548 



BELL SYSTFAf TECHNICAL JOURNAL 



Ye can be obtained as a function of time. It may be that in many cases the 

 real part of the frequency is nearly enough constant during build-up so that 

 only the amplitude vs time need be known . As the input will commonly be a 

 function of time for such experimental data, I\. vs time will yield I'«at vari- 



GIVEN gapI 

 VOLTAGE, Vl^- 



3 



RATE OF 



BUILD-UP, 



OL = 



1 XIO^ 



2 X 10^ 



(a) 



CONDUCTANCE, G 



2 

 1 

 



(b) 



0.5 KG 1.5 2.0 2.5 3.0 



TIME, t, IN MICROSECONDS 



Fig. 56. — a. A plot of the circuit admittance (solid lines) for various rates of build-up 

 specified by the parameters a. The voltage builds up as e"' . The circuit conductance is 

 greater for large values of a. The negative of the electronic admittance is shown by the 

 dashed lines. The circles mark off the admittance at which various amplitudes or voltages 

 of oscillation occur. The intersections give the rates of build-up of oscillation at various 

 voltages. By assuming exponential build up at a rate s])ecified by a between the voltages 

 at these intersections, an api)ro.\imate liuild-u]) can be constructed. 



h. A build up curve constructed from the data in Fig. 56a. 



ous amplitudes and inputs. Curves for various rates of applying input will 

 yield tables of Ye as a function of both input and amplitude. 



It will be noted that to obtain very fast build-up with a given electronic 

 admittance, the conductance should vary slowly with a. This is the same 

 as saying that the susceptance should vary slowly with co, or with real fre- 

 quency. For singly resonant circuits, this means that av/M should be large. 



Suppose the admittance curve for real frequency, i.e. a = 0, has a single 



