LOAlHil) LlSl.S .IMJ COMI'li.XS.ll I.W, M.Tll'OKKS 



425 



In this way, Fig. 3 rcpri-scnls .V and }", and Fig. 4 reprcsLiits A' 

 and 1', all to the same scale. In each of these fiRures the r-rangejs 

 to 1.5, thus including the entire transmitting band and a portion of 

 the attenuating banil half as wide as the transmitting hand. In the 



.2 .4 .6 .8 1.0 1.2 1.4 



Kig. 3 — Components of the ff'-LoatI Relative Im[x;(lancc Z' = A" + iF 



attenuating band, Z' and Z are pure imaginary; in the transmitting 

 band they are complex in general, though real for (7' = 0.5 and o- = 0.5. 



Because in practical applications the transmitting band is much 

 more important than the attenuating band. Fig. 5 has been sup[)iied 

 in order to represent A' and F in the transmitting band only, but to a 

 considerably larger scale and for more values of a. 



If a is read for a' , Fig. 3 will represent U and I' instead of A" and Y' 

 respectively. If a' is read for a, Fig. 4 will represent U' and V instead 

 of .Y and F; so also will Fig. 5. 



From Fig. 5 it will be observed that, in a certain range of a, each 

 curve of X has a maximum at some point within the transmitting 

 band (0<r<l). For any fixed value of a (in the range found below) 

 the corresponding maximum of A' and the particular value of r (critical 

 value) at which the maximum occurs are expressed by the formulas 



Max. A' = !l/4(l-2ff)\/ff(l-<r)|, 



Cnt. r = •J ' ■ ■ ■ 

 \ 4ff(l — <r) 



r(l-<r) 



as is readily found from the formula for A' — namely, the real part of 

 formula (4j. The formula for Crit. r shows that the a-range in which 



