EE 508
Lecture 16
Filter Transformations
Lowpass to Bandpass
Lowpass to Highpass
Lowpass to Band-reject
Review from Last Time
Theorem: If the perimeter variations and contact resistance are neglected,
the standard deviation of the local random variations
EE 508
Lecture 37
High Frequency Filters
A lossy integrator stage
VDD
I s
M2
IB
-gm1/C X
s+gm2 /C X
Vout
Vin
M1
CX
I 0 gm1/CX
L gm2 /CX
A fully-differential voltage-controlled integrator stage
VDD
Vout
Vin
CX
M1
VCTRL
Will need CMFB circuit
Vout
VB
CX
I
EE 508
Lecture 36
Oscillators, VCOs, and
Oscillator/VCO-Derived Filters
Question:
What is the relationship, if any, between a filter and
an oscillator or VCO?
XIN
T s
Oscillator
T s
XOUT
XOUT
XOUT=?
What is the relationship, if any, between a filter and
a
EE 508
Lecture 38
High Frequency Filters
Integrators for High-Speed Operation
Review from last time
IIN
Reasonably Fast
Slow
C
V1
VIN
V2
IOUT
gm
R
VOUT
IOUT
ZL
IOUT
VOUT
C
I s
C
VIN
gm
sC
sRMOSC
IIN
IOUT
C
I s
VOUT
gm
sC
IB1
VDD
I s
1
sRC
IIN
IB1
IB3
C
EE 508
Lecture 43
Basic Filter Components
All Pass Networks
Arbitrary Transfer Function Synthesis
Impedance Transformation Circuits
Equalizers
All-Pass Circuits
Magnitude of Gain is Constant
Phase Changes with Frequency
Used to correct undesired phase
EE 508
Lecture 39
Current Mode Filters
1
Current-Mode Filters
Current-Mode Filters have become a topic of
considerable interest in recent years
Consider first a brief background about filters
2
Recall:
John Hughes introduced the concept of the switched-cu
EE 508 Laboratory Experiment 1
Fall 2012
Filter Operation and Measurements
Purpose:
The purpose of this experiment is to develop familiarity with
measurements of filter characteristics and to start developing an understanding of some of
the nonideal effec
EE 508 Laboratory Experiment 2
Effects of Op Amp Bandwidth on Filter Structures
Introduction:
The active device in a filter structure generally plays a key role in
determining or limiting the performance of the filter. In high-frequency filters the active
EE 508
OTA Laboratory Experiment
The Operational Transconductance Amplifier is widely used in integrated amplifier and
filter applications. There are also some specific discrete applications where the device can be
used. Irrespective whether used in integ
EE 508
Switched Capacitor Amplifiers and
Filters
Capacitor ratios can be very accurately controlled in an integrated circuit with the right
sizing and layout strategies and thus they offer potential for making precision amplifiers. The
good matching prope
EE 508
Lecture 40
What filter architectures are really
being used today?
Today will consider the first 50 responses
1
2
3
4
5
6
Programmable Current Element
7
8
9
EE 508
Lecture 41
What filter architectures are really
being used today?
10
11
12
Mosfet-R integtator
13
Authors claim Op Amp is highly power efficient
14
15
16
17
17
capacitor
ST transistors operating in weak inversion provide linearization of basic
tran
EE 508
Lecture 42
What filter architectures are really
being used today?
21
System requirements appear to not have played a role in defining the filter type
22
23
24
25
26
27
28
29
30
31
32
33
EE 508
Lecture 25
Integrator Design
Review from last time
Parasitic Capacitances on Floating Nodes
Floating Node
Not Floationg Node
Z2
Zk
Z1
CP2
CP1
CP
Parasitic capacitances ideally have no affect on filter when on a non-floating
node but directly affect
EE 508
Lecture 34
Transconductor Design
Transconductor Design
VIN
VOUT
gm
C
Transconductor-based filters depend directly on the gm of the transconductor
Feedback is not used to make the filter performance insensitive to the
transconductance gain
Linearity
EE 508
Lecture 32
Switched Current Filters
Leapfrog Networks
Review from last time
Switched-Current Filters
Basic idea introduced by Hughes and Bird at ISCAS 1989
IOUT nT = AIIN nT-T
Cp is parasitic gate capacitance on M2
VDD
Very low power dissipation
I
EE 508
Lecture 18
Basic Biquadratic Active Filters
Second-order Bandpass
Second-order Lowpass
Effects of Op Amp on Filter Performance
Review from Last Time
Standard LP to BS Transformation
map =0 to =
map =0 to = 0
map =1 to = A
map =1 to = -B
map = 1 to
EE 508
Lecture 16
Filter Transformations
Lowpass to Bandpass
Lowpass to Highpass
Lowpass to Band-reject
Review from Last Time
Flat Passband/Stopband Filters
T j
T j
Lowpass
Bandpass
T j
T j
Highpass
Bandreject
Review from Last Time
Standard LP to BP T
EE 508
Lecture 22
Sensitivity Functions
Root Sensitivity
Bilinear Property of Filters
Root Sensitivities
Review from last time
Homogeniety (defn)
A function f is homogeneous of order
m in the n variables cfw_x1, x2, xn if
f(x1, x2, xn ) = mf(x1,x2, xn)
EE 508
Lecture 21
Sensitivity Functions
Comparison of Filter Structures
Performance Prediction
Design Characterization
Review from last time
Define the standard sensitivity function as
f x
S
x f
f
x
S
f
x
Is widely used except when x or f assume extre
EE 508
Lecture 20
Sensitivity Functions
Comparison of Filter Structures
Performance Prediction
Design Characterization
R
C
R
R
K
Comparison of 4 second-order LP filters
VOUT
R
-K
VIN
VIN
C
C
p
R
Review from last time
R
C
3%
p
p
8.5%
1%
p
C2
RQ
R
C
R
co
EE 508
Lecture 19
Basic Biquadratic Active Filters
Sensitivity Functions
Comparison of Filter Structures
Performance Prediction
Design Characterization
Review from last time
Filter Design/Synthesis Considerations
Most odd-ordered designs today use one
EE 508
Lecture 23
Sensitivity Functions
Transfer Function Sensitivity
Examples
Review from last time
Corollary 3:
If all op amps in an RC
active filter are ideal and there are k1
resistors and k2 capacitors and if pk is any
pole and zh is any zero, then
EE 508
Lecture 24
Sensitivity Functions
- Predistortion and Calibration
Review from last time
Sensitivity Comparisons
Consider 5 second-order lowpass filters
(all can realize same T(s) within a gain factor)
R
C1
L
VOUT
R1
C
VIN
R2
K
VIN
VOUT
C2
Passive RL
EE 508
Lecture 27
Integrator Design
Switched Capacitor Integrators
Review from last time
Consider the Basic Integrator
C
R
VOUT
VIN
T s I0
1
RCs
1
RC
1. Accuracy of R and C difficult to accurately control particularly in integrated applications
(often 2
EE 508
Lecture 28
Integrator Design
Alaising in SC Circuits
Elimination of redundant switches
Switched Resistor Integrators
Review from last time
The SC integrator
C
1
2
VOUT
C
I0eq = 1 fCLK
C
C1
VIN
Observe this circuit has considerable parasitics
C
CBc
EE 508
Lecture 29
Integrator Design
Metrics for comparing integrators
Current-Mode Integrators
Review from last time
Anti-aliasing filter often required to limit frequency content at input to SC filters
VIN t
Continuous-Time
Filter
VINFILT t
Discrete-Ti
EE 508
Lecture 31
Switched Current Filters
Review from last time
Current-Mode Filters
IIN
I0
s+I0
I0
s
IOUT
2
I0
IOUT
T s
2
IIN
s2 +I0s+I0
Basic Concepts of Benefits of Current-Mode Filters:
Large voltage swings difficult to maintain in integrated proce