Miu.it. /.v/'fcr./.vc /i i.\ win: viinns 





As a numerical example of the determiiiatiou of the constants of a 

 filter section of the type uiuier consideration, assume that the lower 

 cut-ofT frequency, /i, is 20,000 cycles, and that the upper cut-off fre- 

 (luency,/3, is 2.5,000 cycles and that the fre(iuenc\' of infinite atlenu- 

 .ition,/», is 30,000 c>clcs. Assume, furthermore, that the value of 

 the mid-series image impedance, Z,,, at the mid-frec|ucncy is (500 ohms. 

 Then from formula (41), w = .742; hence from (37), Li = .0284 henrN-; 

 from (38), C, =.00224 X 10' farad; from (39) Lo = . 00.577 henry and 

 from (40) 6'; = .0048GX lO'* farad. Assuming d = .Ol, the value of 

 Zi AZ-i as given by formula (31) at/m (22,300 cycles) is found to he 

 .30.5 17(i°.4. Referring to formula (22), in which /v=.30.5 and <> = 

 170°. 4, or to the curves of Fig. 11, this value of Zi/AZ^ corresponds 

 approximately to .041 napiers or .30 TU. Similarly, from equation 

 (23), or from the curves of Fig. 12, this value of Zi 4Zo gives l.lo 

 radians, or 07°, for the phase constant. At zero frequency, the value 

 of Z\ AZz is, from equation (31), .542/0°, which corresponds to 1.3G 

 napiers or to 11.8 TU. Likewise, at infinite frequency, the value of 

 Zi 4Z2 is 1.23y'0°, which corresponds to an attenuation loss of 1.97 

 napiers or to 10.0 TU. From the curves of F"ig. 12, the phase constant 

 is zero both at zero and at infinite frequency. 



Composite Wave Filters. It has previously been pointed out that 

 certain groups of the structures listed in Table II have the same mid- 

 series or mid-shunt image impedance characteristics but that the 

 various structures in such a group may have different attenuation 

 and phase constant characteristics. 



If a filter is composed of any number of symmetrical or dissym- 

 metrical sections, so joined together that the image impedances at 

 the junction pwints of the sections are identical, the attenuation and 

 phase constant characteristics of the compxasite structure so formed, 

 are equal to the sum of the respective characteristics of the individual 

 sections. Furthermore, the image impedances of the composite filter 

 w ill be determined by the image imjjedances of the accessible ends of 

 the terminating sections. The desirability of forming such composite 

 filters arises from the fact that a better disposition of attenuation 

 and phase can be obtained by employing, in one composite structure, 

 a number of different types of the characteristics shown in Pig. 7. 



