COLD CATHODE TUBES FOR 



Al Dlo 



KIIEQUENCY SIGNALS 1389 



negative resistance of the tube equals the sum of the source and load 

 resistance. Large values of gain are not practical because this imposes 

 undesirable restrictions on the constancy of the circuit and tube im- 

 pedances. 



Additional restrictions on gain arise from bandwidth and distortion 

 considerations. If it is assumed that both Rt and Lt are independent of 

 frequency over the voice band, it is possible to use the above equation 

 for an approximate calculation of bandwidth. The half-power point 

 occurs at the frequency /, at which the reactive term equals the sum of 

 the other three terms in the denominator, or 



fc = 



Ra + Rl + Rt 

 2tLi 



(6) 



Since the gain does not fall off at low frequency, the upper cut-off 

 frequency fc is a measure of the bandwidth. Substituting Ra and Rl 

 from equation (5) into equation (6) gives 



/c (1 — Low frequency I.V.G.) = 



Rt 



2irLt 



(7) 



Thus for a given tube an increase in gain is accompanied by a decrease 

 in bandwidth. 



As shown in Fig. 12 the impedance of a negative resistance tube is 

 dependent on the current passing through it. This will cause some dis- 

 tortion as the signal current swings above and below the average direct 

 current value. The distortion is small so long as the non-linear tube 

 resistance is small compared to the total circuit impedance. 



It can be seen from the above discussion that for a given tube the 

 gain, bandwidth, and distortion are all dependent on the source and load 

 impedances. Fig. 17 shows the experimental performance of a typical 

 tube for the special case where source and load impedances were equal. 

 Insertion gain has been converted to power gain in db. The distortion 



Rt+ja;Lt 



(a) (b) 



Fig. 16 — Transmission circuits with ami withoiit tube. 



