EE303 Electronics II
Topic 3
Dr Mohamad Rahal
Miller’s Theorem, High Frequency of CS
and CE
CB, CG and Cascode amplifiers,
Emitter follower (CC) amp.
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Outline of Topic 3
•
•
•
•
Miller’s Theorem
High Frequency Response of CS and CE
Frequency Response of CG and CB amplifiers
Frequency Response of Source and Emitter
Followers
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Miller’s Theorem
• Technique employed for replacing Cgd , C by
an equivalent input capacitance
• This technique is based on Miller’s Theorem
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Miller’s Equivalent Circuit
Try out Example 6.7
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High Frequency of CS
Three methods: Miller’s Theorem, Open circuit time constant
Method, exact analysis
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Analysis Using Miller’s Theorem
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Analysis using Open-circuit Time
Constant
Ix 
 v gs
Rsig
At node G
I x  g m v gs 
v gs  v x
RL'
At node D
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Overall Time Constant
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“Exact” Analysis 1
At node D
At node G
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“Exact” Analysis 2
fz 
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2C gd
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Low Frequency Gain
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s0
11
Transfer Functions Poles 1
From open-circuit
time Constant method
P1  P 2
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Transfer Functions Poles 2
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Example 6.9
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Example 6.9
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Example 6.9 Miller
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Example 6.9 OC Time Constants
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Example 6.9 Exact Analysis
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High Frequency of CE
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High Frequency of CE cont.
Miller’s
OC time constant
Exact
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High Frequency of CS Rsig=0
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High Frequency of CS Rsig=0 cont.
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Common Gate Amplifier Models
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N_well CMOS Process
The substrate of each p-MOS device substrate can be
connected to its source
Whereas for n-MOS devices all substrates has to be
connected to the most negative voltage
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Body Effect In CG Amplifier
• Body effect has to be taken into account
• Drain Current g mvgs  g mb vbs
g mb  g m  0.1g m
g m  g mb
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Rin of CG Amplifier
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Operation with RL  
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Voltage Gains for Loaded CG
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Output Resistance of CG 1
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Output Resistance of CG 2
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Impedance Transformation of CG
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CG Current Buffer
i1 
Rs
isig
Rs  Rin
io  
Gi 
Rout
g m v gs
Rout  RL
Gis  g m
Rs
v gs  
isig  Rin
Rs  Rin
io 
Rout
Rs
gm
isig  Rin
Rout  RL
Rs  Rin
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Rout
Rs
gm
 Rin
Rout  RL
Rs  Rin
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Gis  g m
Gis 
Rs
 Rin
Rs  Rin
Rs
Rs 
1
gm

1
gm
g m Rs
g m ro Rs
A R
A R

 vo s  vo s  1
1  g m Rs ro  g m ro Rs g m ro Rs
Rout
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High Frequency Response of CG 1
CL includes Cdb
All caps are grounded at one
End, No Miller
ro
neglected
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High Frequency Response of CG 2
f p 2  f p1
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High Frequency Response of CG 3
ro
included
using OC time
Constant
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CB Amplifier
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Rin of CB Amplifier
io  ii 
vi
r
ii  iro 
vi
re
iro 
vi  vo
v i R
, vo  io RL  iro  i o L
ro
ro

v
vi   ii  i
r
vi

ii  
re
ro

 RL

vi
re r
ro  RL , r  1   re
Rin  
ii re r  ro r  re RL
Rin 
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ro  RL 
1
ro
RL

re 1   re
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Rin of CB Amplifier cont.
r
 RL 
Rin 
r
RL
1 o 
re 1   re
o
1
ro  RL
  , re 
 Rin 
gm
1  g m ro
RL    Rin  re   1  r
r
 RL 
RL
RL
Rin  re
, if
 ro , thenRin  re 
RL
1   
Ao
ro 
1   
o
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Avo of CB Amplifier
Avo  1  gm r0  1  A0
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Rout of CB Amplifier
ix  g m v 
v v v v
    g mv
Re re Re r
 1 1   Re  r
ix  v    v
 Re r   Re r




 Re r
Re r 
ro  
vx  ix  g m v ro  v   ix  g m
Re  r 

 Re  r
vx
Rr
 Rout  ro  e  1  g m ro   ro  1  g m ro Re'
ix
Re  r



Rout  ro  Avo Re'
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Source Follower (SF)
g m RL'
Av 
1
1  g m RL'
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Frequency Response of SF
I x Rsig  Vgs  g mVgs  I x RL'
sC gsVgs  g mVgs  0  sZ  
I x Rsig  RL'   Vgs 1  g m RL' 
gm
Cgs
Vgs Rsig  RL' 
Rgs 

, C  Cgs Rgs
I x 1  g m RL' 
gs
 C  Cgd Rsig , C  CL RL // Ro ,
gd
L
 H C C C
gd
gs
L
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Emitter Follower EF
1
1 1 1
g m   
   
V
 r   s   re r  r    1
sZ CV  g mV    0  sZ  
Z
r
C
C
reC
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Frequency Response of EF
OC Method
For C
'
R  Rin // Rsig
Vo
Vx  V

g
V

I

 g mV  I x
m 
x
'
'
RL
RL
For Rin

Vx  I x r
Vx
r 



g
I
r

I


I
1

g
r

m x 
x
x
m 
'
'
' 
RL
RL
RL 

V

Vx  I x RL'  g m r RL'  r   Rin  x  RL'  rRL'   r  r  RL' 1   
Ix
r
'
 C  C R  C Rsig
// r  RL' 1   

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Frequency Response of EF
V V  V
Ix    o
(1)
r
Rsig
g mV 
V
At B’
V
V
 I x  o' (2)
r
RL
A
OC Method
For C
'
At A’
'
'
I x Rsig
r  V Rsig
 V r
(1)  Vo 
 ( 2)
r
 H C C
'
'
I x Rsig
r  V Rsig
 V r
V
g mV   I x 
r
RL' r


'
'
'
V V Rsig V r I x RL r  I x Rsig r
g mV   '  ' 
r
RL r
RL r
RL' r
'
'
'
'

 Rsig
  1 Rsig
 Rsig

1 Rsig
1 
1 
 g m   '  ' V  I x 1  '     '  ' V  I x 1  ' 
r RL r RL 
RL   re RL r RL 
RL 



'

   C R
RL'  Rsig
V
 R 
C
 
'
Ix
 Rsig
RL' 
1 
 
r
re 



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Exercise for EF
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End of Topic 3
Lectures
HW:6.38, 6.39, 6.80, 6.86, 6.93, 6.116, 6.118
Materials can be found on the Y:\EE303-001
Please check this folder on a daily/weekly basis
Also at //faculty.uoh.edu.sa/m.rahal2
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