Operation of Thermionic Vacuum Tube Circuits 



By F. B. LLEWELLYN 



Synopsis: Given the static rhararteristic of j^rid current-grid potential, 

 and plate current-plate potential, for any three element vacuum tube, the 

 general exact ecjuations for the output current when the tube is connected 

 in circuits of any impedance whatsoever, and excited by any variable 

 voltage, are here derived. The method of derivation is illustrated in the 

 si^ecial case where resistances only are considered, and the adaptation of 

 complex impedance to use in non-linear ecjuations is shown. Ap[)r()xima- 

 tions that are allowable in various practical applications are indicated, 

 and the equations are applied in some detail to grid-leak detectors, and in 

 brief to other types of detectors, modulators, amplifiers and oscillators. 



Certain repetitions of previous work are contained in these pages, as it is 

 believed that the applications of the novel features introduced are illustrated 

 thereby better than by a description dealing only with new material. 



THE equations in use at the present time for the relation between 

 input voltage and output current in thermionic vacuum tubes 

 are those developed by a number of pioneers in Radio Communica- 

 tion. They have been summarized very concisely, and somewhat 

 extended in an important paper by John R. Carson, entitled "A 

 Theoretical Study of the Three Element Vacuum Tube," which 

 appeared in the Proceedings of the Institute of Radio Engineers, 

 April, 1919. For some time past the need of relations which include 

 the effect of the variation of certain quantities, considered constant 

 in Mr. Carson's paper, has been growing. Especially in the case of 

 detection and modulation has this need become pronounced. More- 

 over, in the special case of grid leak detectors, the need for a general 

 theoretical analysis has not, to the author's knowledge, been com- 

 pletely satisfied. 



Purpose 



It is, therefore, the purpose of the present paper to derive general 

 exact equations for the output current from a three-element thermi- 

 onic vacuum tube when it is connected in circuits of general impedance, 

 both on the input and output sides, and to show specific methods of 

 applying these general equations to several special cases, with em- 

 phasis on the case of the grid leak detector. It is also proposed to 

 show that, whether used for detectors, modulators, amplifiers, or 

 oscillators, the same fundamental theory applies. It is iioped that 

 the theory and methods given will form a basis upon which a com- 

 plete rational design of vacuum tube circuits may be biult. 



Theory 



In the derivation of these equations, no limitations whatever should 

 be imposed. Consider a three-element vaciumi tube connected in 

 circuits of general impedance on both input and outi)ut sides. The 



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