Allen and Holberg - CMOS Analog Circuit Design
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M1
Undesired operating point
Allen and Holberg - CMOS Analog Circuit Design |
Page V.5-8 |
Bootstrapped Current Sink/Source - Continued
An examination of the second-order effects of this circuitThe relationship between M1 and R can be expressed as,
I2R = VT1 |
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2I1 |
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β1 |
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Instead of assuming that I1 = I2 because of the current mirror, M3-M4, let us consider the effects of the channel modulation which gives
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1 + λPV G S 4 |
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I2 = I1 1 + λP(VD D - VDS1) |
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Solving for I1 from the above two expressions gives
I1R(1 + λPVGS4) = [1 + λP(VDD-VDS1)] |
2I1 |
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β1 |
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Differentiating with respect to VDD and assuming the VDS1 and VGS4 are constant gives (IOUT = I1),
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2I |
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IOUT |
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20V |
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λ |
V |
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1 |
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DD |
T1 |
β |
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P |
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1 + |
λP(VD D - VDS1 ) |
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VDD |
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IOUT R(1 + λPV GS4 ) - |
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2β1I1 |
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Allen and Holberg - CMOS Analog Circuit Design |
Page V.5-9 |
Bootstrapped Current Sink/Source - Continued
Assume that VDD=5V, KN' = 23.6 µA/V2, VTN=0.79V, γN=0.53V0.5, φP = 0.590V, λN=0.02V-1, KP' = 5.8µA/V2, VTP=-0.52V, γP=0.67V0.5, φP = 0.6V,
λN=0.012V-1. Therefore,
VGS4 = 1.50V, VT2 = 1.085V, VGS2 = 1.545V, and VDS1 = 2.795V which
gives
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IOUT |
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IOUT/IOUT |
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= 0.08 = |
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VDD/VDD |
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VDD |
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V |
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If V |
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= 6V - 4V = 2V, then |
I |
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= 0.08 I |
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= 3.2µA |
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DD |
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DD |
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OUT |
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OUT VDD |
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SPICE Results: |
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120 A |
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100 A |
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80 A |
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IOUT ≈ 2.8 A for |
VDD 4V →6V |
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60 A |
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IOUT |
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40 A |
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20 A |
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0 A |
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0V |
2V |
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4V |
6V |
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8V |
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10V |
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VDD |
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Allen and Holberg - CMOS Analog Circuit Design |
Page V.5-10 |
Base-Emitter Voltage Referenced Circuit
VDD
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M4 |
RB |
M3 |
M5 |
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ID1 = I1 |
iOUT |
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ID2 = I2 |
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M6 |
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M1 |
M2 |
M8 |
Q1 |
R |
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I |
2 |
≈ VBE1 |
= I |
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V = I2R ≈ VBE1
Allen and Holberg - CMOS Analog Circuit Design Page V.5-11
V.5-2 - TEMPERATURE DEPENDENCE
Objective
Minimize the fractional temperature coefficient which is defined as
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TCF = |
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∂Vref |
parts per million per |
°C or ppm/°C |
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∂T |
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Vref |
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Temperature Variation of References |
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PN Junction: |
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v |
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i ≈ Isexp |
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∂I |
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∂(ln I |
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V |
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V |
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Vt |
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3 + |
GO ≈ |
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-V |
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1 s |
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GO |
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I = KT3 exp |
GO |
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Is ∂T |
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∂T |
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TVt |
TVt |
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Vt |
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dvBE |
≈ |
V BE - VG O |
= -2mV/°C at room temperature |
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dT |
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= 1.205 V and is called the bandgap voltage)
Gate-Source Voltage with constant current (Strong Inversion):
dVGS |
dVT |
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2L |
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d |
ID |
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dT |
= dT |
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WC |
dT |
µ |
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ox |
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o |
µo = KT-1.5 |
; VT = VT0 - αT |
or VT(T) = VT(To) - α(T-To) |
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dVG S |
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3 V GS - VT |
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dT = - α + |
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T |
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4 |
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I
Allen and Holberg - CMOS Analog Circuit Design |
Page V.5-13 |
Gate - Source Referenced Circuits
MOS Equivalent of the PN Junction Referenced Circuit
VDD
R 
I
+
VREF
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2(VDD−VT) |
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V R E F = V T − βR + |
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βR |
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β2R2 |
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VDD − VR E F 1.5 |
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1 d R |
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T C F |
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dVR E F |
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− α + |
2βR |
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R dT |
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VREF |
dT |
VREF |
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1 + |
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2βR (VDD − VREF) |
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Allen and Holberg - CMOS Analog Circuit Design Page V.5-14
Example
W = 2L, VDD = 5V, R = 100 KΩ , K’=110 µ, VT = 0.7, T = 300 K, α = 2.3
mV/°C
Solving for VREF gives
VREF = 1.281 V
RdTdR = +1500 ppm/°C
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-3 |
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5 − 1.281 |
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1.5 |
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-6 |
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dVREF |
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−2.3 ×10 |
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-6 |
× 100K |
300 |
− 1500 |
× 10 |
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TCF = |
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2 × 2 110×10 |
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1.281 |
dT |
1.281 |
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-6 |
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2 × 2 110×10 |
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× 100K (5 - 1.281) |
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TCF = - 928 ppm/°C
Allen and Holberg - CMOS Analog Circuit Design Page V.5-15
Bootstrapped Current Source/Sink
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VDD |
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M4 |
RB |
M3 |
M5 |
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ID1 = I1 |
iOUT |
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ID2 = I2 |
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M6 |
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M2 |
M8 
M1
R
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2ID1L |
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VGS1 |
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K'W |
+ V T |
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VON + VT |
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ID2 = R |
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R |
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R |
= ID1 = IOUT |
Assuming that VON is constant as a function of temperature because of the bootstrapped current reference, then
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TC |
F |
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1 |
dVT |
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1 dR |
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-α |
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1 dR |
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VT dT |
R dT |
VT |
R dT |
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If |
R is a polysilicon resistor, then |
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TC |
F |
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-2.3 x 10-3 |
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- 1.5x10-3 = -3800 ppm/°C |
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If |
R is an implanted resistor, then |
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TC |
F |
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-2.3 x 10-3 |
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- 0.4x10-3 = -2700 ppm/°C |
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Allen and Holberg - CMOS Analog Circuit Design |
Page V.5-16 |
Base-Emitter Voltage - Referenced Circuit
VDD
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M4 |
RB |
M3 |
M5 |
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ID1 = I1 |
iOUT |
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ID2 = I2 |
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M6 |
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M1 |
M2 |
M8 |
Q1 |
R |
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I |
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≈ |
vBE1 |
-----> TC |
F |
= |
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dvBE |
- |
1 dR |
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vBE |
dT |
R dT |
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Assuming VBE = 0.6 volts and a polysilicon resistor gives TCF = 0.61 (-2x10-3) - (1.5x10-3) = -4833 ppm/°C