ee 508 lecture 4 - class.ece.iastate.educlass.ece.iastate.edu/ee508/lectures/ee 508 lect 25 fall...
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EE 508EE 508 Lecture 25Lecture 25
Integrator Design
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Parasitic Capacitances on Floating NodesParasitic Capacitances on Floating Nodes
P1
P2
Parasitic capacitances ideally have no affect on filter when on a non-floating node but directly affect transfer function when they appear on a
floating node
Parasitic capacitances are invariably large, nonlinear, and highly process dependent in integrated filters. Thus, it is difficult to build
accurate integrated filters if floating nodes are present
Generally avoid floating nodes, if possible, in integrated filters
Review from last time
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VOUT
VIN
R3 R1 R2
C1
C2
C1
C2
R2R1
VIN
VOUTK
R3
Sallen-Key Type (Dependent Sources)
Infinite Gain Amplifiers
Integrator Based Structures
Which type of Biquad
is really used?Integrator-based structures with no floating
nodes dominantly used in integrated filters
Some high-frequency or programmable
integrated filters with floating nodes are used
Review from last time
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Filter Design/Synthesis ConsiderationsFilter Design/Synthesis Considerations
( ) 1 2 mT s T T T= ii
I1(s)
Integrator
I2(s)
Integrator
I3(s)
Integrator
I4(s)
Integrator
Ik(s)
IntegratorVIN
VOUTIk-1(s)
Integrator
a2a1
+
Cascaded Biquads
Leapfrog
Multiple-loop Feedback – One type shown
Observation: All filters are comprised of summers, biquads
and integrators
And biquads
usually made with summers and integrators
Integrated filter design generally focused on design of integrators, summers, and amplifiers (Op Amps)
Will now focus on the design of integrators, summers, and op amps
Review from last time
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Basic Filter Building BlocksBasic Filter Building Blocks (particularly for integrated filters)(particularly for integrated filters)
• Integrators
• Summers
• Operational Amplifiers
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Integrator Characteristics of Interest
0Is
( ) 0II s = s
( ) 0II jω = ω
( )I∠ 0jω = -90
Unity Gain Frequency = 1
Properties of an ideal integrator:
Gain decreases with 1/ω
Phase is a constant -90o
( )0I Ij = 1
How important is it that an integrator have all 3 of these properties?
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Integrator Characteristics of Interest
− 0Is
0Is+
( ) =20
2 20 0
- IT s
s + αI s + I
0 0ω = Iα1Q =
0Is
( ) 0II s = s
( ) 0II jω = ω ( )I∠ 0jω = -90
How important is it that an integrator have all 3 of these properties?
Consider a filter example:
In many (most) applications it is critical that an integrator be very nearly ideal(in the frequency range of interest)
( )0I Ij = 1
Band edges proportional to I0Phase critical to make Q expression valid
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Some integrator structuresSome integrator structures
VOUT
CVIN
R ( )I s = −1
RCs
Are there other integrator structures?
Inverting Active RC Integrator
I
I=
OUT m IN
OUT OUT
= - g V1V
sC
( )I s = − mgsC 0I = mg
C
Termed an OTA-C or a gm-C integrator
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Some integrator structuresSome integrator structuresAre there other integrator structures?
I
I= −
OUT m IN
OUT OUT
= g V1V
sC
( )I s = − mgsC
Termed a TA-C integrator
VOUT
CVIN RMOS
VC
( )I s = −MOS
1sCR
Termed MOSFET-C integrator
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Some integrator structuresSome integrator structuresAre there other integrator structures?
INI−
=
2 1
2 1OUT
1V = VsC
V - VIR
( ) OUT
IN
II sI
= = −1
sRC
Termed active RC current-mode integrator
• Output current is independent of ZL
• Thus output impedance is ∞
so provides current output
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Some integrator structuresSome integrator structures
( )I s = −1
sRC
VOUT
CVIN
R
VOUT
CVIN RMOS
VC( )I s = −
1sRC
( )I s = −MOS
1sR C
( )I s = − mgsC
( )I s = − mgsC
There are many different ways to build an inverting integrator
There are other useful integrator structures (some will be introduced later)
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Integrator FunctionalityIntegrator Functionality
VOUT
CVIN
R( )I s = −
1sRC
1OUT INk
k
1V VCR s
n
k== − ∑
OUTdiffVINdiffV
OUTdiff INdiff1V V
CRs= −
CVIN
R VOUTRA
RA
( )I s =1
sRC
VIN
VOUTR
C
RF
FOUT IN
F
RRV V
1+CR s= −
Summing Integrator
Fully Differential Integrator
Noninverting Integrator
Lossy
Integrator
Basic Active RC Inverting Integrator
Many different types of functionality from basic inverting integratorSame modifications exist for other integrator architectures
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Integrator-Based Filter Design
− 0Is
0Is+XIN
α
XO1
XO2
VOUT
CVIN RMOS
VC
Any of these different types of integrators can be used to build
integrator-based filters
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Example –
OTA-C Tow Thomas Biquad
− 0Is
0Is+XIN
α
XO1
XO2
1OUT 2 m2V sC =g V+ −1 1 m1 OUT m3 IN m4 1V sC = -g V g V g V
( )+OUT m3 m2
2IN 1 2 m4 2 m1 m2
V g g=V s C C sg C +g g
⎛ ⎞⎜ ⎟⎝ ⎠
⎛ ⎞⎛ ⎞+⎜ ⎟⎜ ⎟
⎝ ⎠⎝ ⎠
2m3 m
2mOUT
2IN 2 m4 m m
2m
g gg CV =
V g g gs s +g C C
Assume gm1
=gm2
=gm
, C1
=C2
=C
20
200Q
⎛ ⎞⎜ ⎟⎝ ⎠
⎛ ⎞+⎜ ⎟
⎝ ⎠
m3
mOUT
2IN
g ωgV =
V ωs s +ω
0mgω =
Cm
m4
gQ = g
express as
where
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0Is
0Is + α
0Is
−
0Is + α
−
0kIs
1
OkOUT
IXs
n
k=
±= ∑
0kk
Is+α 1
OkOUT
k
IXs+α
n
k=
±= ∑
0Is
IN+X
IN-X
OUT+X
OUT-X
( )OUT OUT IN IN+ + + +0IX X X X
s− = −
0IsINdiffX OUTdiffX
OUTdiff INdiff0IX Xs
=
Basic Integrator Functionality
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Basic Integrator FunctionalityBasic Integrator Functionality
0Is
OUTIN 0Is
− OUTIN
Noninverting Inverting
•
An inverting/noninverting integrator pair define a family of integrators•
All integrator functional types can usually be obtained from the
inverting/noninverting integrator pair
•
Suffices to focus primarily on the design of the inverting/noninverting integrator pair since properties of class primarily determined by properties of integrator pair
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Example Example ––
Basic OpBasic Op--Amp Feedback IntegratorAmp Feedback Integrator
VOUT
CVIN
R
CVIN
R VOUTRA
RA
Inverting Integrator of Family Noninverting Integrator
VOUT
CVIN1
R1
VINn
Rn
Summing Inverting Integrator
1OUT INk
k
1V VCR s
n
k== − ∑
OUT IN1V V
CRs= − OUT IN
1V VCRs
=
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Example Example ––
Basic OpBasic Op--Amp Feedback IntegratorAmp Feedback Integrator
VOUT
CVIN
R
Inverting Integrator of Family VOUT
CVIN1
R1
VINn
Rn
Summing Inverting Integrator
1OUT INk
k
1V VCR s
n
k== − ∑
OUT IN1V V
CRs= −
Lossy
Summing Inverting Integrator
1
1
nINk
kOUT
n
R VR
V1+CR s
n
k
−
== −∑
VOUT
CVIN1
R1
VINnRn
RF
1
FIN k
kO U T
F
R VR
V1 + C R s
n
k == −∑
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Example Example ––
Basic OpBasic Op--Amp Feedback IntegratorAmp Feedback Integrator
VOUT
CVIN
R
Inverting Integrator of Family
OUT IN1V V
CRs= −
Lossy
Summing Inverting Integrator
VOUT
CVIN1
R1
VINnRn
RF
1
FIN k
kO U T
F
R VR
V1 + C R s
n
k == −∑
VIN
VOUTR
C
RF
Lossy
Inverting Integrator
FO U T IN
F
RRV V
1 + C R s= −
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Example Example ––
Basic OpBasic Op--Amp Feedback IntegratorAmp Feedback Integrator
VOUT
CVIN
R
Inverting Integrator of Family
OUT IN1V V
CRs= −
Balanced Differential Inverting Integrator
C
R
C
R
IN+V
IN-V
OUT+V
OUT-V
INdiffV OUTdiffV Axis of Symmetry
OUT IN1V V
CRs+ += −
OUT IN1V V
CRs− −= −
OUTdiff INdiff1V V
CRs= −
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Example Example ––
Basic OpBasic Op--Amp Feedback IntegratorAmp Feedback Integrator
VOUT
CVIN
R
Inverting Integrator of Family
OUT IN1V V
CRs= −
Fully Differential Inverting Integrator
OUTdiff INdiff1V V
CRs= −OUTdiffVINdiffV
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Integrator TypesIntegrator Types
0Is
VOUTVIN
Voltage Mode
oOUT IN
IV Vs
=
0Is
IOUTIIN
Current Mode
oOUT IN
II Is
=
0Is
VOUTIIN
Transresistance Mode
oOUT IN
IV Is
=
0Is
IOUTVIN
Transconductance Mode
oOUT IN
II Vs
=
Will consider first the Voltage Mode type of integrators
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Voltage Mode IntegratorsVoltage Mode Integrators
•
Active RC (Feedback-based)
•
MOSFET-C (Feedback-based)
•
OTA-C•
TA-C
•
Switched Capacitor•
Switched Resistor
Sometimes termed “current mode”
Will discuss later
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Active RC Active RC Voltage Mode IntegratorVoltage Mode Integrator
OUT IN1V V
CRs= −
•
Limited to low frequencies because of Op Amp limitations•
No good resistors for monolithic implementationsArea for passive resistors is too large at low frequencies
Some recent work by Haibo
Fei
shows promise for some audio frequency applications•
Capacitor area too large at low frequencies for monolithic implementatins•
Active devices are highly temperature dependent, proc. dependent, and nonlinear•
No practical tuning or trimming scheme for integrated applications with passive resistors
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MOSFETMOSFET--C C Voltage Mode IntegratorVoltage Mode Integrator
•
Limited to low frequencies because of Op Amp limitations•
Area for RMOS
is manageable !•
Active devices are highly temperature dependent, process dependent•
Potential for tuning with VC•
Highly Nonlinear (can be partially compensated with cross-coupled input
VOUT
CVIN RMOS
VC
MOSOUT IN
1V VCR s
= −
A Solution without a Problem
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MOSFETMOSFET--C C Voltage Mode IntegratorVoltage Mode Integrator
•
Improved Linearity •
Some challenges for implementing VC
VOUT
CVIN RMOS
VC
MOSOUT IN
1V VC R s
= −
Still A Solution without a Problem
MOSOUT IN
1V VC R s
= −
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OTAOTA--C C Voltage Mode IntegratorVoltage Mode Integrator
•
Requires only two components•
Inverting and Noninverting structures of same complexity•
Good high-frequency performance•
Small area•
Linearity is limited (no feedback in integrator)•
Susceptible to process and temperature variations•
Tuning control can be readily added
Widely used in high frequency applications
NoninvertingInverting
VOUTVIN
C
gm
= mOUT IN
gV VsC
= − mOUT IN
gV VsC
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OTAOTA--C C Voltage Mode IntegratorVoltage Mode Integrator
Programmable Integrator
= mOUT IN
gV VsC
( )=m ABCg f I
= mOUT IN
gV VsC
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OTAOTA--C C Voltage Mode IntegratorVoltage Mode Integrator
Lossy
Integrator
( )( ) ( )
OUT m FIN F
V s g R = V s 1+s R C
But RF
is typically too large for integrated applications
= mOUT IN
gV VsC
VOUT
VIN
C
gm
RF