1436 THE BI<:LL system technical journal, NOVEMBER 1957 



v^ector representing the leading echo rotates clockwise with respect to 

 the main signal when the frecinency increases, whereas the vector repre- 

 senting the lagging echo rotates counterclockwise by the same amount, 

 and the resultant thus varies in magnitude but not in phase. The magni- 

 tude of the resultant is given, for this case, by the first two terms in 

 parentheses in (4). 



If, on the other hand, if we set Kg — 0, we have the three vectors 

 shown in Fig. 4(b), identical with those in Fig. 4(a) except that the 

 polarity of the lagging echo has been reversed. In this case, the two 

 echos produce a resultant, Cp , which is in ciuadrature with the main 

 signal. For small echos, Cr is thus shifted in phase from the main signal, 

 with substantially no change in magnitude. The resultant in this case is 

 given by the first and third terms in parentheses in (4). This gives a 

 sinusoidal variation in the phase of the resultant. Since envelope delay 

 is defined as rf/3/rfco, where (8 is the phase shift through the circuit in 

 question, the sinusoidal phase ripple will be seen to yield, after differenti- 

 ation, a cosine delay ripple. 



The period of the ripple can be seen from the above expressions to 

 depend on r, the delay between the leading and the main tap, and be- 

 tween the main tap and the lagging tap. Other pairs of echos, each pair 

 symmetrically disposed about the main tap, but with different values 

 for T, will give transmission ripples of different periods. To provide a 

 series of orthogonal terms, the values of r must be integral multiples of a 

 common value, normally that required to produce 180° phase shift 

 across the band of interest. 



A complete ecjualizer must, of course, sum up the various echos and 

 the main signal, taking care that the delay between the tap and the 

 summing point is the same for each echo and the main signal, that 

 parasitic losses such as losses in cabling are the same for each path 

 through the equalizer, and that any frequency characteristic in the tap- 

 ping device or other parts of the ec^ualizer is properly eciualized out so 

 that the over-all equalizer introduces a minimum of distortion of its 

 own. 



VI. directional coupler 



To reduce incidental distortion, it is desirable that the device used to 

 tap the delay line for the main signal and the echos introduce substan- 

 tially no discontinuity in the main line. The device chosen for this pur- 

 pose is a directional coupler. It is shown symbolically in Fig. 5. The di- 

 rectional coupler is a four port device having properties similar to a 



jij 



