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Analysis of Analog IC MOS amplifiers
Dr. D. Meganathan Department of Electronics Engineering, Madras Institute of Technology
Name the amplifier Mid Band Gain= ?
Positive Power Supply Rejection
Ratio ?
Negative Power Supply Rejection
Ratio?
Common-Mode Rejection Ratio?
Input Common Mode Voltage
Range ?
Output Common Mode Voltage
Range?
Output Voltage Swing?
M1
M3
M5
M7
M2
M4
M6
M8
VDD
M9
Vb1
Vb2
Vb1
Vb4
Vb3
Vin- Vin
+
Vb2
Vb3
VO+ VO
-
Feedback Concepts
Feedback concepts new
to us? 6/19/2014 3 D.Meganathan, Anna University
Harold S. Black, 1927
6/19/2014 4 D.Meganathan, Anna University
Feedback Amplifier by D.Meganathan 5
General feedback structure
A
A
x
xA
xxx
xx
Axx
s
of
fsi
of
io
1
Open loop gain
ALoop gain
Closed-loop gain
Mixer network
Voltage series Current shunt
Sampling network
Voltage shunt Current Series
FEEDBACK CONCEPTS in biasing circuit
ID = n/2 (VGS Vt)2
ID D
G
S
IREF
VDD
SIMPLE FEEDBACK
NO EXTRA CIRCUIT IS INVOLVED 6/19/2014 6 D.Meganathan, Anna University
Integrated Circuit Biasing Circuit
ID D
G
S
IREF
VDD CURRENT Source TO BIAS INTEGREATED CIRCUIT
6/19/2014 7 D.Meganathan, Anna University
Analysis of Analog IC MOS amplifiers
Small signal Analysis of Common Source Amplifier
Input and Output Impedance measurement for Common source amplifier
Small signal Analysis of Common Source degenerator Amplifier
Input and Output Impedance measurement for Common source degenerator amplifier
Analysis of Analog IC MOS amplifiers
Small signal Analysis of Common Drain Amplifier
Input and Output Impedance measurement for Common Drain amplifier
Small signal Analysis of Common Gate Amplifier
Input and Output Impedance measurement for Common Gate amplifier
Analysis of MOS amplifiers MID BAND GAIN ANALYSIS
Output Voltage swing
Input common-mode voltage range
Output common-mode voltage range
Power supply rejection ratio
Common mode rejection ratio
Small signal analysis
TO DETERMINE MIDBAND GAIN OF THE CIRCUIT
STEP 1 EVALUATE THE SMALL SIGNAL CIRCUIT CONSTANTS using DC Q-Point voltage and currents (gm, r0) gm = n(VGSQ-Vt) and r0 = VA/IDQ
STEP2 DRAW THE SMALL SIGNAL EQUIVALENT DIAGRAM
STEP 3
DETERMINE THE MID BAND VOLTAGE GAIN AV=VO/VS
+
-
vgs gm
vgs
r0 Vo
+
-
Determining Input impedance Step 1 Draw the small signal equivalent circuit diagram
Step 2 Null the output to the circuit
If it is a voltage source then short it
If it is a current source then open it
Step 3 Remove input voltage source from the circuit
Step 4 Connect known voltage or current source at the input terminal
Step 5 Measure the current supplied or voltage across the input source
Step 6 Determine the ratio of Voltage/ current
Determining Output impedance Step 1 Draw the small signal equivalent circuit diagram
Step 2 Null the input to the circuit
If it is a voltage source short circuit it
If it is a current source open circuit it
Step 3 Remove output voltage source From the circuit
Step 4 Connect known voltage or current source at the output terminal
Step 5 Measure the current supplied or voltage across the output source
Step 6 Determine the ratio of Voltage/ current
Common Source Amplifier
gm
vgs
r0
RD
+
-
Vin Vgs
+
-
+
-
Vo
Av= -gm (r0 // RD)
VDD
RD
Vin
Vo
Input impedance It
r0 Vt gm
vgs
Rin =
RD
Output Impedance
Rout = r0 // RD
It
r0 gm vgs Vt
RD
Common Source with Source Degenerator Circuit
+
-
Vo
+ +
gm
Vgs
r0 Vgs
-
Rs
RD
-
Vr0
+
-
VRs
I1
ID
;
;
;
;
;
1 D
D 1
D
D
S
S
S D
D
Vo = I R
I = -I
-VoI =
R
Vin = Vgs + VR
Vgs =Vin VR
-VoVR I Rs = Rs;
R
(1 )
o
D o D
D o D
D
o
D D D
o o
D D D
o D DV
D o o
Vo=Vr + VRs;
Vo = (I -gmVgs) r +I Rs;
-VoVo -gm(Vin I Rs) r I Rs;
R
-Vo -Vo -VoVo -gm(Vin Rs) r Rs;
R R R
-Vo Vo VoVo+ r gm Rsr Rs=-gmVin
R R R
-gmr R -gmRA
R r gmRsr Rs gmRs
VDD
RD
Rs
Vo
+
-
Vin
Input Impedance
Rin = gm Vgs
r0 Vgs
+
-
Rs
Vt RD
Output Impedance
Vt = Vr0 + VRs;
Vt= (ID-gmVgs)r0 +VRs
Vt= (ID + gmVRs) r0 + VRs;
Vt= (ID+ gm IDRs) r0+ IDRs;
VRs= -Vgs;
VRs= IDRs
gm
Vgs
r0 Vgs
+
-
Rs
+
+
-
VRs
Vt
It
ID
I1
RD -
Vr0
Rout Rout
Rout= r0(1+ gm Rs) + Rs r0(1+ gm Rs); Rout = (r0(1+ gm Rs) + Rs) // RD
Common Drain Amplifier
VDD
Rs
Vo
ID
gm
Vgs
r0 Vgs
-
Rs
-
Vr0
+
-
Vo
+
-
Vin
+
Vo= gm Vgs (Rs // r0);
Vin = Vgs + Vo;
Vin = Vgs (1+gm Vgs (Rs // r0));
+
V
gm (ro//Rs)A =
(1+gm(ro//Rs))
Input Impedance
gm
Vgs
r0 Vgs
+
-
Rs
Vt Rin =
Output Impedance
Vt
gm Vgs
r0
Vgs
+
-
Rs
Vgs=-Vt
A
Apply KCL at junction A
gmVgs + It = Vt/Rs + Vt/r0;
It= Vt/Rs + Vt/r0+ gmVt;
It
OUT o
1R = //r // Rs
gm
Common Gate Amplifier
VDD
RD
Rsi
Vo
Vin
I2= (Vo-(Vgs)/r0;
Vgs= Vo/-Av1; (Av1 is the gain of the circuit);
I2= (Vo+ Vo/Av1 )/r0
I2 Vo/r0
ro
Vin
gm Vgs
Vo
+
-
Rsi
Vgs RD
G
D S
I2
Vo = -Av1 Vgs;
I1=(Vgs-Vo)/r0 Vo= -Av1Vgs; (Av1 is the gain of the circuit);
I1=(Vgs-(- Av1Vgs)/r0 I1=Vgs(1+ Av1)/r0 RM = r0 /(1+ Av1)
I1
Common Gate Amplifier
Vo = -gm Vgs (ro // RD)
Vo/Vin = Av=
Apply KCL at node S
Ii +gm Vgs+ I1=0
Ii = -gmVgs-Vgs/RM Vin = Ii Rsi Vgs Vin = (-gmVgs-Vgs/RM)Rsi-Vgs
( / / )
( )
o Dgm r R
1 gm Rsi
Vo Vin
gm Vgs
+
-
Rsi
Vgs RD
G
D S
ro
Ii
I2
RM
I1
;
M M
M
M
M M
M
M
-(gmR Rsi+Rsi+R )Vin Vgs;
R
-RVgs
Vin (gmR Rsi+Rsi+R )
-RVgs -1
Vin (gmRsi+1)R (gmRsi+1)
Input Impedance
It=-gmVgs+I1;
Vt=-Vgs;
Rin = r0 // 1/gm;
Rin 1/gm;
gm Vgs
+
-
Vgs RD
G
S
Vt
It
ro
D
I1
Output Impedance
Rout =ro // RD
gm Vgs
+
-
Vgs RD
G
D S
ro
Vt
It 0
Output impedance and Small Signal gain of MOS IC amplifier
Vo
VDD
Vbias
Vin
gm1
vgs
r01
+
-
Vin Vgs
+
-
M1
M2
r02
Output Impedance of a IC MOS resistor
r02 gm vgs Vt 0
It
Small signal gain of MOS IC amplifier
+
-
Vo
Rout = r02
Small Signal Gain = -gm1(r01//r02)
Differential Amplifier
VDD
RD
VDD
RD
-Vin/2 +Vin/2
-Vo/2 +Vo/2
ID Rs
ID/2 ID/2
Virtual
ground
Differential Amplifier
ADM = -gm (r0 // RD)
VDD
RD
VDD
RD
-Vin/2 +Vin/2
-Vo/2 +Vo/2
ID
Rs
ID/2+ ID ID/2+ID
Vin Vin
0
Virtual
ground
Differential Mode gain
VDD
RD
+Vin
Vo
Rout = r0
Differential Amplifier
VDD
RD
VDD
RD
-Vo -Vo
ID Rss
ID/2+ ID ID/2+ID
Vin Vin
2ID Vin
VDD
RD
Rss
Vo
(1 2 )
DCM
-gmRA =
gmRss
Vin
Rout = (r0(1+ 2gm Rss) + 2Rss) // RD
COMMON MODE GAIN
Power Supply Rejection Ratio
VDD
-Vin/2 +Vin/2
-Vo/2 +Vo/2
Vb1 Vb1
Vb2
M1 M2
M3 M4
Power Supply Rejection Ratio+ Power supply rejection ratio+ = Adm/A+
Adm = -gm (ro1 // ro3)
A+= Vo/Vdd
Vdd
-Vo/2 +Vo/2
Vb1 Vb1
Vb2
M1 M2
M3 M4
M5
Power Supply Rejection Ratio+
M3 device act as common-gate amplifier
Small Signal gain of the M3 is gm3 (r03 // Rdown)
Vdd
Vo
M1
M3
M5
Rdown
M5
M1
Rdown
Rdown gm1ro1ro5
M1
Rdown
r05
r01
A+ =gm3 (r03 // gm1ro1ro5)
PSRR+ = -gm1 (ro1 // ro3)
gm3 (r03 // gm1ro1ro5)
Power Supply Rejection Ratio- Power supply rejection ratio- = Adm/A-
Adm = -gm1 (ro1 // ro3)
A-= Vo/Vss
Vss
-Vo/2 +Vo/2
Vb1 Vb1
Vb2
M1 M2
M3 M4
M5 M5
Power Supply Rejection Ratio-
Vss
Vo
Vb1
M1
M3
M5
A- = Vo/Vss
M5 transistor act as common-gate
amplifier.
The gain of M5 transistor is gm5 RD
RD= Rup // Rdown
Rup
Rdown
Rup = r03
Rdown = gm1r01r05
A- = gm5 (gm1r01r05 // r03)
PSRR- = -gm1 (ro1 // ro3)
gm5 (gm1r01r05 // r03)
Common Mode Rejection Ratio
VDD
-Vin/2 +Vin/2
-Vo/2 +Vo/2
Vb1 Vb1
Vb2
M1 M2
M3 M4
CMRR = Adm/Acm
CMRR= gm (ro1 // ro3) (1+2gm1ro5)
gm1 ro3
Adm = -gm1 (ro1// ro3);
Acm= -gm1 ro3/ (1+2gm1ro5);
M5
Input Common Mode Range
VDD
RD
Vin
Vout
VCMI
Vin
Vt
time
Voltage
VCMI
Vin
Vt
time
Voltage
VCMI
Input Common Mode Range
Input common-mode range
(VoV5 + Vgs1 )< VCMI
Input Common Mode Range
VoV5
VDD
Vb1
Vb2
M1
M3
Vo
VCMI
+
-
M5
+
-
Vgs1
VCMI (MIN)= Vgs1 + VoV5
From Vss
VDD
Vb1
Vb2
M1
M3
Vo
VCMI
+
-
M5
+
- Vgs1
VoV3
+ +
- M1
+ +
-
+
- -
VoV1
Vgs1
Vdg1 Vdg1
VCMI= VDD-|VoV3|-Vdg1
Vdg1= VoV1-Vgs1 ;
Vdg1= VoV1 (VoV1+Vt1);
Vgs1= VoV1+Vt1
VCMI(MAX) = VDD-|VoV3|-Vt1
VCMI (MIN)
Output Common Mode Voltage
VDD
RD
Vin
VCMO
VCMI
VOUT
VGS-Vt
Voltage
time
VCMO
VOUT
VGS-Vt
Voltage
time
VCMO
Output Common Mode Voltage
VDD
-Vin/2 +Vin/2
-Vo/2 +Vo/2
Vb1 Vb1
Vb2
M1 M2
M3 M4
VoV5 M5
+
-
+
-
VoV1
+
-
VoV3
Output common-mode range
VCMO(MIN) = VoV5+VoV1
VCMO(MAX) = VDD-VoV3
(VoV5+VoV1 )< VCMO< (VDD-VoV3)
Output Voltage Swing
VDD
-Vin/2 +Vin/2
-Vo/2 +Vo/2
Vb1 Vb1
Vb2
M1 M2
M3 M4
VoV5 M5
+
-
+
-
VoV1
+
-
VoV3
Maximum Output Voltage Swing
Differential End
2(VDD-(VoV5 +VoV1+| VoV3|))
Telescopic OTA
Mid Band Gain= ?
M1
M3
M5
M7
M2
M4
M6
M8
VDD
M9
Vb1
Vb2
Vb1
Vb4
Vb3
Vin- Vin
+
Vb2
Vb3
AV=-gm1 RD
RD= Rup // Rdown
Rdown
VO+ VO
-
Vin
RD
M1
VO
Vin+
M1
M3
M5
M7 Vb1
Vb2
Vb3
Virtual
ground
Rup
Single stage
Mid Band Gain of a Telescopic OTA
Rup
M5
M7 Vb1
Vb2
Vo
M1
M3 Vb3
Rdown
Vin+
M5 looks like common source with
degenerator circuit; its output
resistance is (1+gm5ro7)ro5
gm5ro5ro7 Rup gm5ro5ro7
M5
M7 Vb1
Vb2
Vo Rup
M5 r05
r07
Rup
S
D
Mid Band Gain of a Telescopic OTA
M1
M3 Vb3
Rdown
M3
Rdown
r01
r03
M3 looks like common source with
degenerator circuit; its output
resistance is (1+gm3ro1)ro3
gm3ro1ro3
Rdown gm3ro1ro3
Overall gain of the Telescopic OTA is
-gm1 RD
RD= Rup // Rdown
Overall Midband gain -gm1 (gm3ro1ro3)// gm5ro5ro7
Power Supply Rejection Ratio+
Power supply rejection ratio+ = Adm/A+
Adm = -gm1 (gm3ro1ro3)// gm5ro5ro7
Rup
M5
M7 Vb1
Vb2
Vo
M1
M3 Vb3
Rdown
Vdd
A+ =gm7 RD RD = Rup // Rdown
Rup = gm5ro5ro7 and Rdown = gm3ro1ro3
Hence A+ =gm7 (gm5ro5ro7 // gm3ro1ro3)
PSRR+ = -gm1 (gm3ro1ro3)// gm5ro5ro7 gm7 (gm5ro5ro7 // gm3ro1ro3)
Power Supply Rejection Ratio-
Vss
A- = gm1RD RD = Rup // Rdown
Rup gm5ro5ro7 Rdown gm3ro3gm1ro1ro9
Vo
Rup
M5
M7 Vb1
Vb2
Vo
Rdown
M1
M3 Vb3
Vb4 M9 M1
R1
r01
r09
M3 Vb3
Rdown
R1
r03
gm3ro3R1
gm1ro1ro9
Rdown gm3gm1ro1ro3ro9
PSRR- =Adm/A-
PSRR- = -gm1 (gm3ro1ro3)// gm5ro5ro7 gm1 (gm3gm1ro1ro3ro9 // gm5ro5ro7)
Common Mode Rejection Ratio
CMRR = Adm/Acm
Vin+
M1
M3
M5
M7 Vb1
Vb2
Vb3
Virtual
ground
Rup
Single stage
Adm -gm1 (gm3ro1ro3)// gm5ro5ro7
Vo
Vin+
Acm -gm1 (ro3//gm5ro5ro7)
(1+2gm1 ro9) Rup
M5
M7 Vb1
Vb2
Rdown
M1
M3 Vb3
Vb4 M9
CMRR ((gm1 (gm3ro1ro3)// gm5ro5ro7 ) (1+2gm1 ro9))
gm1 (ro3//gm5ro5ro7)
Input Common Mode range
VCMI (MIN) = VOV9 + Vgs1
M5
M7 Vb1
Vb2
Vo
M1
M3 Vb3
VDD
M9
VCMI (MAX) = VDD- |VOV7|- |VOV5| - |VOV3| +Vt1
VCMI (MIN) < VCMI < VCMI (MAX)
Output Common Mode range
M5
M7 Vb1
Vb2
Vo
M1
M3 Vb3
VDD
M9
VCMO(MIN) = VOV9 + VOV1 + VOV3
VCMO(MAX) = VDD- |VOV7 | - | VOV5 |
VCMO (MIN)
Output Voltage Swing
M5
M7 Vb1
Vb2
Vo
M1
M3 Vb3
VDD
M9
For Differential End
2(VDD- |VOV7 | - | VOV5 |- VOV3 VOV1 - VOV9)
Output Voltage Swing is
Mid band gain of Folded Cascoded OTA
VDD
M1
M3
M5
M7 M2
M4
M6
M8
VDD
Vb1
Vb2
Vb1
Vb4
Vb3
Vb2
Vb3 Vin
+ Vin-
M9 M10
Vb4
Vo+ Vo-
Vb5 M11
Mid band gain=?
Vin
RD
M1
AV=-gm1 RD
Vin
VO Vo
Rdown
Rup M1
M3
M5
M7
Vb1
Vb2
Vb3
M9
Vb4
Virtual
Ground
Single Stage
RD= Rup // Rdown
Overall Mid band gain
M5 looks like common source with
degenerator circuit; its output resistance is
(1+gm7ro9)ro7 gm7ro7ro9 Rup gm7ro7ro9
M7
M9 Vb1
Vb2
Vo Rup
M7 r07
r09
Rup
S
D M1
M3 Vb3
Rdown
M5
M3
Rdown
r05
r03
r01
M3 looks like common source with
degenerator circuit; its output
resistance is (1+gm3(ro1 // r05))ro3 Rdown gm3 ro3 (ro1//ro5)
-gm1 RD RD= Rup // Rdown
Overall Midband gain -gm1 (gm3 ro3 (ro1//ro5) //(gm7ro7ro9))
Power Supply Rejection Ratio+ Power supply rejection ratio+ = Adm/A+
Mid band gain of Simple Two Stage OTA
VDD
M1 M2
VDD
M3
Vb3 Vin-
Vin+
Vb1 M4
VDD
M5 M6
M7 M8
Vb1
Vb2 Vb2
Stage 1 Stage 2
Vo- Vo+
Overall Midband gain
Vin
M1
M3
V1 M5
M7
Vo+
V1
Stage 1 Gain
AV1=-gm1 (ro1 // ro3)
Stage 2 Gain
AV2= -gm5 (ro5 // ro7)
Overall gain = AV1 AV2
= gm1 gm5 (ro1 // ro3) (ro5 // ro7)
Mid band gain of Two Stage OTA with telescopic first stage
M1
M3
M5
M7
M2
M4
M6
M8
VDD
M9
Vb1
Vb2
Vb1
Vb4
Vb3
Vin- Vin
+
Vb2
Vb3
M10
M12
Vb5
Vo-
VDD VDD
Vo+
Vb4 M11
Stage 2 Stage 1
Mid band gain
M1
M3
M5
M7 Vb1
Vb2
Vb3
Vin
Stage 1
V1 M9
M11 Vb4
Vo
V1
Stage 2
AV1 -gm1 (gm3ro1ro3)// gm5ro5ro7
AV2= -gm9 (ro9 // ro11)
Overall Midband gain = AV1 AV2
gm1 gm9((gm3ro1ro3)// (gm5ro5ro7)) (ro9 // ro11)
Mid band gain of Two Stage OTA with folded cascode first stage
VDD
M1
M3
M5
M7 M2
M4
M6
M8
VDD
Vb1
Vb2
Vb1
Vb4
Vb3
Vb2
Vb3 Vin
+ Vin-
M9 M10
Vb4
M11
M13 Vb5
Vo+
Stage 2
VDD
M12
M14 Vb5
Vo-
VDD
Stage 1
Vb6 M15
Mid band gain
M1
M3
M5
M7
Vb1
Vb2
Vb3
M9
Vb4
Virtual
Ground
Stage 1
M11
M13 Vb4
Vo
V1
Stage 2
V1
Av1 -gm1 ((gm3 ro3 (ro1//ro5) ) //(gm7ro7ro9)) Av2=-gm11 (ro11 // ro13)
Overall gain gm1 gm11 (gm3 ro3 (ro1//ro5) //(gm7ro7ro9)) (ro11 // ro13)
THE END
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