EE 508
Lecture 11
The Approximation Problem
Classical Approximations
the Chebyschev and Elliptic Approximations
Review from Last Time
Butterworth Approximations
TLP j
1
Analytical formulation:
1
All pole approximation
Magnitude response is maximally fl
EE 508
Lecture 6
Scaling, Normalization and
Transformation
Review from Last Time
Dead Networks
XIN
T s
T s =
XOUT
N s
D s
T s
D s
The dead network of any linear circuit is obtained by setting ALL
independent sources to zero.
Replace independent current s
EE 508
Lecture 7
Degrees of Freedom
The Approximation Problem
Review from Last Time
Desgin Strategy
Theorem: A circuit with transfer function T(s) can be
obtained from a circuit with normalized transfer function
Tn(sn) by denormalizing all frequency depen
EE 508
Lecture 5
Filter Concepts/Terminology
Basic Properties of Electrical Circuits
Review from Last Time
2-nd order polynomial
characterization
s +as+b
2
cfw_a,b
s + s+
Q
s +2 s+
2
cfw_o,Q
2
o
0
2
0
cfw_, o
2
0
s +(p +p )s+p p =
2
1
2
1
2
with complex c
EE 508
Lecture 4
Filter Concepts/Terminology
Basic Properties of Electrical Circuits
Review from Last Time
Filter Concepts and Terminology
XIN(s)
T ( s)
XOUT(s)
Reflecting poles and zeros to maintain stability or establish minimum phase
s-plane
s-plane
Im
EE 508
Lecture 2
Filter Design Process
Review from Last Time
Filter design field has received considerable
attention by engineers for about 8 decades
Passive RLC
Vacuum Tube Op Amp RC
Active Filters (Integrated op amps, R,C)
Digital Implementation (ADC,DA
EE 508
Lecture 3
Filter Concepts/Terminology
Basic Properties of Electrical Circuits
Review from Last Time
Is there a systematic way to design filters?
gm
?
Specifications
T ( s)
?
Energy Storage
Elements Create
Frequency
Dependence of T(s)
Transfer Funct
EE 508
Lecture 8
The Approximation Problem
Review from Last Time
The Approximation Problem
The goal in the approximation problem is simple, just want
a function TA(s) or HA(z) that meets the filter requirements.
Will focus primarily on approximations of t
EE 508
Lecture 9
The Approximation Problem
Review from Last Time
Collocation
Collocation is the fitting of a function to a set of points (or
measuremetns) so that the functin agrees wth the sample
at each point in the set.
f(x)
f(x)
x
x
Often consider cri
EE 508
Lecture 14
Statistical Characterization of
Filter Characteristics
Components used to build filters are not precisely
predictable
R
L
C
Temperature Variations
Manufacturing Variations
Aging
Model variations
Different approaches are used to address
EE 508
Lecture 15
Statistical Characterization of
Filter Characteristics
Review from last lecture
Effects of manufacturing variations on components
R
L
C
A rigorous statistical analysis can be used to analytically predict how
components vary and how comp
EE 508
Lecture 13
The Approximation Problem
Classical Approximating Functions
- Thompson and Bessel Approximations
Review from Last Time
Elliptic Filters
Can be thought of as an extension of the CC approach by
adding complex-conjugate zeros on the imagina
EE 508
Lecture 12
The Approximation Problem
Classical Approximating Functions
- Elliptic Approximations
- Thompson and Bessel Approximations
Review from Last Time
Chebyshev Approximations
TLP j
1
Type II Chebyshev Approximations
(not so common)
Analytic
EE 508
Lecture 10
The Approximation Problem
Classical Approximations
Review from Last Time
Least Squares Approximations of Transfer Functions
n
m
2i
2
c i -H k di2i
N
i=0
C = i=0
n
k=1
di2i
i=0
2
Possible uses of these observations (four algorithms)
1
EE 508
Lecture 1
Introduction to Course
Catalog Course Description:
E E 508. Filter Design and Applications. (3-3) Cr. 4.
Prereq: 501. Filter design concepts. Approximation
and synthesis. Transformations. Continuous-time and
discrete time filters. Discret