NETWORK SYNTHESIS G51 



23. MODIFICATION OF N/D 



Suppose Ni/Di and N2/D2 are two rational fractions, representing 

 special choices of .¥ and D in (82), such that: 



AT *"!* 



Then suppose F is a function of z' such that 



F = (91) 



The following combination represents an approximation to ^ Kkz'', 

 of the order indicated :t 



m = rni , or Wo + ^i, whichever is the smaller. 



The left hand side of (92) may be used as N/D in (84), to match 

 Cik to Cik through A: = m. Adjustment of the function F may be used to 

 satisfy other requirements, in addition to accuracy specifications. 



Frequently, Ni/Di may be the rational fraction corresponding to 

 ti-uncation of the continued fraction, (86), after the term in a„"+n' . 

 Then N2/D2 is likely to be a truncation of order m < n" -\- n'. The 

 corresponding F is likely to be proportional to /'', or at most a simple 

 polynomial in /. When i^ is a constant, and m = 7i" -{- n' — I, the 

 use of these particular rational functions in (92), to determine N/D, 

 corresponds to matching C2k to C2/C through k = n" -\- n' — I, but 

 leaving C2{n"+n') subject to adjustment. Specificially, C2{n"+n') depends 

 on the choice of F, which may hinge upon such special conditions as 

 the elimination of non-physical singularities. 



Problems which call for more complicated combinations are by no 

 means uncommon. Skill may be needed in the choice of specific com- 

 binations which will solve specific problems. Computations may be 



t The relationship is easily established by noting that: 



Ni - N2 - 



— - 2 Kkz'" ^ - 2 Kkz^ 



'^1±I^-^K^^^ = ^ ^F^ (93) 



D. + FD. D, A 



