230 



BELL SYSTEM TECHNICAL JOURNAL 



y 40 



U -40 



-60 



75 1.0 125 150 175 2 00 2 25 2 50 2 75 300 3 25 



FREOUEINCY 



Fig. 3 — Chart for loss computations. 



has been computed for values of / > 1 and is shown plotted for various 

 w's in Fig. 3. The approximate attenuation, in db, for any given 

 values of a and ni can be obtained from the chart by adding 

 20(m + 1) logio 1/q! to the appropriate curve. 



A similar chart for the phase characteristic is furnished by Fig. 4, 



which represents the quantity |^ ^^ - /)'»+i + (i + /-)»'+i J • 



The values given are arithmetic, although the scale is logarithmic. 

 The approximate envelope of the ripple in the phase characteristic 

 about the ideal straight line can therefore be found, in degrees, by 

 multiplying the chart values by 0:'"+^ 



In using these charts it should be remembered that they are based 

 upon the approximate formulae (23) and (24) which fail in the vicinity 

 of the transition interval. The results, therefore, should always be 

 checked by an exact computation. 2" It should also be observed that 

 in complicated filters the numerical departure of tanh djl from its 

 ideal value in most frequency ranges is very small. The effects of 

 slight errors in calculations or of small deliberate variations in the 



^^ See, for example, the comparisons in Figs, 11 and 12. 



