ELECTRIC WAVE-FILTERS 327 



4.4 Supplementary Nehvork 



Shown in both simulating networks of Im^. 17, this network has an 

 impedance expression of the form 



flo + (i\if I • /A"\ 



\ + biif — hf- 

 where 



a I ~ IttRiR^C-i, 



b, = 27r{R,C2-\- R,C.2 + R,Q), 

 and 



The resistance and capacity elements are obtained from the above 

 impedance coefficients as 



Ri = aoa{'/(aQaibi — at^b-i — fli^), 



Co = (flofli^i — 00^62 — fli-)/27rr/oT/i, 



C3 = bojlirau (46) 



and 



Ri = oo. 



From (45) the pair of impedance linear equations is 



flo + fxbi + frbo = r, 



and ^ (47) 



/ai — //-&! -\- f'^xbi = X. 



With the above formulas we can proceed to indicate the method of 

 design. 



Ideally the network should have the impedance characteristic 



z = r-h ix = K,- Zi, (48) 



or 



z = r + ix ^ K.- Z2, (49) 



depending upon which mid-point impedance, Ki or K-z, is being simu- 

 lated. Usually these two values of z are practically the same. To fix 

 the four impedance coefficients, assume that the network has the ideal 

 components of (48) or (49) at two important low frequencies, the data 

 with increasing frequency being, 



/i, rx + ixi ; 

 and 



h, r^ + ix-i. 



