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Home Electric Networks Filters The BandElimination Filter  


The BandElimination FilterA filter of this type is designed to pass freely currents of all frequencies except those within a definite band. Three sections of a constantk bandelimination filter are shown in Fig. 41. By comparison with the bandpass filter,
and
since, for the constantk filter, L_{1}C_{1} = L_{2}C_{2} A filter of this type will pass all frequencies such that Z_{1}/Z_{2} will lie between 0 and 4. Thus,
the solution of which is
and
To find the upper and lower frequency limits, the impedance ratio is equated to zero. Thus, Z_{1}/Z_{2} = ω_{c}^{2}C_{2}L_{1}/(1  ω_{c}^{2}L_{1}C_{1}) = 0, and from this, two values ω_{c} = 0 and ω_{c} = ∞ are obtained. From these two relations and from the preceding paragraph it follows that the bandelimination filter will pass all frequencies from zero to f_{c}' cycles per second, will attenuate all frequencies from f_{c}' to f_{c}", and will pass all currents having frequencies between f_{c}" and infinity. This filter then eliminates the band f_{c}' to f_{c}". The method of finding the design equations is similar to that used for the bandpass filter. If the two expressions of equation 93 are subtracted, it will be found that (f_{c}"  f_{c}') = 1/(4πsqrt(L_{2}C_{1})). Since, for the constantk filter, L_{1}C_{1} = L_{2}C_{2} and Z_{K} = sqrt(L_{2}/C_{1}) = sqrt(L_{1}/C_{2}). this equation can be solved for C_{1}, and
Infinite and zero values occur at
Using these relations and the equations just obtained, it can easily be shown that
Calculations for the various inductors and capacitors for a simple bandelimination filter are made from equations 94 and 95.


Home Electric Networks Filters The BandElimination Filter 