250 BELL SYSTEM TECHNICAL JOURNAL 



tially in series, making up an equivalent resonator oscillating at the n = 1 

 mode frequency. If one considers further, for the sake of argument, that 

 there is no coupling between resonators, all the modes would have the same 

 frequency but the net inductance and capacitance of the equivalent reso- 

 nator for each mode of periodicity n, would be proportional to N/2n and 

 2n/N, respectively. Thus for the n = \ mode, the equivalent L is four 

 times and the equivalent C is one quarter of the respective values for the 

 IT mode. The tuner capacitance added to the equivalent resonator for the 

 w = 1 mode, on the other hand, may be considered to be approximately a 

 series-parallel arrangement of capacitances each of which is that between 

 the tuner and one anode segment, Ct '. the two parallel capacitances at the 

 positive anode segments connected in series through the tuner ring with 

 the two parallel capacitances at the negative anode segments, the combina- 

 tion having a net capacitance Ct ■ For the w mode, the net tuner capaci- 

 tance added per half wavelength potential variation is made up of two 

 capacitances each of magnitude one half of that between the tuner and one 

 anode segment, connected in series through the tuner; the net tuner capaci- 

 tance is thus Cr/4. 



By similar reasoning for any mode, one may conclude that the added 

 tuner capacitance per half wavelength sector increases as n decreases, while 

 the net resonator capacitance across which the tuner is shunted decreases as 

 n decreases. In this way the increased effectiveness of the tuner in varying 

 the mode frequencies of the low periodicity modes is accounted for. In 

 actuality the resonators in the half wavelength variation of RF potential are 

 not in simple series connection because of the phase relations between them; 

 the approximation improves for smaller n. Also because of the phase rela- 

 tion between adjacent resonators, the adjacent tuner to segment capacitances 

 are not charged to the same potential and so are not actually in simple 

 parallel connection. Furthermore, the coupling between resonators is im- 

 portant. These considerations modify the above argument somewhat but 

 do not affect the conclusions reached as to the trend of tuning for the differ- 

 ent modes. In all the tuning schemes described, second order effects come 

 in through change in the electrical lengths of the straps and tuner as the 

 frequency is varied. 



If one arranges to vary the characteristics of the straps by means of a 

 movable tuning member as in the scheme of Fig. 36 (c), considerably greater 

 tuning ranges may be achieved than by the means just described. In this 

 instance, the straps are enlarged to channels of U-shaped cross section, 

 in and out of which the tuning member of "cookie cutter" shape is driven. 

 The effect of insertion of the tuning member is to increase the capacitance 

 per unit length of the strap system by increasing the interstrap capacitance 

 and to decrease the inductance per unit length by effectively increasing the 



