ELECTRICAL WAVE FILTERS 



417 



and hence the capacitance ratio would be 1/2 (125) or 62.5. The band 

 width possible would then be twice that of the crystal alone. However, 

 when the effect of dissipation is considered it is found that not much 

 has been gained by employing the anti-resonant circuit. For the re- 



/TTf\ 



Co 



Hh' - -' 



rHnnrs 



Co 



= 125 



C| 



ABC 

 Fig. 8 — Use of an anti-resonant circuit to broaden the resonance region of a crystal. 



sistance, at resonance of the crystal and electrical circuit combination, 

 will be the resistance of the electrical resonant circuit since that of the 

 crystal is small compared to the electrical element. Hence we have 

 doubled the impedance of the anti-resonant circuit and have the re- 

 sistance of the electrical circuit. Hence the ratio {Q) of reactance to 

 resistance of the anti-resonant circuit is double that of the electrical 

 element alone. Even this Q, however, is insufficient to make a narrow 

 band filter whose band width is 1.6 per cent (twice that possible with 

 a crystal alone) and hence no useful purpose is served by combining a 

 crystal with an electrical anti-resonant circuit. 



I — mn — I 



2 

 Ro-R| 



I — WW — 



FILTER 

 SECTION 



\A/W^ 1 



2 



Ro-R|- 



— WW — ' 



A B 



Fig. 9 — Circuit showing resistances on the ends of filter sections. 



Suppose, however, that all of the dissipation of the filter section be 

 concentrated at the ends of the sections, either in series or in parallel 

 with the filter as shown on Fig. 9. Then provided these resistances are 

 within certain limits, they can be incorporated in the terminal resist- 

 ances of the filter by making these resistances either smaller or larger 

 for series or shunt filter resistances respectively. Between sections the 

 resistances on the ends of the filter can be incorporated with other 



