50 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



The calculated and measured \'alue of time for one round trip is given 

 in Table I. 



In this experiment the operating wavelength was 3.35 centimeters 

 This was obtained by measurements based on group velocit}' in a num- 

 ber of guides as well as information about the pulse generator com- 

 ponents. It represents an effective wa\'elength giving correct time of 

 travel. The pulse occupies such a wide bandwidth that a measurement 

 of its wavelength is difficult by the usual means. 



The dashes in the measured column indicate that the mode was not 

 excited by the probe or was too weak to measure. These modes do not 

 appear on the oscilloscope trace photograph. 



The relative pulse heights can be calculated from a knowledge of the 

 probe coupling factors and the line loss. The probe coupling factors as 

 given by M. Aronoff in unpublished work are expressed by the following 



For TE„„, modes: 



P = 2.390 r—^ 



i 



For TM„^ modes: 



TV- L a -. 



j\. nm ^ "flu 



X X 



P = 1.195€„ — - 



where 



P = ratio of probe coupling power in mode nm to that in mode TEn 



n = first index of mode being calculated 

 Knm = Bessel function zero value for mode being calculated = Td/\c 



X = wavelength in air 



X(, = wavelength in the guide for the mode involved ' 



Xc = cutoff wavelength of guide for the mode involved 



€„ = 1 for w = 



€„ = 2 for n ?^ , 



d = waveguide diameter 



Formulas for guide loss as given by S. A. Schelkunoff on page 390 of 

 his book Elect romagnelir Waves for this case where the resistivity of the 

 aluminum guide is 4.14 X 10~^ ohms per cm cube are: 



