738 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



derived from equation (3.9) as, 

 d4> [1 - mY] + (2Q5)^[2 + 4{Qm + i2Q8Y 



d(2QS) [1 + {QkYf + (205)2[3 + (Qky] + (2Q5)^[3 - 2{Qky 



+ (2Q6)« 

 (3.10) 



The above expression, involving even powers of 2Q5 only, results in a 

 family of curves symmetrical about the vertical axis, the positive half 

 of which is shown in Fig. 6(c). From it the value of (Qk)^ for greatest 

 linearity or most constant slope is seen to lie somewhere between 0.1 

 and 0.2. This is further borne out by Fig. 8, in which this region has 

 been more fully explored. Fig. 8 constitutes a plot quite similar to that 



1.08 



1.04 



.00 



a96 



°0.92 



-r;o.e8 



o 



^0.84 



•0- 



, 0.80 



O 



^ 0.76 



a72 



0.68 



a64 



a 60 



0.1 



0.2 



0.3 



0.4 



0.5 



0.6 



0.7 



0.8 



0.9 



1.0 



Fig. 8 — Rate of change of input phase angle with frequency normalized with 

 respect to its center value for the circuit shown in Fig. 6. This quantity, the 

 constancy of which is a measure of phase angle versus frequency linearity, is seen 

 to stay absolutely constant over a frequency range corresponding to 2Q8 = dbO.3 

 for (Qk)^ = 0.12 while the single resonator case, i.e. (Qk)^ = 0, shows a change of 

 8% over the same frequency range. 



