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# Filters in Network Analysis

## Chebyshev Approximation

Chebyshev Approximation: Chebyshev Approximation – In the earlier section, we have studied that the Butterworth approximation is the best at ω = 0. But as we move towards cut-off frequency, ωc = 1, approximation becomes poorer. It departs from ideal characteristics. Let us consider an approximation which “ripples” about the normalized magnitude, unity, in the pass …

## Butterworth Approximation

Butterworth Approximation: Butterworth Approximation – In low-pass filter design, we have to assume that all transmission zeros of the system function are at infinity. Then the magnitude function in general form can be written as, Where k is called as dc gain constant as it is the magnitude at ω = 0. f (ω2) is …

## Normalized Low Pass Filter Characteristics

Normalized Low Pass Filter Characteristics: Normalized Low Pass Filter Characteristics – The passive filters are the filters consisting only passive components such as resistors, inductors, capacitors. These classical filters are designed starting with filter networks such as T type, Π type etc. Low Pass Filter Characteristics is obtained by connecting inductor in the series arm …

## Composite Filters in Network Analysis

Composite Filters in Network Analysis: Composite Filters in Network Analysis – In prototype filter sections, the attenuation characteristic is not very sharp in the attenuation band as it is expected. This drawback can be overcome by using m-derived filter sections which are derived from respective prototype filter sections. But it is observed that in the …

## Impedance Matching using Half Sections

Impedance Matching using Half Sections: While connecting number of different sections in the filter, it is very important to match the impedances of the sections at the junction points. Thus a T section should not be connected to a π section directly as both the sections have different impedances. Hence it is necessary to use …

## m Derived Band Stop Filter

m Derived Band Stop Filter: The m Derived Band Stop Filter can be derived from the prototype band elimination filter section in the exactly same way as the m-derived band pass filter. The m Derived Band Stop Filter section is as shown in the Fig. 9.37. The relationship between frequency of infinite attenuation (f1∞ , …

## m Derived Band Pass Filter

m Derived Band Pass Filter: We can obtain m Derived Band Pass Filter if the prototype band pass filter is simplified according to the network in the Fig. 9.35 which has been used to obtain m-derived low pass and high pass sections. The T section in each case will have a shunt impedance, Z2/m + …

## m Derived High Pass Filter

m Derived High Pass Filter: The m Derived High Pass Filter T and π sections are as shown in the Fig. 9.32 (a) and (b). Consider that the shunt arm of the T section resonates at a frequency of infinite attenuation i.e. f∞ which is selected just below cut-off frequency fc. The frequency of resonance is …

## m Derived Low Pass Filter

m Derived Low Pass Filter: The m Derived Low Pass Filter T and π sections are as shown in the Fig. 9.29 (a) and (b) respectively. Consider that the shunt arm of T section resonates at the frequency of infinite attenuation i.e. f∞, which is selected just above cut-off frequency fc. The frequency of resonance …

## m Derived Filters

m Derived Filters: m Derived Filters – The first disadvantage of prototype filter sections can be overcome by connecting two or more prototype sections of same type (either all T type or all π type) in cascade. In such a cascade connection, attenuation to the frequencies in pass band remains zero ideally, but attenuation to …