116 



BELL SYSTEM TECHNICAL JOURNAL 



JL _ J. J. J. 



(2) 



where "Q" is the actually measured quantity, Qq is the part due to the line 

 itself, ^0 and Qf the parts due to the near and far end terminations, respec- 

 tively. 



If we now take a quarter-wave line segment, with near end shorted 

 through a movable plunger and far end open, we may make two "^" meas- 

 urements without and with the far end loaded with a dielectric segment, 

 and obtain 



^1 = 14-1 = ^1 



Q' Q, Qo x/4 



(3) 



A _ A 1 1 _ A 



I <2 " <2. "^ <2o "^ (2^ " x/4 



1 1 _ 1 _ d_-^ 

 ^^^ Q~Q'-Qr X/4 



with d' and d equal to the widths of the resonance curves halfway down in 

 power. These two ^'s are, of course, directly measurable. 



When the line is loaded with a dielectric segment the loaded part of the 

 line can be represented as an impedance Z^ connected to the unloaded re- 

 mainder of the line. The effect of the loaded segment upon the imloaded 



V D /Z. 



line (See appendix, eq. 4) appears in the form - - where A/ -is the surge 



impedance of the unloaded line, with "Z" and "Z)" the series impedance 

 and shunt admittance, respectively, for unit length of this line. If we put 



we have 



tanh d = tanh {a^ + ib^) = 



f A _ ^ - ^ ' _ ^df. 

 \Q^~ X/4 -V 



ZTT 



Zi 



(4) 



(5) 



where A^ is the measured plunger movement necessary to retune the line, 

 after adding the dielectric loading, and "/" is the length of the dielectric 

 segment. 



