Filters are used in electronics to produce the desired signal to us a certain frequency, that is, of all applied to the input signal is passed to the output signals of the frequency reference in advance. Active filters are constructed of capacitors, resistors, transistors and amplifiers (operating). Any filter from its input to output only a certain portion of their spectrum. By skipped spekru frequencies are classified:

1. Low pass filter

2. Highpass filter

3. Band-pass filter

4. Rejector

Fig.1. Frequency response

1-LPF, HPF-2, 3. Band-pass filter, 4-suppression filter.

where f_ср - the cutoff frequency.

The low pass filter passes all frequencies from zero to a predetermined cutoff favg and sslablyayut all vyshy favg all frequencies. High pass filter, on the contrary, pass frequencies above favg. Bandpass filter passes frequencies for which lies between two given favg and dams on the contrary weaken the frequency in this region, as seen in Figure 1.

Compared with passive active filters have several advantages:

1. They are not used indiktivnosti coil, which has a number of shortcoming in the application;

2. They are relatively cheap;

3. Provide increased amplitude on bandwidth;

4. They are easy to make multistage;

5. They are relatively easy to set up;

6. They are not large in mass and size.

There are several types of active filters and most rasprastronennye – is Butterworth, Chebyshev, and Bassel.

How do they differ from each other? Answer to this question is their frequency characteristic. Frequency response Battervorda on bandwidth can be considered uniform, and it is as flat. Battervord filters immersed nonlinear frequency response. These filters are used when the task have the same gain for all spectra in the frequency bandwidth of the one shown in Figure 2.

Frequency response Chebyshev filter consists of wavy teeth in the passband and uniformly in the stopband, the higher the order of the filter, the greater the number of teeth. The amplitude of these teeth can be specified in the design of the filter and is usually set at 0.5, 1, 2 or 3 dB, the increase allowable wave amplitude gives a steeper slope of the filter in the transition area.

All this is shown in Figure 3 as an example low-pass Chebyshev filter.

In the transition area slope Chebyshev filter can exceed 6 dB / octave at one pole. Chebyshev filter is very useful in cases where it is desirable to have a transition region is very high rate of change of attenuation, ie, a very steep slope, the unevenness of the filter in the passband – price to pay for it.

Fig. 2. Frequency response Butterworth lowpass.

1 – pole (first order) 2 – two-pole (second order), 3 – pole (third order), 4 – four pole (fourth order), 5 – the fifth order; fCD = l kHz.

On the Bessel filter is referred to as linear-phase filters with linear or delayed. This means that the lag phase of the signal at the output of the filter to the signal at the input increases linearly with frequency. Therefore Bessel filters almost do not give release when applying for their input step signals. This property makes these filters the most appropriate filtering square waves without changing their shape.

Fig. 3. Frequency response Chebyshev’s filters

Treble with the passband 3 dB – sixth order (/), the fourth-order (2), third order (3), second order (4); f – off frequency.

Fig.4. The frequency characteristics of the low pass filter of the second order Bessel.

Now for some definitions. The attenuation coefficient α determines the shape of features on the site and view perehodnom emission characteristics in the passband near the transition area. Thus, the coefficient of damping coefficient ¬ determines the shape of the frequency response of the filter, ie its type. Thus, second-order Butterworth filter has a damping factor α, equal to 1.414, and Chebyshev filter  second order with the unevenness of 3 dB is α = 0,766.

The same scheme, depending on the choice of the values ​​of its components can act as Bessel, Butterworth or Chebyshev filter, and the shape of the frequency response of the filter is determined by the damping.

S one of the sensitivity of the filter parameters with respect to the other parameters is the ratio of the change in the value of the first parameter to the second change, if the change of the second parameter caused the change of the first.

Conclusions.

1. Active filters are used in almost any electronics industry and therefore deserve to be studied.

2. Although active filters have many advantages over passive, they also have disadvantages, which primarily concerns the restriction of the maximum operating frequency. (It is hoped that with the improvement of operational amplifiers, the value of this limit will be reduced.)

3. Procedures for calculating the active filters are not too complex, even if the scheme (such as a universal filter circuit) look complicated. To complete the design of active filter must be calculated and the sensitivity of its parameters, the ratio needed for this calculation are contained in the books of the number listed at the end of this chapter.

4. Active filters Sally and Kay and filters with a parallel loop – a simple circuit, you can rely on, but compared with the more universal and slozhntmi biquadratic active filters, they are less stable. Combining filters second order (and first-order filter, if necessary to obtain a filter of odd order), you can receive multi-stage filters of higher orders. The procedure for calculating multistage filters boring, but not complicated. Using the techniques presented here, you can design their own high-quality active filters.

1. Allen Е., Modern Techniques and Applications of Active Filters, Department of Electrical Engineering and Computer Science, Santa Barbara, Calif. 1974.
2. Berlin H. M., Design of Active Filters with Experiments, Howard W. Sams and Co., Indianapolis, Ind., 1977.
3. Hilbura J. L., Johnson D. E., Manual of Active Filter Design, McGraw-Hill, New York, N. Y., 1973.
4. 4.Johnson D. E., Johnson J. R., Moore H. P., A Handbook of Active Filters, Prentice-Hall, Englewood Cliffs, N. J., 1980.
5. Lancaster D., Active Filter Cookbook, Howard W. Sams and Co., Indiana-polis, lnd., 1975.
6. Toby G. E., Graeme J. G., Huelsman L. P., Operational Amplifiers, Design – and Application, McGraw-Hill, New York, N. J., 1971. [Имеется перевод: Грэм Дж., Тоби Дж. Хьюлсман Л. Проектирование и применение операционных усилителей. Пер. с англ./ М.: Мир, 1979.]

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