Calculation of Necessary Resonator Q 



points 



PERMISSIBLE TEMP. READING ERROR 

 RANGE .04- ' C 



FREQUENCY- TEMPERATURE 

 COEFFICIENT /O CYCLE5/°C 



;. ALLOWABLE FREQUENCY 



DEVIATION .04 X 10= .4 CYCLES 



assume amplifier phase variation 

 of 45° : 

 then a cycles ^^ 



WHERE Af = FREQ. RANGE 

 BETWEEA/ 70° PHASE ANGLE CHANGE 



Af= .8 CYCLES 

 f 



Q 



Af 



Q= 



= 45-000 



36000 

 .8 



increasing frequency — - 

 Universal Resonance Curve 



Fig. 3- Calculation relating error, amplifier characteristics and resonator Q. 



measurements because this repeatability or fre- 

 quency-temperature stability determines directly 

 the accuracy. To test this repeatability a 

 special double resonator, shown in Fig. 6, has 

 been fabricated with two built-in Veco 51A1 ther- 

 mistors. It is housed in a brass container and 

 evacuated. This arrangement permits the greatest 

 flexibility for measurements and comparisons 

 between the four temperature measuring devices. 



The double resonator was checked for repeata- 

 bility by submerging the entire housing in a 

 water bath. The bath was alternately heated and 

 cooled over a one degree temperature range near 

 25 C. The resonators were incorporated one at a 

 time in an oscillator circuit consisting of a 

 60 db amplifier with automatic gain control and 

 the previously mentioned sharp cut-off, low pass 

 filter. The frequencies were monitored by a 

 counter which read to 6 places . 



The best indication of repeatability is the 

 plot of Fig. 7 which is one resonator's frequency 

 against the other. Ideally the points should lie 

 in a single straight k^° line. Actually, the 

 points lie close to a line and the width of the 

 cluster determines the repeatability. The points 

 on this plot are numbered in the order of their 



being taken and they show a repeatability, and 

 therefore a potential accuracy, of about 0.01 C. 

 This indication of repeatability must be verified 

 by a plot of one of the sensors against a ther- 

 mistor (Fig. 8) to indicate any frequency- 

 temperature hysteresis in the aluminum or tempera- 

 ture gradients due to insufficient time for tem- 

 perature equalization. Either effect would show 

 as increasing temperature points lying con- 

 sistently to one side of the line and decreasing 

 points to the other. This plot shows no such 

 error. The final plot (Fig. 9) is of one ther- 

 mistor against the other to show the thermistor 

 repeatability . 



Of course, these tests fail to indicate the 

 long term repeatability that might be expected of 

 the temperature sensor. Barring any loss of 

 vacuum, the only change in calibration that can 

 occur is perhaps through some aging of the alumi- 

 num; the resonator's frequency is otherwise inde- 

 pendent of the external circuit, changes in the 

 ceramic elements or any environmental factor 

 except temperature. 



38 



