436 



nEI.l. SVSTF.M TECIISICAL JOVRXAI. 



X= 1. Tlu- following tabic sliows the locations and widths of the first 

 ei^jht transmitting bands and attenuating bands. The critical fre- 

 quency is /i =3140, and the /-width of each compound Ijand is 5732. 



Comparison of this table with that of the first exani[)k' brings out the 

 great diversity between the two examples: the minor transmitting 

 bands in the second example are relatively and absolutely much wider 

 and situated at much lower frequencies than in the first example. In 

 the second example the first or principal transmitting band is some- 

 what wider than the first attenuating band. 



A further application of the foregoing formulas and graphs is to 

 obtain a precise and explicit solution of the important practical problem 

 f)f loading a given smooth line with lumped loading to secure specified 

 values of the critical frequency A and nominal impedance k. The 

 design-problem con.sists in determining the reciuisitc values of the load 

 inductance L' and load spacing .? in terms of /i and k and tlu' known 

 values of the inductance and capacity, L" and C", per unit length 

 of the given smooth line. Since L = sL" and C = sC'\ the solution 

 can be obtained as follows: Substituting L' = sL'\\ into (1) and 

 solving for X gives 



L"/C" 



\ = 



F--L"/C"' 



Then /J, becomes known b\- means of Fig. 7 or Fig. 7.1 or formula (22) 

 or (22.1). Next, 5 becomes known from (23) or (24): 



5=/?i Tr/i-\/L"C". 



l'"inalK-. from these formulas for X anrl .t logt'tlicr with the Halation 



L' = sL" X. it Iniinw- til, It 



j,_ D,{k--L",C") 



