Equivalent Networks of Negative-Grid Vacuum Tubes at 

 Ultra-High Frequencies 



By F. B. LLEWELLYN 



It is shown that the equivalent network of negative-grid vacuum tubes 

 both at low and at very high frequencies may be expressed in many different 

 forms. Several are suggested and the advantages of two are described in 

 some detail. One of these is closely analogous to that which is in general 

 use at low frequencies and requires only the addition of resistive components 

 in series both with the cathode-grid and the grid-plate capacitances to make 

 it applicable to frequencies where transit time effects are appreciable 

 though moderately small. The resistance in series with the grid-plate 

 capacitance is negative in sign. In this form of the equivalent network, 

 electron transit times do not introduce a phase angle into the amplification 

 factor. 



The paper is divided into two parts. The first gives a descriptive in- 

 terpretation of the results while the second contains the mathematical 

 manipulations. 



Part I 



TT 7'HEN the equivalent network of a vacuum tube is mentioned, 

 ^ ^ it brings to the mind of practically every radio engineer a 

 certain combination of resistances and capacitances together with an 

 internal /^-generator which has become familiar through years of use. 

 Historically, this equivalent network did not spring into being full 

 grown like Athena from the forehead of Zeus, but was the result of a 

 slow and painful development. The beginnings of the equivalent 

 network of negative-grid vacuum tubes are to be found in the work of 

 Nichols where it was pointed out that a non-linear resistance is the 

 equivalent of a fixed resistance in series with a generator. As a 

 second step, Van der Bijl's relation states that the plate current in a 

 vacuum tube is a function of the plate voltage plus a constant times 

 the grid voltage. This constant was identified with our well-known 

 amplification factor n and it was an easy step thereafter to combine 

 the Van der Bijl and Nichols relations and represent the vacuum tube 

 by the equivalent network shown in Fig. 1. 



Here the cathode is located at C and the plate at P. Between them 

 the vacuum tube is represented by the internal plate resistance rp 

 acting in series with the fictitious generator noVg. This equivalent 

 naturally represents conditions between the cathode and plate at very 

 low frequencies only, because the low-frequency impedance between 

 the grid element and the other electrodes is so high that it can safely 

 be disregarded. Such an equivalent network was satisfactory only so 



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