A09 sedra ch 9 frequency response

1. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 19/21/2020
Frequency Response

2. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 29/21/2020
The Three Frequency Bands

3. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 39/21/2020
STC RC Circuits
3
1
dB
RC
 
1
1
o
i
V SC
V R
SC


LP:
RC 
1
1SCR



4. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 49/21/2020
STC RC Circuits

5. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 59/21/2020
STC RC Circuits
3
1
dB
RC
 
HP: 1
o
i
V R
V R
SC


RC 
1
SCR
SCR


1
2 1
SCR
SCR


2
1
o
i
RV
V R
SC





6. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 69/21/2020
STC RC Circuits

7. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 79/21/2020
LOW FREQUENCY RESPONSE
OF THE CS & CE AMPLIFIERS

8. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 89/21/2020
Capacitively Coupled Common-Emitter Amplifier
CB
CC
CE

9. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 109/21/2020
The Low-Frequency Response of The CE Amplifier
CB
CC
CE

10. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 119/21/2020
The Low-Frequency Response of The CE Amplifier
CB CC
CE
The Mid-Frequency equivalent Circuit
Consider the effect of each C separately.

11. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 129/21/2020
The Low-Frequency Response of The CE Amplifier
CB CC
CE
Consider the effect CB only.
3
1
dB
RC
 
 
1
||
B
B Sig BR r R C
 

 ||B SigR R r R 

12. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 139/21/2020
The Low-Frequency Response of The CE Amplifier
CB CC
CE
Consider the effect CE only.
3
1
dB
RC
 
 ||B SigR R R r 
 
1
||
E
B Sig ER R r C





Neglecting the effect of rO.
1
||
1
E
B Sig
e E
R R
r C



 
  

13. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 149/21/2020
The Low-Frequency Response of The CE Amplifier
CB CC
CE
Consider the effect CC only.
3
1
dB
RC
 
2
||
1
||
C O
o C L
C O L
R r
V i R
R r R
SC

 
 
1
||
C
C O L CR r R C
 


14. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 159/21/2020
The Low-Frequency Response of The CE Amplifier
The Overall Frequency Response
  _
  
   
    
     
V V MB
B E C
s s s
A A
s s s

15. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 169/21/2020
The Low-Frequency Response of The CE Amplifier
1
||
1
E
B Sig
e E
R R
r C



 
  
The Overall Frequency Response
 
1
||
B
B Sig BR r R C
 
  
1
||
C
C O L CR r R C
 

𝑓𝐶 𝑓𝐵 𝑓𝐸
fL = fE
, 5:10
 
 
 
 
 
E E
B C

16. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 179/21/2020
The Low-Frequency Response of CS Amplifier

17. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 189/21/2020
In the mid-band, the Cs are SC. Moving towards DC, the impedance of
each C increase. We will study the effect of each capacitor separately.
The Low-Frequency Response of CS Amplifier

18. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 209/21/2020
 || ||G
M m O
O
Sig
D L
G Sig
R
A g r R R
R R
V
V



The Low-Frequency Response of CS Amplifier

19. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 239/21/2020
 || ||O D
G
G
L
Sig
M mg RA
R
r R
R
R 

  1
1
PG
G Sig CR R C
 

1
1
m
PS
CS
CS
m
g
CC
g
     2
1
||
PD
O D L Cr R R C
 

The Low-Frequency Response of CS Amplifier

20. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 249/21/2020
The Low-Frequency Response of CS Amplifier
𝑓𝐺 𝑓𝐷 𝑓𝑆

21. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 259/21/2020
 1
Sig G
m
R R
g
Q =
 
1
D L
m
R R
g
Q =
S G  
S D  
L S  ;
Selecting Values for the Capacitors
SC
1 2
& &
10
; L
PG PS C C
C C

    
   
   


22. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 279/21/2020
INTERNAL CAPACITIVE
EFFECTS AND THE HIGH
FREQUENCY MODEL OF THE
MOSFET AND BJT

23. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 289/21/2020
The High-Frequency Hybrid- Model

24. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 299/21/2020
The Base-Charging or Diffusion Capacitance Cde
in the active or saturation modes, minority-carrier charge is
stored in the base region.
The Base-Emitter Junction Capacitance Cje
depletion-layer capacitance
The Collector-Base Junction Capacitance Cµ
In active-mode operation, the CBJ is reverse biased, and
its junction or depletion capacitance
n
de
BE
dQ
C
dv

DBE
je
BE
dQ
C
dv

DBC
BC
dQ
C
dv
 
The High-Frequency Hybrid- Model

25. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 309/21/2020
Minority-Carrier Concentrations of an Active npn
Transistor
 DBE
je
BE
dQ
C
dv
DBC
BC
dQ
C
dv
  n
de
BE
dQ
C
dv

26. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 319/21/2020
The Resistance of The Silicon
Material of The Base Region
The High-Frequency Hybrid- Model
Cπ = Cde + Cje

27. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 329/21/2020
The Cutoff Frequency
 C mI g sC V  
V 
c
fe
b
I
h
I
 
    ?fes h s  
mg V
 1
mg
s C C
r
 


   1
mg r
s C C r

   
 || ||bI r C C   
1
bI
sC sC
r
 

 

28. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 339/21/2020
The Cutoff Frequency
 
0
1
feh
s C C r  


   
1
C C r

  
 


29. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 349/21/2020
0
m
T
g
C C

 
   

The Cutoff Frequency
fairly accurately up to a frequency of about O.2fT
𝑎𝑡 𝜔>≈ 5~10 𝜔 𝛽
Rπ is short Circuited, Rx
becomes dominant.
𝜔 𝑇 ≈ 100𝑠 𝐺𝐻𝑧

30. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 359/21/2020

31. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 369/21/2020
The MOSFET Internal Capacitance
and High-Frequency Model

32. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 379/21/2020
The High Frequency MOSFET Model
The MOSFET Internal Capacitance and High-Frequency
Model

33. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 389/21/2020
High-Frequency Equivalent Circuit
Model for the MOSFET
Source connected to the substrate (body).

34. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 399/21/2020
High-Frequency Equivalent Circuit
Model for the MOSFET
Neglecting Cdb

35. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 409/21/2020
High-Frequency Equivalent Circuit
Model for the MOSFET

36. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 419/21/2020
Determining the Short-circuit Current Gain Io /Ii.
O m gs gd gsI g V sC V 
gd gs m gssC V g V=
O m gsI g V
 
o m
i gs gd
I g
I s C C


 
m
T
gs gd
g
C C
 

 i gs gd gsI s C C V 
≈ 𝑚𝑎𝑛𝑦 𝐺𝐻𝑧

37. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 429/21/2020
HIGH FREQUENCY RESPONSE
OF THE CS & CE AMPLIFIERS

38. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 439/21/2020
The High-Frequency Response of The CE Amplifier

39. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 449/21/2020
CB
CC
CE
The High-Frequency Response of The CE Amplifier
SC

40. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 459/21/2020
The High-Frequency Response of The CE Amplifier

41. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 469/21/2020
The High-Frequency Response of The CE Amplifier

42. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 479/21/2020
The High-Frequency Response of The CE Amplifier

43. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 489/21/2020
The High-Frequency Response of The CE Amplifier
?

44. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 499/21/2020
The High-Frequency Response of The CE Amplifier
 
1
o
C
I V V
z 
  
 1 m LRI V S C g    
 1 m LI V SC g R   
 m LI SC V g V R    
eqCI V S 
= mI g V 
Miller Effect
  '
O m LV g V R 

45. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 509/21/2020
The High-Frequency Response of The CE Amplifier
in eqC C C 
 1in m LC C C g R   
STC LPF
3dB 
1
RC '
1
Sig inR C


46. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 519/21/2020
FREQUENCY RESPONSE OF
THE CS AMPLIFIER

47. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 529/21/2020
O
M
Sig
V
A
V
 
The Mid-Frequency Bands
 || ||G
m O D L
G Sig
R
g r R R
R R


H LBW f f 
T Mf GB A BW 
H Lf fQ ?
HBW f 

48. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 539/21/2020
The High-Frequency Response

49. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 549/21/2020
The High-Frequency Response

50. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 559/21/2020
The High-Frequency Response
?
gd m gsI g V=
  '
O m gs LV g V R 
 gdC gd gs OI sC V V 
 '
1gdC gd m L gsI sC g R V 
 '
1eq gd m LC C g R 
 '
1in gs eq gs gd m LC C C C C g R    
  '
gdC gd gs m gs LI sC V g V R  
Miller Effect

51. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 569/21/2020
'
1
H
in SigC R
 
'
1
1
G
Sig
G Sig in Sig
R
V
R R sC R
 
    
gsV 
The High-Frequency Response
'
1
1
G in
Sig
G Sig
Sig
in
R sC
V
R R R
sC
 
    
1
1
G
gs Sig
G Sig
H
R
V V
sR R

 
     

52. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 579/21/2020
  '
O m gs LV g V R 
The High-Frequency Response
1
1
G
gs Sig
G Sig
H
R
V V
sR R

 
     
 '
1 1
G
m L
G SigO M
Sig
H H
R
g R
R RV A
s sV
 
 
     
 
'
1
m L
M
Sig
G
g R
A
R
R
 


53. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 589/21/2020
The High-Frequency Response

54. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 599/21/2020
'
1
H
in SigC R
 
G SigR R?
'
Sig SigR R;
1
H
in SigC R
 
Sig HR  
The High-Frequency Response

55. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 609/21/2020
 '
1in gs gd m LC C C g R  
 '
1gd m L gsC g R C 
gd gsC C=
The High-Frequency Response

56. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 619/21/2020
HIGH FREQUENCY RESPONSE
OF THE COMMON GATE

57. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 629/21/2020
High Frequency Response of the CG Amplifier
All Capacitors are grounded → No Miller
Effect → Wider Bandwidth
Neglecting r0
𝑓𝑝1 =
1
2𝜋𝐶𝑔𝑠 𝑅 𝑠𝑖𝑔||
1
𝑔 𝑚
𝑓𝑝2 =
1
2𝜋 𝐶𝑔𝐿 + 𝐶𝐿 𝑅 𝐿

58. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 639/21/2020
USEFUL TOOLS FOR THE ANALYSIS OF THE
HIGH-FREQUENCY RESPONSE OF AMPLIFIERS

59. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 649/21/2020
Using Open-Circuit Time Constants for the
Approximate Determination of fH
1. Consider one capacitor at a time, O. C. the others.
2. Reduce the input signal source to zero.
3. Determine the resistance Ri seen by Ci.
Open Circuit Time Constant = 𝜏 𝐻 =
𝑖=1
𝑛
𝑅𝑖 𝐶𝑖
𝜔 𝐻 =
1
𝜏 𝐻

60. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 659/21/2020
Example 9.6 Rsig = 100 kΩ, RG = 420 kΩ, Cgs, = Cgd = 1 pF,
gm = 4 mA/V, and RL = 3.33 kΩ.
Find the midband voltage gain, 𝐴 𝑀 =
𝑉𝑜
𝑉 𝑠𝑖𝑔
, and fH.

61. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 669/21/2020
Example 9.6
𝐴 𝑀 =−
𝑅 𝐺
𝑅 𝐺 + 𝑅 𝑠𝑖𝑔
𝑔 𝑚 𝑅 𝐿
′
= −
420
420 + 100
4 × 3.33
= −10.8

62. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 679/21/2020
Example 9.6
𝑅 𝑔𝑠 = 𝑅 𝐺||𝑅 𝑠𝑖𝑔 = 420||100
= 80.8 kΩ
𝜏 𝑔𝑠 = 𝐶𝑔𝑠 𝑅 𝑔𝑠 = 80.8 ns
Find fH

63. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 689/21/2020
Example 9.6
𝐼 𝑋 =
𝑉𝑔𝑠 =𝑅 𝑠𝑖𝑔
′
= 𝑅 𝐺||𝑅 𝑠𝑖𝑔
𝑔 𝑚 𝑉𝑔𝑠 +
𝑉𝑔𝑠 + 𝑉𝑥
𝑅 𝐿
′ = 𝑉𝑔𝑠 𝑔 𝑚 +
1
𝑅 𝐿
′ +
𝑉𝑥
𝑅 𝐿
′𝐼 𝑥 1 + 𝑅 𝑠𝑖𝑔
′
𝑔 𝑚 +
1
𝑅 𝐿
′ =
𝑉𝑥
𝑅 𝐿
′
= −𝐼 𝑥 𝑅 𝑠𝑖𝑔
′
𝑔 𝑚 +
1
𝑅 𝐿
′ +
𝑉𝑥
𝑅 𝐿
′
𝑅 𝑔𝑑 =
𝑉𝑥
𝐼 𝑥
= 𝑅 𝐿
′
+ 𝑅 𝑠𝑖𝑔
′
𝑅 𝐿
′
𝑔 𝑚 + 1
−𝐼 𝑥 𝑅 𝑠𝑖𝑔
′
= 1.16 MΩ

64. Copyright  Muhammad A M Islam.SBE202A Device Structure and Physical Operation 699/21/2020
Example 9.6
𝜏 𝑔𝑑 = 𝐶𝑔𝑑 𝑅 𝑔𝑑
= 1 × 10−12 × 1.16 × 106
= 1160 ns
𝜏 𝐻 = 𝜏 𝑔𝑠 + 𝜏 𝑔𝑑 = 1240.8 ns
𝜔 𝐻 =
1
𝜏 𝐻
=806 krad/s 𝑓𝐻 =
𝜔 𝐻
2𝜋
= 128.3 kHz