Test: Filters - Electrical Engineering (EE) MCQ

A filter is called a low pass filter if it passes all frequencies up to the cut-off frequency f_c without attenuation and attenuates all other frequencies greater than f_c. This transmits currents of all frequencies from zero up to the cut-off frequency.

A band pass filter passes frequencies between two designated cut-off frequencies and attenuates all other frequencies. A band pass filter has two cut-off frequencies and will have the pass band f₂-f₁; f₁ is the lower cut-off frequency, f₂ is the upper cut-off frequency.

For a T-section, the value of input impedance when it is terminated in Z_o is
Z_in=(Z₁/2)+(Z₂((Z₁/2)+Z_o))/((Z₁/2)+Z₂+Z_o) and Z_in=Z_o. On solving, the expression of the characteristic impedance of a symmetrical T-section is Z_OT=√(Z₁²/4+Z₁Z₂).

On short circuiting the port 2 of T-section, we get the expression of short circuit impedance Z_sc as Z_sc=(Z₁/2)+((Z₁/2)xZ₂)/((Z₁/2)+Z₂). On solving we get Z_sc=(Z₁²+4Z₁Z₂)/(2Z₁+4Z₂).

sinhϒ/2=√((1/2(coshϒ-1)/(1/2(1+Z₁/2Z₂-1))). The value of sinh⁡ϒ/2 in terms of Z₁ and Z₂ is sinh⁡ϒ/2=√(Z₁/4Z₂).

The value of one decibel is equal to 0.115 N. One decibel = 0.115 N where N is the number of nepers and N = log_e(V₁/V₂).

A filter is called high pass filter if attenuates all frequencies below a designated cut-off frequency f_c and passes all other frequencies greater than f_c. Thus the pass band of this filter is the frequency range above f_c and the stop band is the frequency range below f_c.

A band elimination filter passes all frequencies lying outside a certain range, while it attenuates all frequencies between the two designated frequencies. It is also referred to as band stop filter.

On open circuiting the port 2 of T-section, we get the expression of the open circuit impedance Z_oc as Z_oc=Z₁/2+Z₂.

Z_oc=Z₁/2+Z₂ and Z_sc=(Z₁²+4Z₁Z₂)/(2Z₁+4Z₂) => Z_ocxZ_sc=Z₁Z₂+Z₁²/4 =Z_o²T. The relation between Z_OT, Z_oc, Z_sc is Z_OT=√Z_ocZ_sc.