dr. eman azab microelectronics elct 703 (w19) lecture 7...

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



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



3Figure from Dr. Ahmed Nader Microelectronics Lectures (Winter 2015)

FILTER DESCRIPTION

DR. EMAN AZAB



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



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



6Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.

FILTER DESIGN PROCESS

DR. EMAN AZAB



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


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)


DR. EMAN AZAB



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



DR. EMAN AZAB



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


DR. EMAN AZAB



10

Once the filter desired response is selected, selection of

T(s) that meets the desired response is done

Filter Approximation


FILTER TRANSFER FUNCTION

DR. EMAN AZAB



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



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




FILTER APPROXIMATION

DR. EMAN AZAB



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



15

All pole filter

All transmission zeros are

located at ∞

Maximally flat response

Magnitude response of Nth

order filter


BUTTERWORTH FILTER

DR. EMAN AZAB



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


BUTTERWORTH FILTER

DR. EMAN AZAB



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


BUTTERWORTH FILTER

DR. EMAN AZAB



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


CHEBYSHEV FILTER

DR. EMAN AZAB



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




CHEBYSHEV FILTER

DR. EMAN AZAB



21

Є is a parameter that depends on Amax

The order of the filter ‘N’ is selected according to Amin


FIRST ORDER FILTER FUNCTIONS

Passive and active

realizations

DR. EMAN AZAB



22

FIRST-ORDER FILTER FUNCTIONS

DR. EMAN AZAB



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:


DR. EMAN AZAB



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


DR. EMAN AZAB




dr. eman azab microelectronics elct 703 (w19) lecture 7...

Documents