1410 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



inverting and inverting cases are different, (24) may become negative 

 so that the 4-pole cannot ahvays be matched and (26) and (27) are dif- 

 ferent so that the gains through the 4-pole are not the same in the two 

 directions. Furthermore, (26) can be greater than unity so that modula- 

 tors may have gain. However, as will be shown, the converter gain 

 given by (27) is still restricted to values less than unity. It is also seen 

 that the matching susceptances are no longer zero and that the gain 

 varies with frequency so that the bandwidth is limited. 



If we remove the restriction that a conjugate match exists and operate 

 the 4-pole between arbitrary admittances, it may be shown in (11) and 

 (12) that the conductance of the 4-pole may become negative, and in (14) 

 and (15) that the gain may have any value, however large. This is true 

 for both noninverting and inverting modulators and converters. How- 

 ever, we see in (14) and (15) that the ratio of the modulator gain to the 

 converter gain is | F21/F12 1". This is greater than unity, so that for the 

 same operating conditions the modulator gain will be greater than the 

 converter gain. Although increased gain is possible, it is obtained at the 

 expense of reduced bandwidth and increased sensitivity to changes in the 

 terminating admittances, particularly in the case of converters. The 

 present analysis will therefore be restricted to the case where a conjugate 

 match exists. 



1.0 



0.9 



0.8 



0.7 



6 



0.5 



0.4 



0.3 



0.2 



0.1 



1 2 3 4 5 6 7 8 9 10 11 12 13 14 



X 



Fig. 2 — Conductance contours of noninverting transducer. 



