Allen and Holberg - CMOS Analog Circuit Design
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Allen and Holberg - CMOS Analog Circuit Design |
Page V.4-10 |
Output Impedance of the Wilson Current Source
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iout |
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iin=0 |
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v3 rds3 |
gm3(v1-v2) |
gmbs3v2 |
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vout |
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gm1v2 |
rds1 |
v1 |
gm2v2 |
rds2 v2 |
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vout = rds3[iout - gm3v1 + gm3v2 + gmbs3v2] + v2
vout = rds3iout - gm3rds3(-gm1rds1v2) + gm3rds3v2 + gmbs3rds3v2 + v2
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rds2 |
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out 1 + gm2 rd s 2 |
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vout = ioutrds3 + [gm3rds3 + gmbs3rds3 + gm1rds1gm3rds3]v2 + v2
r |
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= r |
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+ r |
1 + gm3rds3 + gmbs3rds3 + gm1rds1gm3rds3 |
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out |
ds3 |
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1+gm2rds2 |
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ds2 |
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rout ≈ |
rds2gm1rds1gm3rds3 |
≈ rd s 1 |
× (gm 3 rd s 3 ) if gm 1 |
= gm 2 |
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gm2rds2 |
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M1
M2
Allen and Holberg - CMOS Analog Circuit Design |
Page V.4-12 |
Regulated Cascode Current Mirror
VDD |
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iOUT |
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IB |
M4 |
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IIN |
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M3 |
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vOUT |
M1 |
vGS4 |
M2 |
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VSS
Small Signal Equivalent Model (gmbs effects ignored) -
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iout |
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rds4 |
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gm4vgs4 |
v4 |
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vout |
rds3 |
rds2 |
v3 |
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gm3 v3 |
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vout = (iout - gm4vgs4)rds4 + ioutrds2 vgs4 = v4 - v3
v3 = ioutrds2
v4 = -gm3v3rds3
vout = ioutrds4 - gm4(-gm3ioutrds2rds3 - ioutrds2)rds4 + ioutrds2 rout = rds4 + gm4gm3 rds2rds3rds4 + rds2 + gm4rds2rds4
vOUT(min) = |
2IB |
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2Iout |
K'(W/L)4 |
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+ VT4 |
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K'(W/L)3 |
Allen and Holberg - CMOS Analog Circuit Design |
Page V.5-1 |
V.5 - REFERENCE CIRCUITS
Introduction
What is a Reference Circuit?
A reference circuit is an independent voltage or current source which has a high degree of precision and stability.
Requirements for a Reference Circuit
1.) Output voltage/current should be independent of power supply.
2.) Output voltage/current should be independent of temperature.
3.) Output voltage/current should be independent of processing variations.
V-I Characteristics of an Ideal Reference
i
Voltage Reference
Iref
Current Reference
v
Vref
Allen and Holberg - CMOS Analog Circuit Design |
Page V.5-2 |
Concept of Sensitivity
Definition
Sensitivity is a measure of dependence of Vref (Iref) upon a parameter or
variable x which influences Vref (Iref).
Vref |
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∂Vref |
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Vref |
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S |
∂x |
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Vref |
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where
x = VDD or temperature
Application of Sensitivity
∂Vref |
Vref |
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∂x |
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Vref |
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S |
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For example, if the sensitivity is 1, then a 10% change in x will cause a 10% change in Vref.
Vref
Ideally, S → 0
x
Allen and Holberg - CMOS Analog Circuit Design |
Page V.5-3 |
V.5-1 - SIMPLE REFERENCES
Objective is to minimize,
Vref |
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∂ V r e f |
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Vref |
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S |
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∂ V D D |
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VDD |
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VDD |
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Types of references include,
1.Voltage dividers - passive and active.
2.MOS diode reference.
3.PN junction diode reference.
4.Gate-source threshold referenced circuit.
5.Base-emitter referenced circuit.
Allen and Holberg - CMOS Analog Circuit Design |
Page V.5-4 |
Passive Divider
Accuracy is approximately equivalent to 6 bits (1/64).
VDD
RA
V1
I RB
V2
RC
VSS
Active Dividers
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V3
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VDD |
VDD |
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V2 |
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M2 |
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M2 |
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V1 |
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M1 |
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M1 V |
M1 V |
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ref |
ref |
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Allen and Holberg - CMOS Analog Circuit Design Page V.5-6
Gate-Source Referenced Circuits
(MOS equivalent of the pn junction referenced circuit)
VDD |
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2(VDD-VREF) |
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VREF = VGS = VT + |
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βR |
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R |
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2(VDD-VT) |
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V R E F = VT − βR |
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βR |
+ β2R2 |
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VREF |
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Sensitivity: |
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VREF |
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VDD |
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S |
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= VREF 1 + βR(VREF - VT ) |
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VDD |
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If VDD = 10V, W/L = 10, R = 100kΩ and using the results of Table 3.1-2 gives
VREF
VREF = 1.97V.and S = 0.29.
VDD
Modifying the Value of VREF
VDD
R |
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R1 +R2 |
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VREF |
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R2 |
VGS |
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IR1 |
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R1 |
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VREF |
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R2 |
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