Transcript Ideal Frequency Response for a Butterworth Filter

ACTIVE LEARNING
ASSIGNMENT
AVS(2151101)
130800111009-SHAH BRIJESH
130800111010-SHAH RIYA
 Introduction
 Elliptical, Butterworth, Chebyshev, Bessel, Cauer
 Butterworth had a reputation for solving "impossible"
mathematical problems
"An ideal electrical filter should not only completely reject the
unwanted frequencies but should also have uniform sensitivity for
the wanted frequencies".
Such an ideal filter cannot be achieved but Butterworth showed that successively
closer approximations were obtained with increasing numbers of filter elements of
the right values. At the time, filters generated substantial ripple in the passband,
and the choice of component values was highly interactive. Butterworth showed
that a low pass filter could be designed whose cutoff frequency was normalized to
1 radian per second and whose frequency response (gain)
What Are Diodes Made Out Of?
• Silicon (Si) and Germanium (Ge) are the two most common
single elements that are used to make Diodes. A
compound that is commonly used is Gallium Arsenide
(GaAs), especially in the case of LEDs because of it’s large
bandgap.
• Silicon and Germanium are both group 4 elements,
meaning they have 4 valence electrons. Their structure
allows them to grow in a shape called the diamond lattice.
• Gallium is a group 3 element while Arsenide is a group 5
element. When put together as a compound, GaAs creates
a zincblend lattice structure.
• In both the diamond lattice and zincblend lattice, each atom
shares its valence electrons with its four closest neighbors.
This sharing of electrons is what ultimately allows diodes to
be build. When dopants from groups 3 or 5 (in most cases)
are added to Si, Ge or GaAs it changes the properties of
the material so we are able to make the P- and N-type
materials that become the diode.
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
Si
+4
The diagram above shows the
2D structure of the Si crystal.
The light green lines represent
the electronic bonds made when
the valence electrons are
shared. Each Si atom shares
one electron with each of its four
closest neighbors so that its
valence band will have a full 8
electrons.
 Filter Specification
Transmission specifications for a bandpass filter. The magnitude response of a filter that just meets
specifications is also shown. Note that this particular filter has a monotonically decreasing
transmission in the passband on both sides of the peak frequency.
 Filter Specification
Specification of the transmission characteristics of a lowpass filter. The magnitude response of a filter that just
meets specifications is also shown.
Frequency-Selection function
Passing
Stopping
Pass-Band
Low-Pass
High-Pass
Band-Pass
Band-Stop
Band-Reject
Passband ripple
Ripple bandwidth
Summary – Low-pass specs
-the passband edge, wp
-the maximum allowed variation in passband, Amax
-the stopband edge, ws
-the minimum required stopband attenuation, Amin
 Butterworth Filters
The magnitude response of a Butterworth filter.
 Butterworth filter calculation for
frequency response
As the Butterworth filter is maximally flat, this means that it is designed so that
at zero frequency, the first 2n-1 derivatives for the power function with respect
to frequency are zero.
Thus it is possible to derive the formula for the Butterworth filter frequency
response:
Where:
f = frequency at which calculation is made
fo = the cut-off frequency, i.e. half power or -3dB
frequency
Vin = input voltage
Vout = output voltage
n = number of elements in the filter
Butterworth also showed that his basic low-pass filter could be modified to
give low-pass, high-pass, band-pass and band-stop functionality.
 Frist orde law pass butter
worth filter
Fig;a circuit diagram
Fig;b frequency response
Frist order high pass butter worth filter
Fig;a circuit diagram
Fig;b frequency response
 2nd order law pass butterworth filter
Fig;a circuit diagram
Fig;b frequency response
 2nd order high pass butter worth filter
Fig;a circuit diagram
Fig;b frequency response
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Note that the higher the
Butterworth filter order, the higher
the number of cascaded stages
there are within the filter design,
and the closer the filter becomes
to the ideal “brick wall” response.
In
practice
however,
Butterworth’s ideal frequency
response is unattainable as it
produces excessive passband
ripple.
Refrances;
 https://www.google.co.in/url?sa=i&rct=j&q=&esrc=s&so
urce=images&cd=&cad=rja&uact
 http://www.electronicstutorials.ws/filter/fil67.gif?81223b
 http://www.electronics-tutorials.ws/filter/fil13.gif?81223b
 http://www.radio-electronics.com/info/rf-technologydesign/rf-filters/butterworth-rf-filter-calculationsformulae-equations.php
 Refrances book . Ramakant Gayakwad 8th ,edotion,
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