1388 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



a switching tube can be adjusted by changing this spacing so long as the 

 upper limit is not exceeded. 



Although the above discussion is limited to only one adjustable cathode 

 dimension, the cathode gap, other variations are of course possible. The 

 length and depth of the hollow should be at least a few times the width 

 of the cathode gap in order that an efficient hollow be formed. Increasing 

 the hollow length or depth requires larger currents and, if carried too far, 

 the glow may not completely fill the hollow at the optimum current for 

 negative resistance. This is undesirable because the unused portion of 

 the cathode may change its properties with time and produce unstable 

 characteristics. The entire geometry may be scaled to a larger size if 

 the density of the filling gas is reduced by approximately the same 

 factor. 



The choice of cathode material is restricted by the high current 

 densities of hollow cathodes. Coatings of alkafine earth oxides or similar 

 materials have too short a Ufe. Pure molybdenum has found to give a 

 satisfactorily low sustaining voltage together with long life and stable 

 operating characteristics. Life tests have shown that tubes can be made 

 which will operate satisfactorily for the equivalent of 20 to 40 years in 

 central office service. 



It is seen from the above that by changing the cathode geometry and 

 density of the filling gas a variety of impedance properties can be ob- 

 tained. The final choice must be determined by the overall transmission 

 requirements. As an example, the transmission performance of a typical 

 tube will now be discussed. 



TRANSMISSION PERFORMANCE OF A TYPICAL NEGATIVE RESISTANCE DIODE 



The circuit of Fig. 16(a) shows a cold cathode switching tube in series 

 with a transmission path. The voltage across the load resistor Rl under 

 conditions of Fig. 16(a), divided by the voltage across Rl with no tube 

 in the circuit. Fig. 16(b), is one measure of the transmission performance. 

 This ratio, called the insertion voltage gain, is given by 



IVG = ^"^ ^J^ (^^ 



Rs + Rl +Rt + jc^L, ' ^ ^ 



The derivation of this expression assumes that the transformers are ideal 

 and that the reactance of the condenser C is negligible. Maximum gain 

 occurs at low frequency where the reactive component of tube impedance, 

 jc^Li , can be neglected. If the resistive component of tube impedance, 

 Rl , is negative, the gain will be greater than unity. The gain approaches 

 an infinite value as the unstable condition is approached where the 



