1434 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



in magnitude but of opposite polarity are added in the summing circuit 

 to the main signal. 



To achieve a practical eciualizer for operation over the GO- to 80-mc 

 band recjuires the following components: delay line or delay networks, 

 means for tapping off small portions of the signal controlled both in 

 amount and polarity, and a suitable summing circuit. 



V. DERIVATION OF THE EQUALIZER CIRCUIT 



A brief analysis of the operation of the equalizer will be given at this 

 point as a basis for discussion of the method of tapping the signal and 

 controlling the amplitude and polarity of the tapped portion. 



Fig. 3 shows the basic delay line PQ as well as the means used for 

 producing the main signal and a single pair of leading and lagging echos. 

 The tap labeled "o" in the center of the line produces the main signal. 

 The tap "a", being closer to the input, produces a signal which leads the 

 main signal by time t. The tap "5" produces a signal which lags the main 

 signal by the same amount. The boxes "/va" and "/vb" control the ampli- 

 tude and polarity of the leading and lagging signals which are to be com- 

 bined with the main signal to produce one term of the desired equaliza- 

 tion characteristic. It will be shown that these three signals will provide 

 one cosine gain term and one cosine delay term, both having the same 

 period, but being independently controllable as to amplitude and 

 polarity. 



We will choose as our reference point for phase the main output sig- 

 nal, eo = -E'c^"'. The output from tap "a" is then 



After passing through box "Ka", this becomes 



Similarly, 



Here the terms Ka and Kh are of the form 



K = is"" 



where a is the attentuation in nepers of the box K. Note that \K\ is 

 less than unity, assuming the box represents a passive network. Combin- 

 ing these two signals with the main signal, we have 



er = Co + e„ + e, = Ee''"[l + A^a^"'"^ + /Uf^^l- (1) 



