Download ECE 342 – Jose Schutt-Aine

ECE 342
Solid-State Devices & Circuits
10. MOS Amplifiers
Jose E. Schutt-Aine
Electrical & Computer Engineering
University of Illinois
[email protected]
ECE 342 – Jose Schutt-Aine
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Biasing of MOS Transistors
• Bias Characteristics
– Operation in saturation region
– Stable and predictable drain current
1
W
2
I D  nCox VGS  VT 
2
L
ECE 342 – Jose Schutt-Aine
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Two-Supply MOS Bias
1
W
2
I D  nCox VGS  VT 
2
L
RG provides DC ground at gate and high input
resistance to signal source.
ECE 342 – Jose Schutt-Aine
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Single-Supply MOS Bias
–
–
–
–
Choose R1 and R2 to fix VG
Choose RS and R2 to fix VS
VGS determines ID
Choose RD to fix VD
ECE 342 – Jose Schutt-Aine
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Bias with Feedback Resistor
VGS  VDS  VDD  RD I D
VDD  VGS  RD I D
Negative feedback (degeneration) provided by RG
ECE 342 – Jose Schutt-Aine
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Common Source MOSFET Amplifier
Bias is to keep MOS in saturation region
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Common Source MOSFET Amplifier
Small-Signal Equivalent Circuit for MOS (device only)
1 'W
2
I D  kn VGS  VT 
2 L
I D
VGS
Which leads to
2I D
Veff
g m  2kn' W / L
where VGS  VT  Veff
gm is proportional to 
gm 

VGS VGSQ
ECE 342 – Jose Schutt-Aine
ID
W /L
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MOSFET Output Impedance
To calculate rds, account for l
VDS
rds 
I D

VGS VGSQ
I DP
1
2
W
l Cox VGS  VT 
2L
1

l I DP
1 'W
2
 kn VGS  VT 
2 L
rds, accounts for channel width modulation resistance.
ECE 342 – Jose Schutt-Aine
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Midband Frequency Gain
Incremental model for complete amplifier
AMB
vout
rds RD
RB


gm
vin
RB  Rg rds  RD
ECE 342 – Jose Schutt-Aine
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Example
In the circuit shown, VT=1 V, l=0, CoxW/2L=0.1
mA/V2. Select RD and R1 to result in midband
voltage gain of –4 and VDSQ=7 V.
RD 
VDD  VDSQ
I DQ

AMB   g m RD   g m
AMB  4  0.1 I DQ 
ECE 342 – Jose Schutt-Aine
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I DQ
5
I DQ
5
I DQ
3.162

 4
I DQ
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Example (Cont’)
2
I DQ
5
 3.162 

 8 k
  0.625 mA  RD 
0.625
 4 
0.625  0.1VGS  1 leads to 6.25  1  VGS  3.5 V
2
VDD R2
80
960

 12  3.5 
 80  R1  194 k 
R1  R2 80  R1
3.5
RD  8 k
R1  194 k
ECE 342 – Jose Schutt-Aine
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Example
For the circuit shown, k=75 mA/V2, VT=1 V, l=0
(a) Find VDQ, VSQ
(b) Find the midband gain
VGQ  VDD
R2
20  5

 4V
R1  R2
25
VGSQ  VGQ  VSQ  4  2 I DQ
2
I DQ  K VGSQ  VT   0.075  4  2 I DQ  1
2
2
I DQ  0.075(9  12 I DQ  4 I DQ
)
2
2
4 I DQ
 12 I DQ  9  13.3I DQ  I DQ
 6.33I DQ  2.25  0
ECE 342 – Jose Schutt-Aine
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Example (Cont’)
6.33  9
 3.167 
 0.378 mA or 5.953 mA
2
reject since voltage
2
I DQ
I DQ  0.378 mA
drop across RD will
be too large
VDQ  VDD  RD I DQ  20  10  0.378  16.22 V
VSQ  RS I DQ  2  0.378  0.756 V
VDQ  16.22 V
VSQ  0.756 V
ECE 342 – Jose Schutt-Aine
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Example (Cont’)
W
g m  2k
I DQ  4  0.075  0.378  0.337
L
'
n
AMB   gm RD  0.337 10  3.37
AMB  3.37
ECE 342 – Jose Schutt-Aine
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MOS Body Effect
• The threshold voltage VT
– Depends on equilibrium potential
– Controlled by inversion in channel
• The body effect
– VT varies with bias between source and body
– Leads to modulation of VT
ECE 342 – Jose Schutt-Aine
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Body Effect
Potential on substrate affects threshold voltage
1/ 2

VT (VSB )  VTo    2 F  VSB    2 F

 kT
F  
 q
  Na 
 ln  n 
  i 
2qN a s 



1/ 2


Fermi potential of material
1/ 2
Cox
Body bias coefficient
ECE 342 – Jose Schutt-Aine
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Body Effect – (Con’t)
Define gmb as the body transconductance
g mb
Can show that
I D

VBS
VGS  constant
VDS  constant
gmb   gm
VT

where  

VSB 2 F  VSB
ECE 342 – Jose Schutt-Aine
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Source Follower Configuration
Since source is not tied to the substrate,
we need to model the body effect. Note:
substrate is always tied to ground.
1
GL 
RL
1
Define g ds 
and G  g ds  g mb  GL
rds
ECE 342 – Jose Schutt-Aine
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Source Follower
vout 
g mvgs
G
g m  vin  vout 

G
vout g ds  vout GL  g mbvout  g mvgs
vout G  g mvgs  vout 
g mvgs
G
g m  vin  vout 

G
vout G  gmvin  gmvout
ECE 342 – Jose Schutt-Aine
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Source Follower
vout G  g mvgs  vout  G  g m   g mvin
gm
gm
AGS 

g m  G g m  g mb  g ds  GL
gm
gm
AGS 

g m  G g m  g mb  g ds  GL
ECE 342 – Jose Schutt-Aine
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Source Follower
Neglecting GL and gds (since they are small)
gm
AGS 
1
g m  g mb
This value is close to 1
Output impedance of source follower
Rout
1

gm
1
rds RL
g mb
Internal output impedance
1
rout 
gm
1
rds  This value is low
g mb
ECE 342 – Jose Schutt-Aine
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Common Gate Amplifier
Circuit
Small-Signal
Model
ECE 342 – Jose Schutt-Aine
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Common Gate Amplifier
AMB
g m  g mb  g ds

GL  g ds   g m  g mb  g ds  GL / Gg
g ds
 gm  gmb  to get
g m  g mb  RL

AMB 
1   g m  g mb  Rg
•
Common Gate (CG)
– CG amplifier is non-inverting
– CG amplifier has low input impedance
– CG is unity current-gain amplifier
ECE 342 – Jose Schutt-Aine
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MOS Topologies - Ideal
CS
Avo  gm RD
Rin
Rout

RD
CG
SF
gm RD
1
1
gm

RD
1
gm
ECE 342 – Jose Schutt-Aine
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