54 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



ordinary modulation methods. Darlington gives this formula: 



^) ^^^^ 



iLLi/ Vnm 



where : 



jB = base bandwidth for 180° out of phase sidebands 



/ = operating frequency (in same units as jB) 



X = wavelength in air 



L = waveguide length (in same units as X) 



Vnm = X/Xe 



Xc = cutoff wavelength for the mode involved 



With this equipment, the base bandwidth of the pulse is about 175 

 mc, and when/5 from the formula above is about equal to or less than 

 this, pulse distortion should be observed. The following Table III gives 

 fB calculated from this formula for the arrangement shown on Fig. 12. 



It is interesting to note that pulses in the TMu and TE31 modes, for 

 which jB is less than the 175-mc pulse bandwidth, are broadened, but 

 not badly distorted. For the higher modes, where jB is much less than 

 175 mc, broadening and severe distortion are evident. Another example 

 is given in the next section. 



9. DELAY DISTORTION EQUALIZATION 



If the distance which a pulse travels in a waveguide is increased, its 

 delay distortion also increases. Since the group velocity at one edge of 

 the band is different than at the other edge of the band, the amount 

 by which the two edges get out of phase with each other increases with 

 the total length of travel, causing increased distortion and pulse broaden- 

 ing. The Darlington formula in the previous section shows that jB 

 varies inversely as the square root of the length of travel. This efTect 

 is shown on Fig. 14. In this arrangement the transmitter was connected 

 to the end of a 3" diameter round waveguide 107 feet long through a 

 small hole in the end plate. A mode filter was used so that only the 

 TEoi mode would be transmitted in this Avaveguide. Through another 

 small hole in the end plate polarized 90° from the first one, and rotated 

 90° around tlu^ plate, a directional coupler was connected as shown. 

 The direct through guide of this directional coupler could be short cir- 

 cuited with a waveguide shorting switch. Energy reflected from this 



