Formulas a re deri ved for t h e electromag netic field ge nerated by an a rbi t ra ry current d ist rib ut io n wit hin waveguid es of rectang ular, circular, and coaxia l cross Rect io ns. These formula s are ob ta in ed by ge nera li zing a na logous formula s obtained in a previo us paper 2 for cavities of th,e sam e cr oss sectio n. As a check on t h e formulas, it is sh ow n t hat t he fi eld from a n axially d irected dip ole w it h in a circular g uide redu ces to t he free s pace valu e a t he radius increase indefi nite ly.
A general expression for the noise-power spectrum generated by t he random emission of electrons of arbitrary trajectori es within a wavegu ide is obtained. A n ume rical solut ion of t he potential distribution within a plane d iode is effected , and a famil y of curves from wh ich the potential di stribu t ion may be obtained is graphed. A graphical co mparison bet ween several actual potential distribution s and Von Laue's solu tion is gi,·en. The above resul ts are u t ili zed to derive t he equ ivalent mean-square fl uctuation current du e to the space charge w ith in a diode for two cases of potential d istribution, namely, t he linear di s tribution, and t hat di stribu tion which occur at the neighborhood of the beginning of the retarding field. For t he case of t he li near potent ial distribution, the equivalent no ise temperatu re of the diode con ductance is sho\\'l1 to be eq ual to th e cathode tempe ratu re.
The noise power spectrum of a diode with a temperature limited current and also for a diode with a retarding field is shown to be the sum of two parts. One, the ``pure'' shot effect, is the spectrum which would obtain if the electrons were all emitted with zero velocity, that is, if the cathode were at zero temperature (and still maintained the same emitting properties). The second is the thermal contribution, namely, 4kTg, where T is the cathode temperature and g is the conductance of the electron stream.
The contribution of space charge to the admittance of a diode with a retarding field is calculated by computing the instantaneous electronic current induced in an external circuit. A discussion of the variation of the susceptance of a typical diode with frequency is given.
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