IMPEDANCE CORRECTION OF WAVE FILTERS 787 



portion of the second series condenser. The maximum reflection 

 coefficient over about 95 per cent of the nominal transmitting band is 

 slightly greater than 1 per cent. We can summarize these quantitative 

 results in the rough statement that each of the three stages in the prog- 

 ress from the most primitive filter section to the relatively complicated 

 network of Fig. 12-C appears to reduce the reflection coefficient ob- 

 tainable over a given frequency range by a factor of about three or four. 



Impedance Correction for Filters Operating in Parallel 



The modifications which must be made in these sections in order to 

 adapt them for use with filters which must operate in parallel are simi- 

 lar to those which were made in adapting "m-type" sections to this 

 service. The final branch of each termination is omitted, its place 

 being taken within the transmitting band of the filter to which it be- 

 longs, by the impedance of the parallel, attenuating, filters of the 

 system. The parallel filters cannot however be relied upon to simulate 

 the missing branch, even in this frequency range, with great accuracy. 

 If we wish to preserve the high standards achieved by the terminations 

 in other circumstances, therefore, it is, in general, necessary to in- 

 troduce an auxiliary network in shunt with the circuit as a whole to 

 improve the approximations to the missing branches. When this is 

 done the reflection coefficient of the complete system is substantially 

 identical in any transmitting range with that which would be obtained 

 from the corresponding filter operating alone. 



The thorough exploitation of the possibilities of these auxiliary net- 

 works leads to a marked improvement in the performance even of the 

 well-known .r-terminations. The reflection coefficient characteristic 

 of a typical pair of high- and low-pass filters has already been shown 

 by Curve I of Fig. 9. The high value of the reflection coefficient of 

 these filters is largely due to the fact that neither filter in its attenuating 

 range supplies quite enough admittance to take the place of the missing 

 shunt branch of the other filter. The addition of a simple tuned cir- 

 cuit resonating between the transmitting bands to compensate for this 

 deficiency in admittance reduces the reflection coefficient to the level 

 shown by Curve II. The results for x-terminated band-pass filters are 

 even more striking. Fig. 18 gives the susceptance at the line terminals 

 of a set of three filters for several different conditions. The suscep- 

 tance should ideally be zero. Curve I gives its value when no aux- 

 iliary network is added, Curve II, the level to which it is reduced by 

 the auxiliary network suggested by Mills, and Curve III the charac- 

 teristic which can be obtained with the help of a more elaborate aux- 

 iliary network. These curves can be given quantitative significance if 



