Electric wave filters

Physical operation of symmetrical T- and π-Sections. The condition imposed on the above equations are Z in =Z out. Hence I 1 =V 1 /Z 0 and I 2 =V 2 /Z 0. I 1 /I 2 =V 1 /V 2 and W 1 /W 2 =V 1 I 1 cos/V 2 I 2 cos=

The ratio of the input current to output current is completely defined by the series arm impedance and shunt arm impedance. From KVL

Transmission constant of a filter section  The filter section is terminated on an image impedance basis The transmission constant: is the transfer impedance from the input terminals of the filter section to the output terminals, V 1 /I 2. Z I1 is the image impedance seen looking to the right of the input terminals, V 1 /I 1 ∞ is the attenuation of the filter section is the phase-shift constant of the filter section W 1 is the power entering the input terminals W 2 is the power leaving the output terminals is the angle of lead I 1 with respect to I 2. ∞ is a measure of the ratio of the power input to the power output of a filter section which is terminated in its characteristic impedance.

Units of attenuation of transmission loss Attenuation in nepers= W general is any particular power level which might be under discussion W reference is the power level employed as the reference from which W general is to be measured Attenuation in decibel=

General consideration Low pass filter: pass currents of all frequencies below a critical or cutoff frequency Reduce the amplitude of currents of all frequencies above this critical frequency Pass all frequencies from zero upto a predetermined number of cycles with theoretical zero attenuation The frequency at which the theoretical attenuation takes on a finite value is called the cut-off frequency  High pass filter: pass currents of all frequencies above a critical or cutoff frequency Reduce the amplitude of currents of all frequencies below this critical frequency Attenuates all frequencies from zero upto a predetermined number of cycles The frequency at which the theoretical zero attenuation obtains is called the cut-off frequency

Fundamental filter equation