Differential Voltage & Current amplifiers Willy Sansen KULeuven, ESAT-MICAS Leuven, Belgium
[email protected] Willy Sansen
10-05 031
Two-transistor circuits iin
IB
iout
2
IB
+ ic
2
- ic
ic
1:B
iout = B iin Current mirror/amp.
vin
vin
2
2
IB
vin
ic = gm 2
Differential Voltage amp. Willy Sansen
10-05 032
Table of contents
Current mirrors Differential pairs Differential voltage and current amps
Willy Sansen
10-05 033
Diode-connected MOST IDS
VDS = VGS-VT IDS
VDS = VGS
+ VGS
VDS = VGS
-
saturation
G=D
W IDS = n (VDS-VT) 2 L gm = diDS /dvDS K’
0
VT
VDS Willy Sansen
10-05 034
Current mirror iDS
iin
∆iout vGS
iout M1
M2 1:B
iout = B iin
vDS1 = vGS1 ∆iout iout
=
vDS2
vDS
vDS2 - vDS1 VEL2 Willy Sansen
10-05 035
Improved current mirrors iin
iin
iout
iout
Rin
vDS2 = vDS1 M3
M4
M3
1:B M1
Rout = rDS2 gm4rDS4
1:B M2
1:B
M4
M1
M2 1:B
vOUTmin = vGS+vDS ≈ 0.9+0.2=1.1 V
Feedback T ≈ gm1Rin
Is too large !!! Willy Sansen
10-05 036
Low-voltage current mirror iDS iin
vOUTmin
iout
Rout
vGS1
VB M3
vDS M4
vDS2 = vDS1 M1
M2
Rout = rDS2 gm4rDS4 vOUTmin = vDS2+vDS4 ≈ 0.2 + 0.2 = 0.4 V is low ! Willy Sansen
10-05 037
Examples of low-voltage current mirrors iin
VB M3
M5
iout = iin M4
W/L
W/L
n2
n2
W/L
IB
IB
M3
iout = iin M4
M5
M6
M2
M1
(n+1)2
iin
M2
M1 W/L W/L
Willy Sansen
10-05 038
Low-voltage diode-connected MOST
IB
VDSmin ≈ 0.2 V
Vref ≈ 0.2 V
VRef
Rout = rDS2
+
-
M1
M2
Willy Sansen
10-05 039
Lowest-voltage current mirrors iin
More noise !
M3
iin
iout
M4
iout
M3
M4 + -
- + M1
Better !
M2
M1
vOUTmin ≈ 50 mV
M2
Ref.: Charlon, .., ESSCIRC 2004 Willy Sansen
10-05 0310
Current mirror
iin
iin iout
iin
iout
iout M1
M1
M2
M2 1:B
iout = B iin
1:1
R1 iout iin
=
M1
M2 1:B
R2 R1 R2
iout =
kT/q R
R
ln B
iin iout
Ref.: Widlar, JSSC Aug 69, 184-191 Willy Sansen
10-05 0311
Improved current mirrors iin
iin 2iB
iout
2iB
iout
β M3
iB
iB
M1
iB M2
1:B
Error ~
R
2
β
iB
M1
M2 1:B
R
Error ~
2
β2
Willy Sansen
10-05 0312
Improved current mirrors iin
iin
iout
iout
vCE2 = vCE1 M3
M4
M3 1:B
1:B M1
M2 1:B
M4
M1
M2 1:B
Rout = ro2 gm4ro4 vOUTmin = vBE+vCE ≈ 0.7+0.1= 0.8 V
Ref.: Wilson, JSSC Dec.68, 341-348
Is too large ! Willy Sansen
10-05 0313
Current mirror at high frequencies Rout = rDS
iin iout CDS1 M1 1
M2
CG
iout = B iin
B
CG = (1 + B) CGS + CDS1 BW =
gm 2π (CG+CDS1)
≈ fT
1 (2 + B)
Ref.: Gilbert, JSSC Dec.68, 353-365 Willy Sansen
10-05 0314
Current Miller effect Ai = B
iIN
vIN
1 RIN = gm1
RL vOUT
CM
RS = 1/gm1
M1
M2
RS 1 :
vIN ≈ iIN RS B=
B
gm2 gm1
Ref.: Rincon-Mora, JSSC Jan. 2000, 26-32 Willy Sansen
10-05 0315
Current Miller equivalent circuit Miller effect : RL RS
CM
vOUT
vIN M2
f-3dB =
1 2π RSAv2CM
RS = 1/gm1 f-3dB = fz = -
Av2 = gm2RL 1
2π (1+B)CMRL gm2 2π CM Willy Sansen
10-05 0316
Table of contents
Current mirrors Differential pairs Differential voltage and current amps
Willy Sansen
10-05 0317
Voltage differential amplifier VDD RL vo1 CL
Two equal transistors vo2
- + vod
Redefine vin & vo :
CL
vin1
vin2 IB VSS
[
vind = vin1- vin2
[
vod = vo1 - vo2
vinc =
vin1+ vin2 2
voc = ... Willy Sansen
10-05 0318
Voltage differential amplifier : DC VDD IB/2 vo1 CL
RL
IB/2 vo2
- + vod
vin1 = vin2 = 0
CL
vin1
vin2
vo1 = vo2 = VDD - RL IB/2 vod = vo1 - vo2 = 0
IB VSS
Willy Sansen
10-05 0319
Voltage differential amplifier : AC Gain VDD io1 vo1 CL vin1
RL
io2
Differential input voltage
vo2
- + vod
vind = vin1- vin2
CL
v Circular current ic = gm ind
ic
vin2 vind
vind 2
2
vod = 2 RL ic
2
IB VSS
vod = gm RL Av = vind Willy Sansen
10-05 0320
Voltage differential amplifier VDD io1 vo1 CL
RL
io2 vo2
- + vod
Av = gm RL Same as single-tr. !!
CL
ic
Independent of :
vin1
vin2 IB VSS
Noise on VDD : PSRRDD Noise on VSS : PSRRSS Noise on Ground : CMRR Willy Sansen
10-05 0321
CMOS Voltage differential amplifier : DC range VDD io1 vo1
RL
vod
io2 RLIB
- +
vo2
vod
vind
slope gmRL
0
ic
-RLIB
vin1
√2 (VGS -VT)
vin2 IB VSS
VGS -VT sets slope and range and …. Gain ! Willy Sansen
10-05 0322
Bipolar Voltage diff. amplifier : DC range VDD io1 vo1
RL
vod
io2
-1% at 6kT/q
RLIB
- +
vo2
vod
vind
slope gmRL
0
ic
-RLIB
vin1
vin2 IB VSS
kT/q sets slope and Gain and range Insert RE to increase range ! Willy Sansen
10-05 0323
MOST Voltage diff. amplifier : large input signals iOd IB
=
vId (VGS-VT)
1-
1 4
(
vId VGS-VT
)2
vId is the differential input voltage iOd is the differential output current (gmvId) or twice the circular current gmvId /2 IB is the total DC current in the pair Note that gm =
IB VGS - VT
= K’ W/L (VGS - VT) Willy Sansen
10-05 0324
Bipolar Voltage diff. amp. : large input signals iOd IB
= tanh
VId 2 kT/q
tanh x =
ex - e-x ex
+
e-x
=
2ex - 1 2ex + 1
vId is the differential input voltage iOd is the differential output current (gmvId) or twice the circular current gmvId /2 IB is the total DC current in the pair Note that gm =
IB 2 kT/q Willy Sansen
10-05 0325
Voltage differential amplifier: transfer function -1% VId ≈ 2.67 x 2kT/q = 0.14 V iOd
1 0.9
IB
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
vId
VId = √2 (VGS-VT) = √2 x 0.2 V Willy Sansen
10-05 0326
Voltage differential amplifier with gmrDS gain IB M1
vin1
M1
vo2
vo1
VB
M2
vin2
Av = gm1(rDS1//rDS2)
Willy Sansen
10-05 0327
Diode-connected MOSTs with resistors 2 gm
2 R//ro R
R
Willy Sansen
10-05 0328
Voltage differential amplifier with high gain IB M1
vin1 vo1
M1
R
R
vo2
vin2
Av = gm1 (R // ro ) M2
ro = ro1//ro2 Willy Sansen
10-05 0329
Differential diode-connected MOSTs 2 gm
2 gm
Willy Sansen
10-05 0330
Differential diode-connected MOSTs 2
gm2 - gm1
M2
M1
M2
Values close to ∞ ! Willy Sansen
10-05 0331
High gain because of current cancellation IB M1
vin1
M1
vo1
M2
vin2
vo2
M3
M2
Av =
gm1 gm2 - gm3
Willy Sansen
10-05 0332
Input impedance ZIN
ZIN
CIN =
CGS 2
RIN = 2 rπ
CIN =
Willy Sansen
Cπ 2 10-05 0333
Low-Pass Voltage Differential amplifier R
|Av|
R
Av0
-20 dB/dec
vOUT 1 φ (Av)
CL
vIN
GBW f
fp
90o
f
0o -90o
Av0 = gmR
AV =
Av0 (1 + j
f fp
fp = )
1 2π 2RCL
GBW =
Willy Sansen
gm 2π 2CL
10-05 0334
High-Pass voltage differential amplifier R
|Av|
R
Av0
20 dB/dec
vOUT vIN
C
fp
φ (Av)
90o
f
0o
j Av0 = gmR
Av = Av0
-90o
f fp
(1 + j
f
f fp
fp = )
gm 2π 2C
Willy Sansen
10-05 0335
Calculation High-Pass differential amplifier R
R
vOUT vIN
C
R
R
vOUT/2
vOUT/2
vIN/2
vIN/2 Z
2C
Av =
- gm R (1 +
gm 2Cs
Av = )
- gm R 1 + gm Z
Willy Sansen
10-05 0336
Table of contents
Current mirrors Differential pairs Differential voltage and current amps
Willy Sansen
10-05 0337
Operational Transconductance Amplifier (OTA) VDD
VDD IDD
IDD M1
M2
M1
M2
-
+
vOUT
vOUT ZL
M4
M3
DC
ISS=IDD
IL M4
M3
VSS
AC
ZL
ISS=IDD+IL Willy Sansen
VSS 10-05 0338
Single-stage OTA: operation
Willy Sansen
10-05 0339
Single-stage OTA VDD
Av = gm1 Rout Rout = rDS2 // rDS4
-
M1
+
M2
vOUT
BW = CL
M3
M4
VSS
1 2π RoutCL
GBW =
gm1 2π CL
Willy Sansen
10-05 0340
Bootstrapping for low input capacitance A1 vIN
vOUT
-
+ +
-
A2
Ccoax ≈ 0 !!! Willy Sansen
10-05 0341
Bootstrapping for high input impedance fz = CC
ZIN
-
vOUT
+
vIN
R1
CF
f2 =
1 2π (R1+R2)CF 1 2π R2CF
ZIN
R2 R1+R2
fz
f2.GBW Willy Sansen
f 10-05 0342
Bootstrapping for high input impedance CIN
vIN+
+ R3
vB
CB
-
vOUT+ R1
R4 R2 CB
vIN-
A1
R3
-
+ CIN
R1
vOUT-
A2
ZIN ≈ ∞ !!! Willy Sansen
10-05 0343
Bootstrapping out a load resistance R IB1 Q3 Q4
R
Q5 Q2
R is bootstrapped out : Very high gain !
Q6
Q1
vIN
IB2
vOUT
Ref.: Nordholt JSSC June 85, 688-696 Willy Sansen
10-05 0344
Bootstrapping out an output resistance IB1
vIN +
M1
ro4 is bootstrapped out !
-
M2
Av ≈ gm1 ro2 M5
M3
M4
IB2
vOUT Same GBW !
Willy Sansen
10-05 0345
Bootstrap for high gain Av2
Rm -> x β3 M1
Rout -> x Rm
M3
M2
Rout
1 β3
Av2 ≈ gm1 ro2 x β3 Same GBW ! Ref.De Man JSSC June 77, pp. 217-222 LT1008, LT1012 Willy Sansen
10-05 0346
Current differential amplifier
M1
Rin
M2
M3
iout iin
IB 1 iout = IB + iin Rin = g m1
Is the same ! Willy Sansen
10-05 0347
Current differential amplifier
M1
Rin
M2
Rin M1
M3
M2
M3
iout iin
IB 1 iout = IB + iin Rin = g m1
iout iin
IB 1 1 Rin = gm1 gm3ro3 Willy Sansen
10-05 0348
Current differential amplifier
Rin1 M1
M2
M3
M4
i1
Rin2
i2 IB
iout
iout = IB + i1 - i2 1 1 Rin1 = gm1 gm3ro3 Rin2 =
1 gm4
Ref. Fischer, JSSC June 87, 330-340 Willy Sansen
10-05 0349
4-input current amplifier
Rin1 M1
M2
M3
M4
i1
Rin2
i2 i3
i4
iout
iout = i1 - i2 + i3 - i4
Willy Sansen
10-05 0350
Low voltage operation VDD = 1 V M1 0.85 V M3
0.15 V
iout = IB + i1 - i2
M2 0.85 V
0V
VGS = 0.85 V VDSsat = 0.15 V
M4
i1
i2
Voutmax = 0.7 V
0.15 V
IB
iout VSS = 0 V
For VT = 0.7 V VDDmin ≈ 0.6 V For VT = 0.3 V VDDmin ≈ 0.6 V Willy Sansen
10-05 0351
Table of contents
Current mirrors Differential pairs Differential voltage and current amps
Willy Sansen
10-05 0352
