CLASSICAL FILTER 

 Putting in RIcoq for Ljl and IjcocR for C 



2 



z = 



coq 2 \ CO J 



R+J 



CO 



R— -^ 



Rco, 



a>. 



2 CO 



which simpHfies eventually to 



Z = R 



COc' 



,2coj 



+ j 



[coc) +I2W 



In Graphs 26, 27 and 28 the transmission characteristic, phase shift and 

 terminal impedances for a classical low-pass filter section are plotted. The 

 transmission characteristic is clearly much superior to an R-C filter section, 

 since it possesses an attenuation slope of 18, instead of 6, dB's per octave. 

 Furthermore, it is better than a 3-stage R-C filter of tapered sections, for 

 whereas the latter would be 9 dB's down at the cut-off frequency, the L-C 

 filter is only 3 dB's down. The characteristic is therefore squarer, more Hke 

 the ideal filter, than anything that can be done with passive-element filters 

 comprising R's and C's. 



The impedance presented to the generator and load is substantially 

 resistive and equal to R in the pass-band. 



High-pass filter 

 In the classical high-pass section {Figure 5.18) the series arms are capaci- 



2C 



2C 



/? = (Vc)V2 



R = (L/Cf'^ 



Figure 5.18 



tances, and the shunt arm an inductance. We have, as before 



but now, Zi = — 7/coC and Z^ =J(oL. So Z^Z^, is still L/C, but Z1/4Z2 = 

 — \l(4co^LC). At the cut-off frequency, series resonance occurs in the filter 

 and Zq goes to zero. (1 — (1 /(4a) ^^LC)}) is therefore also equal to zero, 

 hence co^ = ll{2(LCy''^}. In the pass-band, Z^^ ^ LjC, R = (L/Q^^^ 



87 



