NEGATIVE-GRID VACUUM TUBES 585 



it is evident that the internal generator is eliminated from the cathode- 

 grid path if Zo is chosen so that 



V = zJZ,. (9) 



The impedance Zo will accordingly be taken to be defined by (9). 

 The result is that the fundamental equations for Fig. 9 become: 



,^here 



The various definitions in (13) are seen to be slightly simpler than 

 those in (3) but it must be remembered that the delta-network involves 

 one more current-path than the original ultra-high-frequency network, 

 Fig. 1. The delta corresponding to (10)-(13) is shown in Fig. 10. 



At frequencies only moderately high, all of the impedances in Fig. 10 

 are composed of combinations of ordinary resistances and capacitances. 

 Both ZpA and Zo consist of a condenser and resistor in series. 



In the case of the cathode-plate path in Fig. 10, the equivalent 

 combination of resistance and capacitance may be represented by 

 either a parallel combination of resistance and capacitance which is in 

 series with the At-generator, as shown at (6) in Fig. 11, or a //-generator 

 of different value acting in series with a resistance, and the whole being 

 shunted by a capacitance connected between cathode and plate, as 

 shown at (c) in Fig. 11. The latter picture is in more strict accord 

 with conventional practice but the mathematical relationships involve 

 a choice of definitions for 11. It is found by trial that this choice may 

 be made so that ii in Fig. 12 is defined merely as /zo, its low-frequency 

 value, and is independent of frequency. When this definition is 

 adopted, we have in general the equivalent netw-ork of Fig. 12 which 

 holds at high as well as low frequencies. This differs from Fig. 10 in 

 the cathode-plate path only, and Z', Z" are defined as follows, where mo 



