WAVEGUIDE AS A COMMrxrCATTOX M 1,1)1 IM 1230 



In tlio 5" liiu> there are several modes for which the delay factor 

 2(1/^1 — 1 t'l) does not result in a separation hetween the reconverted 

 pulse and the signal pulse until z is on the order of 5,000 feet. Thus, we 

 might (^xpect the conversion-recouN-eision i)henomenon to broaden the 

 signal pulse. This does indeed take i)lacc ev(Mi for the fa\-orahle piston 

 setting of the bare waveguide, as shown by tlic toj) line of pulses in 

 Fig. 15. The pulses at the distance 3,500 yards are sharper than those 

 pulses at the distance 27,700 yards. However, addition of the mode filter 

 (which introduces negligible signal attenuation) does a])i)reciab]y shar])en 

 the pulse at the 27,700 yard distance (row 3). 



Thus, on the basis of pulse transmission observations on the 5" line 

 and a simple theoretical analysis, we conclude that the conversion- 

 reconversion phenomenon w'ill be important in a waveguide system, and 

 that it is important to have as much dissipation as possible present in the 

 unused modes of propagation. 



ANALYSIS FOR CONTINUOUS MODE CONVERSION 



The traveling pulse type of theoretical analysis utilized in the pre- 

 ceding section can be extended to describe a more realistic spatial dis- 

 tribution of conversion points and to include a series of unused modes 

 instead of only one. An extension of this type is reciuired in order to cal- 

 culate directly the behavior which might be expected in a waveguide 

 composed of randomly disposed irregularities. 



A much simpler mathematical treatment, originally suggested to the 

 writer by J. R. Pierce, is to assume uniform mode conversion along the 

 direction of propagation and to represent this condition by a differential 

 equation. An analysis of this type is attached as an appendix. The work 

 includes the assumption of quadrature addition of conversion and recon- 

 version components, and the total magnitude of such components given 

 by the analysis may be thought of as the rms average of the conversion 

 magnitudes in waveguide lines containing randomly located imperfec- 

 tions. Any single line might show somewhat more or less conversion 

 effects, a factor of ±10 db probably being adeciuate to cover most lines 

 containing randomly located imperfections. If practical lines show ap- 

 preciable correlation between the spacings of the conversion ] joints, the 

 reconverted-wav(> magnitude would become greater. The analysis has 

 the advantage of being simple and understandable and should give 

 overall trends accurately. 



This analysis shows that the waveguide performance with regard to 

 conversion-reconversion effects is completely specified witii knowledge 



