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
Al
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
inde
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 transf
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
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
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 (
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
Elem
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 re
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
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
Mode
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 t
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 ap
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
Typ
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
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. Transformati