Chebyshev filter
General immunity of radio, the passage of noise through the path of the device. Calculated the data transmission speed and the duration of single elements, bandwidth filters transmission and reception, the effective value of interference in the channel.
Рубрика  Коммуникации, связь, цифровые приборы и радиоэлектроника 
Вид  курсовая работа 
Язык  английский 
Дата добавления  12.12.2014 
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Abstract
In the first section describes the General immunity of radio, the passage of noise through the path of the receiving device. And also made the choice and justification of the structural scheme and the circuit diagram. The second section consists of part of the settlement, where calculated the necessary data transmission speed and the duration of single elements, bandwidth filters transmission and reception, the effective value of interference in the channel, time of entry into synchronism and time synchronization reference fluctuations.
The characteristic of Bessel filters that makes them valuable to digital designers. Very few filters are designed with square waves in mind. Most of the time, the signals filtered are sine waves, or close enough that the effect of harmonics can be ignored. If a waveform with high harmonic content is filtered, such as a square wave, the harmonics can be delayed with respect to the fundamental frequency.
The content
Normative references
Conventions and abbreviations
Introduction
1. Classification of the filter
1.1 The filter on the concentrated elements
2. The review of similar schemes
3. The choice and justification of the filter circuit
4. Topological model of the filter and the transfer function of the voltage
4.1 Implementation of the normalization HPF
4.2 Definition of the polynomial Bessel
4.3 the Reverse transition from a fixed to a planned HPF
5. Calculation of elements of the circuit
5.1 Preparation of a complete scheme of filter
Conclusion
List of the used literature
Normative references
In this course work used references to the following documents:
Table №1  Used normative references:
Symbol 
Name 

ГОСТ 2.70184 
The scheme. The kinds and types. General requirements to the implementation 

ГОСТ 2.70275 
Rules of execution of electrical circuits 

ГОСТ 2.70881 
Rules of execution of electrical circuits and digital computer technology 

ГОСТ 2.70972 
The system of marking of circuits in electrical circuits 

ГОСТ 2.75271 
Conventions document in graphical diagrams. Device telemechanics 

ANSI 
American national standard notation 

DIN 
The European standard notation 

ГОСТ 2.20180 ЕСКД 
Designation of products and design documents 

ГОСТ 2.60195 
Operational documentation 

Ф.7.142008 СМК 
Rules for the registration of training documentation. General requirements to graphic documents 

radio noise reception channel
Conventions and abbreviations
RC  filters of lower
Op  operational amplifier
BPF  bandpass filter
LPF  low pass filters
BSP  band stop filter
HPF the high pass filter
SV  source voltage,
VC voltagecontrolled
NF  negativefeedback
Introduction
Since 1926, for the first time have been measured by nonlinear distortion, proposed more than 20 different measurement methods. All of these methods can be divided into 5 main groups: one tone, two tones, with discrete spectrum, with continuous spectrum, with the working signal. Each of these groups has its varieties, which differ according to the method of registration and allocation of products of nonlinear distortions.
In General, the methods of measurement of nonlinear distortions in paths in the STI is a great variety. Widely spread method of harmonics as the most simple in experiments and convenient for calculations. Less common other methods: the difference of tone modulated tone intermodulation (twotone).
For the mentioned methods has its own field of application. In this case, each of them uses a special signals, ensuring the most efficient detection products distortion.
Visibility of nonlinear distortions of the real input signal is connected with the fact, how often, if we consider the process in time, or with what probability, if you apply to him statistical measure of the instantaneous values fall within the essential nonlinearity tract STI. Many, probably, had to observe, as the decrease of the signal level in congested channel disappears less of the hoarse sound. It the less, the less emissions signal fall within the overload.
In this work is discussed in detail strip Chebyshev filter, included in the composition of the installation for measurement of nonlinear distortion by the method of bands noise.
Filters with the characteristic of Chebyshev have a relatively high ratio cost/efficiency.
1. Classification of the filter
The filter this frequencyselective device which passes signals of certain frequencies and detains or weakens signals of other frequencies. The filters finding application in processing of signals happen: analog or digital, passive or active, linear and nonlinear, recursive and not recursive.
Filters can be classified by a number of signs:
1) by the form they are divided on: filters of the lower frequencies (FLF); filters of the top frequencies (FTF); strip filters (SF); the projector (blocking) filters (RZh). In separate group the phase filters (PF) can be allocated;
2) depending on the polynoms used at approximation of transfer function distinguish filters: critical attenuation, Bessel, Butterworth, Chebyshev;
3) on element base filters are divided on: passive and active filters. Active filters include in the scheme RLC  the filter of an active element as which operational amplifiers are often used.
The Amplitudefrequency Characteristics (AFC) of various filters are submitted in fig. 2.23. The filter of the lower frequencies  passes low frequencies and detains high (fig. 2.23, a), the filter of the top frequencies  detains low frequencies and passes high (fig. 2.23, b), the strip filter  passes a strip of frequencies from щ1 to щ2 and detains those frequencies which are located above or below this strip of frequencies (fig. 2.23, c), the rezhektorny filter  detains a strip of frequencies from щ1 to щ2 and passes the frequencies located above or below this strip of frequencies (fig. 2.23, d). In the specified filters the coefficient of transfer and phase shift depend on the frequency of an entrance signal. Filters at which the coefficient of transfer remains to constants, and phase shift depends on frequency, are called as phase filters.
Figure 1 Amplitudefrequency characteristic
As it was mentioned earlier, depending on the approximating polynom filters are divided into filters of critical attenuation, Bessel, Butterworth, Chebyshev. At a statement of the principle of creation of the approximating functions of filters as a basis usually use the FILTER of the LOWER FREQUENCIES. In fig. 2.24 AMPLITUDEfrequency characteristics of the specified filters of the lower frequencies are shown.
Figure 2 Filter passes low frequencies and detains the high
Amplitudefrequency characteristics the filter of the lower frequencies of Butterworth has quite long horizontal site and sharply falls down behind cut frequency. The transitional characteristic of such filter at a step entrance signal has oscillatory character. With increase in an order of the filter of fluctuation amplify. The characteristic of the filter of Chebyshev falls down more coolly behind cut frequency. In a passband it has wavy character with a constant amplitude. Fluctuations of transition process at a step entrance signal are stronger, than at Butterworth's filter. Bessel's filter is characterized by the smaller length of a horizontal site, than Battevort's filter and more flat recession AMPLITUDEFREQUENCY CHARACTERISTICS behind cut frequency, than Butterworth and Chebyshev's filters. This filter possesses the optimum transitional characteristic (transition process has practically no fluctuations). The filter of critical attenuation possesses considerably the worst amplitudefrequency characteristic in comparison with Bessel's filter, but has no reregulation. Generally the filter of critical attenuation is inferior to Bessel's filter concerning quality of working off of an entrance step signal.
Bessel's filter  in electronics and processing of signals one of the most widespread types of linear filters which distinctive feature is the maksimalnogladky group delay (the straightline phasefrequency characteristic). Bessel's filters vsegoispolzut for audiocrossovers more often. Their group delay practically doesn't change on polosypropuskaniye frequencies owing to what the form of the filtered signal at the exit of such filter in polosepropuskaniye remains the almost invariable.
1.1 The filter on the concentrated elements
In drawing the example of the elementary LC filter of the lower frequencies is shown: when giving a signal of a certain frequency on a filter entrance (at the left), tension at the filter exit (on the right) is defined by the relation of jet resistance of the coil of inductance (X_L = \omega L) and the condenser (X_C = 1/\omega C)
The transfer coefficient can be calculated the FILTER of the LOWER FREQUENCIES, considering tension divider formed by frequencydependent resistance. Complex (taking into account shift of phases between tension and current) resistance of the coil of inductance is Z_L = j\omega L = jX_L and the Z_C condenser = 1 / (j\omega C) =  j X_C, where {j} ^ {2} =1, therefore, for not loaded LC filter
K = {Z_C Z_C Z_C} { Z_L + Z_C}\\, \!. (1.1)
Substituting values of resistance, we will receive for frequencydependent coefficient of transfer:
K (\omega) = \frac {1} { 1\omega^2 \, LC } = \frac {1} { 1(\omega/\omega_0) ^2 }\\, \!. (1.2)
Figure 3 Simple LC filter of the lower frequencies
Apparently, the coefficient of transfer not loaded ideal the FILTER of the LOWER FREQUENCIES beyond all bounds grows with approach to the resonant frequency \omega_0=1/\sqrt {LC}, and then decreases. At very low frequencies transfer coefficient the FILTER of the LOWER FREQUENCIES is close to unit, on very high  to zero. It is accepted to call dependence of the module of complex coefficient of transfer of the filter on frequency the amlitudnofrequency characteristic (AMPLITUDEFREQUENCY CHARACTERISTICS), and dependence of a phase on frequency  the phasefrequency characteristic.
In real schemes active loading which lowers good quality of the filter is connected to an exit of the filter and prevents a sharp resonance AMPLITUDEFREQUENCY CHARACTERISTICS near frequency \omega_0. Sizes \rho = \call sqrt {L/C} the characteristic resistance of the filter or wave resistance of the filter. The FILTER of the LOWER FREQUENCIES loaded on the active resistance equal characteristic, has not resonant AMPLITUDEFREQUENCY CHARACTERISTICS, approximately constant for frequencies \omega <\omega_0, and decreasing as 1/\omega^2 at frequencies above \omega_0. Therefore, frequency \omega_0 is called cut frequency.
2. The review of similar schemes
The term Bessel refers to a type of filter response, not a type of filter. It features flat group delay in the passband:
Figure 4 the flat group delay in the pass band
This is the characteristic of Bessel filters that makes them valuable to digital designers. Very few filters are designed with square waves in mind. Most of the time, the signals filtered are sine waves, or close enough that the effect of harmonics can be ignored. If a waveform with high harmonic content is filtered, such as a square wave, the harmonics can be delayed with respect to the fundamental frequency if a Butterworth or Chebyshev response is used. The Fourier series of a square wave is:
(2.1)
This means that a square wave is an infinite series of odd harmonics, or sine waves, summed together to create the square shape. Obviously, if a square wave is to be transmitted without distortion, all of the harmonics  out to infinity  must be transmitted. This means that the square wave can be high pass filtered without distortion, if the 3 dB point of the filter is significantly lower than the fundamental. If the square wave is low pass filtered, however, the situation changes dramatically. Harmonics will be eliminated, producing distortion in the square wave. It is the job of the designer to decide just how many harmonics must be passed and what can be eliminated. Suppose that the designer wants to keep five harmonics. The resulting waveform looks something like this:
Figure 5  Form of a wave of five harmonicas
This may be acceptable to the designer  it depends on the timing of the leading and trailing edge of the waveform. The elimination of harmonics will result in rounding of the edges, and therefore delay in the leading and trailing edges of the digital signal. Of more importance, the harmonics that are passed will not be delayed.
The Bessel approximation has a smooth passband and stop band response, like the Butterworth. For the same filter order, the stop band attenuation of the Bessel approximation is much lower that that of the Butterworth approximation.
The following figures are representative of a low pass filter. The response characteristics are mirror imaged for high pass filters.
Figure 6 Passbands of the filter of Bessel
The designer can see that there is no ripple in the passband of a Bessel filter, and that it does not have as much rejection in the stop band as a Butterworth filter.
The phase response of the three filter types is shown below. The Bessel response has the slowest rate of change of phase.
Figure 7  The phase response of the three filter types
3. The choice and justification of the filter circuit
Input voltage, Uin 
9 мВ 
0,009 

Amplification factor, КU 
1000 
1000 

Input resistance, Rin 
15 kОм 
15000 

The range of amplifi frequency, fН .. fВ 
1000..10000hz 
1000 

The recession of the amplitudefrequency characteristics 

on the bottom, fН 
40 дб/дек 

the upper frequency, fВ 
40 дб/дек 

Type of filter 
the Bessel filter 

Output current Iout, 
12 мА 
0,012 

Power supply voltage Ups, 
± 15 В 

Solution 

Proceeding from the formula of determining the coefficient of the gain: 

found R2 = 100Ч100000 = 10 МОм. 
1500000 

To reduce the dependence of the offset of the input current is found resistance R3: 

14851,48515 

Selected resistance R3 = 100 кОм. 

The calculation of the filter high frequency. 

As the HPF chosen the filter on ИНУН. This scheme allows you to build a filter in the minimum number of elements. It has lowimpedance output, the small dispersion of the values of elements and the possibility to receive relatively high values of the coefficient of amplification. 

For the Butterworth filter of the second order, from the application A[1], selected coefficients:В = 1,414214; С = 1,000000; 

The gain for the HPF took KU = 10; 

Choose the value of capacitance of C1 and C2 according to the formula: 

С1 = С2 = 10 / fC = 10 / 1 = 10 мкФ 
0,01 

Took C1 = C2 =10 мкФ. 

Calculated the value of the resistors 

where: 

wc = 2ЧpЧf = 2Ч3,14Ч1 = 6,283 рад/с. 
6280 

Chosen R5 = 6.2 кОм. 

кОм 

Chosen R4 = 39 кОм. 

Chosen R7 = 6.8 кОм и R6 = 62 кОм. 

The gain level shall be determined by the formula [1]: 

The resulting gain HPF KU = 10; 

3.4 . The calculation of the lowfrequency filter. 

To obtain the total gain to the voltage, satisfying job, from the condition of the KU preamplifier =100, and the KU HPF= 10, calculated the required HPKU 

1 

Ratios: В = 1,414214; С = 1,000000; 

The gain for the LPF took KU = 10; 

Choose the value of capacitance C3 according to the formula: 
C3= 

С3 = 10 / fC = 10 / 1000 = 0,01 мкФ 

Took С3 = 10 нФ. 

Found C4, satisfies the condition: 

Ф 
9,5E08 
C4 

Took С4 = 91 нФ. 

Calculated value сопротивленй by the formulas 

Ом 

where: 

wc = 2ЧpЧf = 2Ч3,14Ч1000 = 6,283Ч103 рад/с. 
62800 

Chosen R8 = 12 кОм. 

Ом 

Chosen R9 = 2.4 кОм. 

Ом 
1357,497938 

Ом 

The gain level shall be determined by the formula 

Chosen R10 = 150 кОм R11 = 16 кОм. 

The resulting gain LPF KU = 10; 

To select a chip, you want to find current and voltage on the elements of the scheme. 

To simplify the calculations take some assumption  operational amplifier will be considered ideal. 

Take marginal input parameters: Uin = 0,2 •103 В и f = 1000 Hz. 

The voltage at the output of the first stage is: 

Uout1 = КU1 * Uin = 100 • 0,2•103 = 0,02 V. 
0,9 
Eoy1 

The output voltage of the second stage as well: 

Uout2 = КU2 * Uout1 = 10 • 0,02 = 0,2 V. 
9 
Eoy2 

The output voltage of the third cascade as well: 

Uout3 = КU3 * Uout2 = 10 • 0,2 = 2 V. 
9 
Eoy3 

Load resistance is defined from the following expression: 

Ом 

For determining the loads were scheme of replacement (Annex 2). For this input voltage presented voltage source Евх = 0,2 •103 In, OA replaced voltage sources Eoy1 = 0.02 V Eoy2 = 0.2 V, Еоу3 = 2 V equal to voltage on their output, the input current of the op neglected, but capacitors replaced capacitive resistance 

, 
1,59236E11 

15923,56688 

15923566,88 

1676164,88 

where f is the upper frequency range bandwidth. 

According to the scheme of substitution, using Kirchhoff's laws, amounted to a system of equations: 

I1 + Ioy1  I2 = 0 
I1 
5,88119E07 

I2 + I3  I4 = 0 
I2 
59518801981 

I4 + Ioy2  I5 = 0 
I3 
0,000003 

I5+ I6  I7 = 0 
I4 
59518801981 

I7 + Ioy3 = Iн 
I5 
0,037029252 

I1·(R1 + R2) = Eвх  Eoy1 
I6 
0,0000001 

I2·( j·Xc1)  I3·(R5  j·Xc2) = Eoy1 
I7 
0,037029352 

I3·(R5  j·Xc2) + I4·R4 = Eoy2 
Ioy1 
59518801981 

I5·R8  I6·(R9  j·Xc4) = Eoy2 
Ioy2 
59518801981 

I6·(R9  j·Xc4) + I7·( j·Xc3) = Eoy3 
Ioy3 
0,025029352 

As a result of solution of the system were the currents in the branches of the system: 

I1 = 2 нА, I2 = 3,77 мкА, I3 = 1,81 мкА, I4 = 5,58 мкА, I5 = 1,07 нА, 

I6 = 0,114 мкА, I7 = 0,113 мкА, Ioy1 = 3,77 мкА, Ioy2 = 5,58 мкА,Ioy3 = 10мА. 

Select from the directory of the op type К140УД6А with the following parameters: 

The nominal value of the supply voltage Ups = ±15 В. 

Amplification factor КU = 70000 

Input offset voltage UВХ.СМ. = 5 мВ. 

Input bias current IВХ.СМ. = 30 нА. 

Differential input resistance RВХ.ДИФ = 3 MОм. 

Maximum output current IВЫХ.MAX. = 25 мА. 

Slew rate output voltage VUВЫХ = 2,5 В/мкс. 
2,5 

That is, the maximum output current of the circuit does not exceed the permissible values for the opamp, the gain to the voltage of the opmuch more than the gain of the cascades and the input resistance many times more than the resistance of a resistor R1. 

The dependence of the rate of rise of the output voltage has the form: 

The maximum slew rate output voltage is equal to the amplitude: 

В/мкс 
0,157 

4. Topological model of the filter and the transfer function of the voltage
Filter Topology
The most common filter topologies are SallenKey and Multiple Feedback filters. The major differences are:
SallenKey 
Multiple Feedback 

Noninverting 
Inverting 

Very precise DCgain of 1 
Any gain is dependent on the resistor precision 

Less components for gain = 1 
Less components for gain > 1 or < 1 

Opamp input capacity must possibly be taken into account 
Opamp input capacity has almost no effect 

Resistive load for sources even in highpass filters 
Capacitive loads can become very high for sources in highpass filters 

4.1 Implementation of the normalization HPF
In electronics and signal processing, a Bessel filter is a type of linear filter with a maximally flat group delay (maximally linear phase response). Bessel filters are often used in audio crossover systems. Analog Bessel filters are characterized by almost constant group delay across the entire passband, thus preserving the wave shape of filtered signals in the passband.
The filter's name is a reference to Friedrich Bessel, a German mathematician (17841846), who developed the mathematical theory on which the filter is based. The filters are also called BesselThomson filters in recognition of W. E. Thomson, who worked out how to apply Bessel functions to filter design.
The transfer function
Figure 8  The schedule of the amplitudefrequency characteristic and group delay for the lowfrequency filter of Bessel of the fourth order.
A plot of the gain and group delay for a fourthorder low pass Bessel filter. Note that the transition from the pass band to the stop band is much slower than for other filters, but the group delay is practically constant in the pass band. The Bessel filter maximizes the flatness of the group delay curve at zero frequency.
A Bessel lowpass filter is characterized by its transfer function:
(4.1)
where is a reverse Bessel polynomial from which the filter gets its name and is a frequency chosen to give the desired cutoff frequency. The filter has a lowfrequency group delay of .
4.2 Definition of the polynomial Bessel
The roots of the thirdorder Bessel polynomial are the poles of filter transfer function in the s plane, here plotted as crosses.
Figure 9  Bessel polynomials
The transfer function of the Bessel filter is a rational function whose denominator is a reverse Bessel polynomial, such as the following:
The reverse Bessel polynomials are given by:
(4.2)
Where
(4.3)
Example
(a) (b)
Figure 7 (a,b)  Gain plot of the thirdorder Bessel filter, versus normalized frequency
Group delay plot of the thirdorder Bessel filter, illustrating flat unit delay in the passband
4.3 the Reverse transition from a fixed to a planned HPF
The transfer function for a thirdorder (threepole) Bessel lowpass filter, normalized to have unit group delay, is
The roots of the denominator polynomial, the filter's poles, include a real pole at s = ?2.3222, and a complexconjugate pair of poles at s = ?1.8389 ± j1.7544, plotted above. The numerator 15 is chosen to give a gain of 1 at DC (at s = 0).
The gain is then
(4.4)
The phase is
(4.5)
The group delay is
(4.6)
The Taylor series expansion of the group delay is
(4.7)
Note that the two terms in щ2 and щ4 are zero, resulting in a very flat group delay at щ = 0. This is the greatest number of terms that can be set to zero, since there are a total of four coefficients in the third order Bessel polynomial, requiring four equations in order to be defined. One equation specifies that the gain be unity at щ = 0 and a second specifies that the gain be zero at щ = ?, leaving two equations to specify two terms in the series expansion to be zero. This is a general property of the group delay for a Bessel filter of order n: the first n ? 1 terms in the series expansion of the group delay will be zero, thus maximizing the flatness of the group delay at щ = 0.
5. Calculation of elements of the circuit
From the task it is visible, that it is necessary to provide recession AFC on the bottom and top frequency. Hence, it is necessary to u^e filters of the botton and top frequencies (FBF and FTF). As recession AFC both on bottom and on the top frequency is equal a db/deck it is clear that it is necessary to use filters of the first order. Also it is impossible to forget that is necessary to provide the fixed input impedance, size in 75 kOhm. On the basis of these reasons the block diagramme of the amplifier of an alternate current is made. It is presented on fig. 1
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Figure 10. The Block diagramme of the amplifier of an alternate current where P  a preamplifier, FBF  the filter of the bottom frequencies, FTF  the filter of the top
Frequencies
The recommended design procedure is shown on an example. Proceeding from the block diagramme of amplifiers of an alternate current it is necessary to develop the basic circuit.
The preamplifier is represented by not inverting scale amplifier captured by an individual feedback. That is its amplification factor Kl=10. In parallel to its input
terminal there is resistor Rl, 75kOhm. By means of 1 his resistor the set fixed input impedance is provided. The preamplifier exit is jointed to input terminal FBF. FTF free passes a signal with frequency, below 1MHz and carries out recession AFC on limit inferiors of frequencies a 15db/deck on frequencies, above 100 Hz. Exit FBF is jointed to input terminal FBF. FTF free passes a signal with frequency, above certain frequencies in 100Hz and carries out recession ACF on a complete limit a + 15db/deck on frequencies, below limit inferiors of frequencies of 1MHz.
In the given course work it is necessary to apply active filters on operating amplifiers (OA). Active filters usually have one or several active components (transistors, etc.) and, unlike passive, have the big complexity and can use on low frequencies (more low 0,5 mHz) owing to absence in them of reactors.
If in the task kind ACF of the amplifier filters Battervort are applied to realisation FBF and FTF in other cases, or filters Bessell or Chebishev is not specified. As already it was spoken earlier filters of the first order us?.
The amplification factor of consistently jointed links thus accordingly is multiplied.
5.1 Preparation of a complete scheme of filter
Full scheme shall be drawn up in accordance with the results of calculations of the circuit elements HPF, and LPF. When this is taken into account, that for creation of the bandpass filter (PF), filters of high and low frequencies should be connected in series. As shown by engineering practice, to get a good range filter, it is advisable to first place the HPfilter to suppress the lowfrequency components of the signal and noise at the output of the LPF. In figure 7, the full scheme of band pass filter with the indication of values of parameters of elements of the circuit, received in the result of calculations. On the basis of this scheme after incorporating additional elements will be developed drawing of the basic electric circuit of the filter.
Figure 11 Complete the calculation scheme of the bandpass filter
5.2 Development of the basic electric circuit
Development of the basic electric circuit is the most important point of work. The basic electric circuit of the block of the bandpass filter determines the full composition of its elements and links between them and gives a detailed presentation on the work of the filters. The diagram depicts all the electrical elements, links between them, as well as elements, which ends the input and the output circuits. Grounds for execution of the basic electric circuit is the scheme of band pass filter (figure 11).
Conclusion
In fact Bessel filter with a maximally flat response in the pass band is not so attractive as it may seem, because in any case have to put up with some uneven performance in bandwidth (for the filter Butterworth it will be a gradual lowering of the characteristics of the approach to frequency fc, and for the Chebyshev filter  pulsation, distributed throughout the bandwidth). In addition, active filters, built from elements, ratings of which have a certain tolerance, will possess the characteristic different from the target, and this means that, in reality, the characteristics of the Butterworth filter will always have a place some unevenness in bandwidth.
In the light of very rational structure is the Chebyshev filter. Sometimes it is called filter, because of its characteristics in the field of transition has a large slope due to the fact that the amount of bandwidth allocated several equal ripple, the number of which increases with the order of the filter. Even with a relatively small ripple (order 0, 1dB) Chebyshev filter provides much greater slope of the characteristics of the area than the Butterworth filter. To Express this difference quantitatively, suppose that you want to filter with the uneven performance in a bandwidth of not more than 0.1 dB attenuation at the frequency by 25% from the limit of the frequency bandwidth. The calculation shows that in this case it is required 19pole Butterworth filter, or just a 8pole Bessel filter.
The idea that you can put up with the pulsations of the characteristics of the bandwidth for the sake of the steepness of the transition area characteristics, be brought to its logical conclusion in the idea of the socalled filter (or filter Cauer), which allowed pulsation characteristics as the amount of bandwidth, so, and in the store for the sake of the security of the slope of the transition area even more than the characteristics of the Chebyshev filter. With the help of computer it is possible to construct elliptic filters so as easy as the classical Chebyshev, Butterworth filters and Bessel.
List of the used literature
1. Opadchy Yu.F., Gludkin O. P. Analog and digital electronics: The textbook for higher education institutions. Under the editorship of O. P. Gludkin.  M.:goryachy liniyaTelkom. 2005.  768s.
2. Gorbachev G. N., Chaplygin E.E. Industrial electronics. M.: Energoatomizdat, 1988.
3. Zhigalov A.A. Electronics bases. M:energoatomizdat, 1985.
4. Tokheym R. Microprocessors. Courses and exercises. М: World of 1988.
5. Gusev of V. G. Elektronik and microprocessor equipment: The textbook for higher education institutions.  M of a.:vyssh.shkol., 2006.  799s.
6. Apsemetov A.T., Ismailov S. U. Development and calculation of relaxation generators on operational usilitelyakh./Methodical instructions to a term paper on discipline of "Electronic engineer": Shymkent, 2000.Steven W. Smith The Scientist and Engineer's Guide to Digital Signal Processing.  Second Edition.  SanDiego: California Technical Publishing, 1999.
7. Britton C. Rorabaugh Approximation Methods for Electronic Filter Design.  New York: McGrawHill, 1999.
8. B. Widrow, S.D. Stearns Adaptive Signal Processing.  Paramus, NJ: PrenticeHall, 1985.
9. S. Haykin Adaptive Filter Theory.  4rd Edition.  Paramus, NJ: PrenticeHall, 2001.
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