WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES 51 



For TE„,„ modes: 



a = 3.805 ! — 2 2 + V.an ) (1 " Vnm) 



\l\n,n — n / 



For TM„,„ modes: 



a = 3.805(1 - VnJy''' 

 where: 



a = attemiation of this aluminum guide in db 



n — first index of mode being calculated 

 Knm — Bessel function zero value for mode being calculated = TrtZ/Xc 



Vnm = A/Ac 



X = operating wavelength in air 



Xc = cutoff wavelength of guide for the mode involved 



d = waveguide diameter 



Table II gives the calculated probe coupling factor, line loss, and rela- 

 tive pulse height for each mode. In the calculation of the latter, wave 

 elUpticity and loss due to mode conversion were neglected, but the heat 

 loss given by the preceding formulas has been increased 20 per cent for 

 all modes, to take account of surface roughness. Relative pulse heights 

 were obtained by subtracting the relative line loss from twice the rela- 

 tive probe coupling factor. The relative line loss is the number in the 

 itable minus 2.33 db, the loss for the TEn mode. 



The actual pulse heights on the photo of the trace on Fig. 12 are in 

 fair agreement with these calculated values. Differences are probably 

 due to polarization rotation in the guide (wave ellipticity) and conver- 

 sion to other modes, effects which were neglected in the calculations, 

 and which are different for different modes. 



Calculated pulse heights with this guide length, except for modes 

 near cutoff, vary less than the probe coupling factors, because line loss 

 is high when tight probe coupling exists. This is to be expected, since 

 both are the result of high fields near the guide walls. 



The table of round trip travel time shows that the TE41 and TE12 

 modes are separated by only three millimicroseconds after the round 

 trip in this waveguide. They would not be resolved as separate pulses 

 by this e(iuipment. However, the table of calculated pulse heights shows 

 that the TE41 pulse should be about 22 db higher than the TE12 pulse. 



