MICROELECTRONICS ELCT 703 (W19) LECTURE 7: ACTIVE FILTERS (1)
Dr. Eman Azab
Assistant Professor
Office: C3.315
E-mail:
[email protected]. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
1
INTRODUCTION
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
2
Filters are used in all communication systems
Oldest Technology used for Filter design is Passive LC
Filters
Passive LC filters works well for high frequencies, however
for low- frequencies the inductors used are large and
bulky
Large inductors can’t be fabricated in ASIC, therefore
inductor-less filters became a need for electronics
engineers
Different techniques are used to realize inductor-less
filters, we will focus on these methods in our Course
EXAMPLES OF FILTER APPLICATIONS
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
3Figure from Dr. Ahmed Nader Microelectronics Lectures (Winter 2015)
FILTER DESCRIPTION
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
4
A voltage Filter circuit is a linear circuit that can be
represented as a two-port network with transfer function
T(s)
Gain G(ω) of the filter is the magnitude of T(s) in dB, and
Attenuation A(ω) function is the inverse of the Gain
Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
FILTER DESCRIPTION
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
5
The filter shapes the magnitude and phase of the input
signal according to the transmission function
Magnitude of T(s) is defined as 𝑇 𝑗𝜔
Phase function of T(s) is defined as ∅ 𝑗𝜔
The filter job is to select from the frequency spectrum the
desired signal or to change the phase of the input signals
Pass signals within a certain frequency range and stop
signals outside this range
Thus a filter must have passband(s) and stopband
FILTER TYPES: IDEAL RESPONSE
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
6Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
FILTER DESIGN PROCESS
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
7
Filter design begins with the
user identifying the desired
filter response
However, ideal response cannot
be achieved by physical circuits
The filter user must define
acceptable deviations from the
ideal response
Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
Amax ‘Passband ripple’ is the
maximum attenuation in the
passband (0.05 to 3dB)
Amin is the minimum attenuation
in the stopband (20 to 100dB)
FILTER DESIGN PROCESS
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
8
Filter design begins with the
user identifying the desired
filter response
A transition band between the
passband and stopband is
defined as the response
cannot fall abruptly
Transition band is defined
between ωp and ωs
Selectivity factor is the ratio
between ωs andωp
Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
FILTER DESIGN PROCESS
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
9
Filter response is defined by:
Passband frequency ωp
Stopband frequency ωs
Amax and Amin
Selectivity factor ωs/ωp
The ideal filter response
have unity selectivity factor,
very small Amax and very
large Amin
Higher order filter and
complex hardware
FILTER DESIGN PROCESS
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
10
Once the filter desired response is selected, selection of
T(s) that meets the desired response is done
Filter Approximation
Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
FILTER TRANSFER FUNCTION
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
11
T(s) is defined by a ratio between two polynomials
The filter order is N, and for stable system M ≤ N
Zeros of T(s) are called transmission zeros
Poles of T(s) are called natural modes
FILTER TRANSFER FUNCTION
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
12
Zeros and poles can be real or complex (Complex
conjugate)
Transmission zeros occur in the stopband of the filter (jωaxis)
We have transmission zeros at ∞ (N-M zeros)
Poles must be in the LHP (negative real parts)
Poles are located in the passband
FILTER TRANSFER FUNCTION: EXAMPLE
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
13Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
FILTER APPROXIMATION
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
14
There are two famous filter approximations for lowpass
response
Butterworth and Chebyshev Filters
These filters responses can realize different responses
via frequency transformations
These functions can be used directly to design the filter
as long as the filter specs are defined
BUTTERWORTH FILTER
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
15
All pole filter
All transmission zeros are
located at ∞
Maximally flat response
Magnitude response of Nth
order filter
Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
BUTTERWORTH FILTER
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
16
Є is a parameter that
depends on Amax
As N increase the degree of
passband flatness increases
The order of the filter ‘N’ is
selected according to Amin
Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
BUTTERWORTH FILTER
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
17
Poles (natural modes) of
the filter is defined from a
graphical representation
given below
Poles are located in a
circle with radius
ωp(1/Є)1/N
Poles are spaced by
equal π/N
Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
BUTTERWORTH FILTER
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
18
All poles have radial
distance from the origin
with ωo=ωp(1/Є)1/N
The gain of the filter can
be adjusted as required
K is DC gain
Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
CHEBYSHEV FILTER
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
19
All pole filter
Equiripple response in passband
Number of maxima and minima in the passband is the
filter’s order
Magnitude response of Nth order filter
CHEBYSHEV FILTER
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
20Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
CHEBYSHEV FILTER
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
21
Є is a parameter that depends on Amax
The order of the filter ‘N’ is selected according to Amin
Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
FIRST ORDER FILTER FUNCTIONS
Passive and active
realizations
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
22
FIRST-ORDER FILTER FUNCTIONS
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
23
A cascade of first-order filters can realize higher order
ones
First-order filters can be cascaded with second order
sections to realize odd order filters
In case of cascading Active-RC sections, the loading effect
is negligible
Transfer function is the product of each section T(s)
General first-order transfer function:
FIRST-ORDER FILTER FUNCTIONS
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
24
Natural mode at 𝑠 = −𝜔𝑜
Transmission zero at 𝑠 = − 𝑎𝑜𝑎1
High frequency gain at a1
Values of a1 and ao will determine the filter’s response
FIRST-ORDER FILTER FUNCTIONS
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
25Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.
FIRST-ORDER FILTER FUNCTIONS
DR. EMAN AZAB
ELECTRONICS DEPT., FACULTY OF IET
THE GERMAN UNIVERSITY IN CAIRO
26Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.