Lecture 23
Frequency Response of Amplifiers (III)
OTHER AMPLIFIER STAGES
Outline
1.
2.
6.012 Spring 2009
Frequency Response of the
Common­Drain Amplifier
Frequency Response of the
Common­Gate Amplifier
Lecture 23
1
1. Frequency Response of the
Common­Drain Amplifier
VDD
signal source
RS
+
vs
iSUP
vOUT
signal
load
RL
VBIAS
VSS
Characteristics of CD Amplifier:
•
•
•
•
Voltage gain ≈ 1
High input resistance
Low output resistance
⇒ Good voltage buffer
6.012 Spring 2009
Lecture 23
2
High­frequency small­signal model
G
S­B
D
Could use OTC to solve for bandwidth.
To estimate bandwidth it is easier to use the
2­port models.
6.012 Spring 2009
Lecture 23
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Low Frequency Analysis Using
2­Port Model
Capacitors ­open circuit
 R
 

R
in
L
 (1)

Avo = 
 RS + Rin   R L + Rout 
g m RL
≈
≤1
1 + g m RL
In the calculation of the intrinsic
voltage gain we assume that ro||roc
was large. That is why we do not
have RL|| ro||roc
6.012 Spring 2009
Lecture 23
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High Frequency Analysis Using
2­Port Model ­ Add capacitors
Use Miller Approximation
RL
gm RL
AvC gs =
=
Rout + RL 1+ gm RL
(
CM = Cgs 1 − AvCgs

Cgs
gm RL 
 =
= Cgs 1−
 1+ gm RL  1 + gm RL
)
Total capacitance at input

gm RL 
 + Cgd
CT = Cgs 1 −
 1 + gm RL 
RT = RS || Rin = RS
Add time constant due to Cdb capacitance at output
RC db = Rout
6.012 Spring 2009
Rout RL
RL
RL =
=
Rout + RL 1+ gm RL
Lecture 23
5
Frequency Response of Common­
Drain Amplifier
ω 3dB ≈
1
 Cgs

RL
RS 
+ Cgd  + Cdb
1+ gm RL
1+ gm RL

If RS is not too high, bandwidth can be rather high
and approach ωT.
6.012 Spring 2009
Lecture 23
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2. Frequency Response of the
Common­Gate Amplifier
VDD
iSUP
iOUT
VSS
signal
load
RL
signal source
is
RS
IBIAS
VSS
Characteristics of CG Amplifier:
•
•
•
•
Current gain ≈ 1
Low input resistance
High output resistance
⇒ Good current buffer
6.012 Spring 2009
Lecture 23
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High Frequency Small Signal Model
Could use OTC to solve for bandwidth.
To estimate bandwidth it is easier to use the
2­port models.
6.012 Spring 2009
Lecture 23
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High­frequency small­signal 2­port model
Assume backgate is shorted to source
Low frequency transfer function:
iout  RS   Rout   (1)

Aio =
= 
is
 Rin + RS   R L + Rout 
Use OTC to find ω
ω3dB:
Thevenin resistance across Cgs +
Csb
RTCgs = RS || Rin = RS || (1 / (gm + gmb ))
Thevenin resistance across Cgd +
Cdb
RTCgd = Rout || RL = ((ro + g m ro RS ) || roc ) || RL
6.012 Spring 2009
Lecture 23
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High­frequency small­signal 2­port model con’t
Open circuit time constants:
τC
+Csb
= (RS || (1 / gm + gmb ))(Cgs + Csb )
τC
+Cdb
= (((ro + gm ro RS ) || roc )) || RL ) Cgd + Cdb
gs
gd
(
)
Summing the open circuit time constants:
ω 3dB = 1 (RS || (1 / gm + gmb ))(Cgs + Csb )
(
)
+ (((ro + gm ro RS ) || roc )) || RL ) Cgd + Cdb 
If RL is not too high, bandwidth can be rather high
and approach ωT.
6.012 Spring 2009
Lecture 23
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What did we learn today?
Summary of Key Concepts
•
Common­drain amplifier:
– Voltage gain ≈ 1, Miller Effect nearly completely
eliminates the effect of Cgs
– If RS is not too high, CD amplifier has high bandwidth
•
Common­gate amplifier
– No Miller Effect because there is no feedback capacitor
– If RL is not too high, CG amplifier has high bandwidth
•
RS, RL can affect bandwidth of amplifiers.
6.012 Spring 2009
Lecture 23
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6.012 Microelectronic Devices and Circuits
Spring 2009
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