DIELECTRIC CONSTANTS AND POWER FACTORS 115 



"(2" Definition 

 At low frequencies the resonance selectivity factor of lumped circuits is 

 identified as the "Q" and is defined as — . It is measured by a detuning 

 process. For a length of transmission line with negligible shunt conduc- 

 tance losses this process gives -— as for a coil; when this process is applied 



R 



to complex circuits the physical embodiment of the "Q" becomes difficult to 

 realize and it is preferable to define the "Q" in terms of the detuning process 

 itself. This is equally true for tlie resonant, centimeter wave, line element 

 and we proceed as follows: For this element some current or voltage ampli- 

 tude, conveniently measurable, is selected and three values of it are measured 

 as the line tuning is varied. This variation may be either in generator fre- 

 quency for constant line length or in line length for constant generator fre- 

 quency. 

 Thus, for example, 



Q = T^f^ where /. > /o > /i 

 h ~ h 



Q = J , where 4 > ^ > A 



At = Al = ^ (1) 



^2 — /l 



with ^0 as the resonant amplitude. For low-loss lines the two definitions 

 will give the same results in practice. Neither is ideal for second order 

 accuracy since there is a variation of line constants with frequency in the 

 first and a variation in total attenuation in the second. 



For practical reasons it is usually preferable to excite and observe the line 

 resonance in terms of the current at one end, this end shorted. The ele- 

 mentar}' line lengths are then the quarter and the half-wave ones, the former 

 with open circuit far end, the latter with shorted far end. The latter is the 

 more nearly ideal unit. In order to short effectively the input end, the in- 

 put and output couplings must be made as loose as possible. As these 

 couplings are reduced the observed "Q" will asymptotically approach the 

 line "Q"- At the present moment the line variation in length is the most 

 convenient process, the chief trouble being the micrometric measurement 

 of the tiny length changes involved. Thus for 10 cms wave-length and a 

 half-wave coaxial line, a "()" of 1000 involves a plunger movement of .0019 

 inches. 



Theory of Measurement 



It is shown in the appendix that the "Q" of a given resonant line segment 

 can be broken up into parts representing the equivalent "^'s" of the ter- 

 minal impedances and the line itself. Thus 



