
1
A  
I S e VBE / VT RC
VT
IC RC
VRC
A  

VT
VT
(5.56)
VRC  VCC  VCE
(5.57)
3
A.3 Graphical Analysis
VCC
1
iC 

CE
RC RC
CE  VCC  iC RC
4
A.3 Graphical Analysis
IB must be defined previously.
Q is quiescent bias point
5
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A.3 Graphical Analysis
Small signal analysis around the bias Q point
7
A.3 Operation as a Switch
iB 
 I  VBE
RB
iC   iB
C  VCC  RC iC
IC (EOS)
I B (EOS)
VCC  0.3

RC
IC (EOS)


VI (EOS)  I B (EOS) RB  VBE
Utilize the cutoff and
saturation modes.
ICsat
Edge of saturation (EOS)
8
VCC  VCEsat

RC
A.4 Small Signal Operation and Models
DC bias conditions are set by these equations.
I E  IC /
I C  I S e VBE / VT
I B  I C /
VC  VCE  VCC  IC RC
9
A.4.1 collector current and transconductance
 BE  VBE   be
iC  I S e BE / VT  I S e (VBE be )/ VT  I S e 
be / VT
iC  IC e
iC
VBE / VT 
e
be / VT 
  be 
IC  1 
 for small be
VT 

IC
iC  I C 
 be
VT
Small signal approximation
Small signal component
IC
ic 
 be
VT
or
ic  gm be
where
gm is called transconductance !
10
IC
gm 
VT
or
iC
gm 
 BE
iC  IC
A.4.1 collector current and transconductance
Small signal approximation is restricted to an almost linear
segment of i-v curve.
11
A.4.2 base current and input resistance at base
iC
IC
1 IC
iB  

be
   VT
1 IC
ib 
be
 VT
iB  I B  ib
r 
 be
ib
Therefore,
or
ib 
gm
Small signal r is defined for small signal ib
r 

gm
VT
r 
IB
or
is called small signal base resistance
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
 be
A.4.3 emitter current and input resistance
iE 
iC


IC


iC

i E  I E  ie
iC
IC
IE
ie  
be 
be
  VT
VT
re 
 be
ie
Therefore,
For small signal vbe
Small signal reis defined for small signal ie
VT
re 
IE
r and re relationship
is called small signal emitter resistance
re 

gm
13
1
gm
r  (   1)re
Figure 6.38 Illustrating the definition of rπ and re.
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Figure 6.39 The amplifier circuit of Fig. 6.36(a) with the dc sources (VBE and VCC) eliminated (short-circuited). Thus only the signal
components are present. Note that this is a representation of the signal operation of the BJT and not an actual amplifier circuit.
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A.4.4 Voltage Gain
C  VCC  iC RC  VCC  ( I C  ic ) RC
 (VCC  I C RC )  ic RC  VC  ic RC
 c   ic RC   gm be RC
 (  gm RC ) be
Voltage gain of amplifier is
c
A 
  gm RC
be
or
IC RC
A  
VT
Voltage gain is directly proportional to collector current Ic.
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A.4.5 Separating Signal and DC quantities
• Voltage and current are composed of DC and signal components.
• since ideal dc supply voltage does not change, the signal voltage
across it will be zero.
Amplifier circuit with DC sources
Eliminated (short circuited)
=> We will make equivalent small signal
circuit using equivalent small signal
transistor model
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A.4.6 The Hybrid- Model
• the equivalent small signal circuit model
ie 

 be
r
 be
r
 gm be 
 be
r
(1   )   be
(1  gm r )
 r 
 1  


  be / re
18
gm be  gm ( ib r )
 ( gm r )ib   ib
A.4.7 The T Model
ib 


 be
re
 be
re
 be
 gm be 
(1   ) 
 be
(   1)re

re
 be 
(1  gm re )
 
1
re 
  1 
 be
r
19
gm be  gm ( ie re )
 ( gm re )ie   ie
A.4.8 Application of small signal equivalent circuits
1. Determine DC operating point of BJT (particularly Ic)
2. Calculate values of small signal model parameters such as
gm = Ic/VT, r = /gm, and re = VT/IE.
3. eliminate DC sources by replacing DC voltage with short
circuit and DC current with open circuit.
4. Replace BJT with one of small signal equivalent circuit models.
5. Analyze the resulting circuit !
20
A.4.8 Application of small signal equivalent circuits
DC operating point
VBB  VBE
IB 
 0.023 mA
RBB
IC   I B  2.3 mA
VC  VCC  iC RC  3.1 V
Small signal model parameters
 - model used !
VT
re 
 10.8 
IE
gm 
r 
21
IC
 92 mA/V
VT

gm
 1.09 
A.4.8 Application of small signal equivalent circuits
r
 be   i
r  RBB
1.09
 i
 0.011 i
101.09
(5.105)
 o   gm be RC
 92  0.011 i  3  3.04 i
o
A 
 3.04 V/V
i
(5.106)
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A.4.8 Application of small signal equivalent circuits
DC operating point
IE 
10  VE
 0.93 mA
RE
IC  0.92 mA
VC  10  IC RC  5.4 V
Small signal model parameters
  0.99
re 
VT
25 mV

 27 
I E 0.93 mA
o
A 
 183.3 V/V
i
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A.4.10 Small signal model to account for Early effect.
Early effect
VA +VCE
ro 
IC
VA
IC
o   gmbe ( RC // ro )
In most cases, since ro >> RC, reduction in gain is not critical.
Furthermore, we can neglect ro in our analysis for simplifying the
circuit analysis.
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A.4.10 Small signal model to account for Early effect.
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A.5 Single Stage BJT Amplifier
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A.5 Single Stage BJT Amplifier
Table 5.5
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A.5.1 The common emitter (CE) amplifier
- AC ground at emitter
- CE is bypass capacitor
- CC1 is coupling
capacitor
Rin 
i
ii
 RB Rib
Rib  r
Rin
Small signal model for circuit
28
r
A.5.2 CE Amplifier with emitter resistance
Small signal model for circuit
Rin  RB Rib
Rib 
i
b
ie 
i
re  Re
and
ie
ib  (1   )ie 
 1
Rib  (   1)(re  Re )
- It says that input resistance looking into base is +1 times total
resistance in emitter (resistance reflection rule)
29
A.5.2 CE Amplifier with emitter resistance
Rib (with Re included) (   1)( re  Re )
Re

 1
 1  gm Re
Rib (without Re )
(   1)re
re
- Inclusion of RE in emitter can substantially increase the input resistance.
- Therefore, designer can control Rin by controlling value of RE.
Now we determine the voltage gain
 o   ic ( RC RL )
  ie ( RC RL )
( RC RL )
A  
re  Re
o
 ( RC RL )
A 

i
re  Re
~1
A o  
and
 RC
re  Re
- voltage gain from base to collector is equal to ratio of collector resistance to
emitter resistance.
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A.5.2 CE Amplifier with emitter resistance
Avo can be expressed in other form.

RC
A o  
re 1  Re / re
gm RC
gm RC
A o  

1  Re / re
1  gm Re
There is trade between increase in input resistance and decrease in
voltage gain by factor of 1+gmRe
Output resistance :
ios   ie
A is  
and
 ( RB Rib )
re  Re
Rout  RC
ii   i / Rin
if RB >> Rib
Rib=(+1)(re+Re)
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 Rin ie
Ais  
i
 (   1)( re  Re )
A is 
 
re  Re
A.5.2 CE Amplifier with emitter resistance
Summary of CE amplifier with emitter resistance
- Input resistance is increased by factor of 1+gmRe.
- The voltage gain from base to collector is reduced by factor of
1+gmRe.
- For the same nonlinear distortion, input signal can be increased
by factor of 1+gmRe.
- The overall voltage gain is less dependant on .
- The high frequency response is significantly improved.
32
A.5.3 The Common Base (CB) Amplifier
Small signal model for circuit
Rin  re
ie  
i
re
and
o   ie ( RC RL )
o 
A 
 ( RC RL )  gm ( RC RL )
 i re
33
A.5.3 The Common Base (CB) Amplifier
Summary of CB amplifier with emitter resistance
- Input resistance is very low (re).
- Short circuit current gain is nearly unity ().
- Like CE amplifier, it has high output resistance RC.
- A very importance application of CB amplifier is current buffer.
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A.5.4 The Common Collector (CC) Amplifier
CC amplifier is commonly used and known by name of emitter follower.
Redrawn for rO parallel with RL.
Unlike CE and CB, CC amp. is not
unilateral because Rin depends on
output RL !
35
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Figure 5.2 The enhancement-type NMOS transistor with a positive voltage applied to the gate. An n channel is induced at the top of the
substrate beneath the gate.
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Figure 5.10 Cross-section of a CMOS integrated circuit. Note that the PMOS transistor is formed in a separate n-type region, known as an n
well. Another arrangement is also possible in which an n-type body is used and the n device is formed in a p well. Not shown are the
connections made to the p-type body and to the n well; the latter functions as the body terminal for the p-channel device.
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Figure 5.20 The relative levels of the terminal voltages of the enhancement-type PMOS transistor for operation in the triode region and in the
saturation region.
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Figure 5.28 Biasing the MOSFET amplifier at a point Q located on the segment AB of the VTC.
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Figure 5.31 Graphical construction to determine the voltage transfer characteristic of the amplifier in Fig. 5.29(a).
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Figure 5.33 Two load lines and corresponding bias points. Bias point Q1 does not leave sufficient room for positive signal swing at the drain (too
close to VDD). Bias point Q2 is too close to the boundary of the triode region and might not allow for sufficient negative signal swing.
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Figure 5.43 The three basic MOSFET amplifier configurations.
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Figure 5.49 Illustrating the need for a unity-gain buffer amplifier.
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Figure 5.57 (a) Common-source amplifier based on the circuit of Fig. 5.56. (b) Equivalent circuit of the amplifier for small-signal analysis.
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