420 BELL SYSTEM TECHNICAL JOURNAL 



specific situations where some mode other than the TE Oln gives a smaller 

 W/P. For example, it may be shown that for P between 0.97 and 1.14 

 the TE 021 mode yields a smaller W than the TE 013 or TE 014 modes. 

 However, the margin is small, and for larger P, the TE 02n modes become 

 progressively poorer. 



Limitation on Frequency Range of Tunable Cavity as Set 

 BY Ambiguity 



In the design of a tunable cylindrical resonant cavity intended for use 

 in the TE 0\n mode, the requirements on Q may dictate a diameter large 

 enough to sustain TE 02n' or TE 03n' modes. Also, the range of variation 

 of cavity length may be such that the TE 01 (w + 1) mode is supported. As 

 the cavity is required to tune over a certain range of frequency, the maximum 

 frequency range possible in the TE 01« mode without interference from the 

 TE 01 (w + l)t or any TE 02 or TE 03 modes is of interest. The interference 

 from the TE 0\(n-\- 1) limits the useful range of the TE 01« by the presence 

 of extraneous responses at more than one dial setting for a given frequency 

 or more than one frequency for a given dial setting. In applications so far 

 made, it has been possible to eliminate extraneous responses from the TE 02 

 and TE 03 modes, but crossings of these modes with the main TE Oln mode 

 have not been permitted. No designs have had diameters sufficiently large 

 to support TE 04 modes. 



The desired relations are easily obtained by simple algebraic manipula- 

 tion of equation (1). For simplicity in presentation of the results, we in- 

 troduce some symbols applicable to this section only: 



A = r^T B = r^T = 2.247 X 10=^" 



Ao = value of A for TE 01« modes = 13.371 X 10 

 / = A/Ao 



:Vo = (a/Ly at low frequency end of useful range of TE 01m mode 



maximum/ 



frequency range ratio = 



minimum /" 



The values of A and / depend upon the interfering mode under considera- 

 tion. For the TE Oln modes, A = 44.822 X lO'", / = 3.3522. 



The two typical cases of interest are shown on Fig. 3. For case I, am- 



t It is easy to show that the extra,neous respo^nse from the TE 01 (m — 1) mode is not 

 limiting. The proof depends on the inequality n* > (« -f 1) (w — 1). 



