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BELL SYSTEM TECHNICAL JOURNAL 



realizability of a driving-point impedance function. If this function is chosen 

 as the Z = R-\- jX in the figures, the necessary condition of interest is that Z, 

 as an analytic function, have no poles in the right half of the complex fre- 

 quency plane and that Z approach ~^ as co approaches infinity. By inte- 



grating this function over the appropriate path in the right half of the X 

 (complex frequency) plane and setting the result equal to zero, the desired 

 expression becomes 



*'0 



*<'" = 2C.- 



To show that the resistance R is related to the ratios 



(1) 



it is 



Z = RtJx 



^ Ro<fEL 



Fig. 6 — Modified output coupling circuit of Fig. 4. 



Fig. 7 — Modified input coupling circuit of Fig. 5. 



necessary to examine the transfer of power through the output circuit of 

 Fig. 6. The power driven into this circuit is | / \''R. Since the network N is 

 lossless, this is the same power, | II I'Ro , which reaches the line. In addition, 



if the transfer impedance of the circuit is defined as ZioCjco) = -rr- = i^oy, 



the relationship sought is 



_ Zn{joi) 



R, 



R 



Ro 



(2) 



For the input coupling circuit, the ratio 



impedance and R in a similar manner. 

 ^Ref. 1, pp. 278-281, 



E^ 



Er. 



is related to the transfer 



