The preliminary aims of the experiment were to search for a break in the f - a (a.i. 1 ) spectral density component of semiconductor noise and to try to establish the "true" value of a i f a unique value e x i s t s . An almost periodic component (with a period of 1 year) was thus observed in two of the noise sources which are contained in a p l a s t i c integrated c i r c u i t package. The remainder of the thesis involves the experiment and the analysis of the data derived from the experiment.
A method was described that would have essentially increased the relative variance of the low-frequency estimates close by. The derivation of the important results will be set out here, although for further information the original sources should be consulted. In the Blackman and Tukey algorithm (Eq. 2), the maximum delay for ~ ~ where the autocovariance function is estimated is denoted by T,.
If the details of the spectral density to be estimated are not knotty, then it appears to be. In section 2.8, the bias will be evaluated for several specific spectral densities, which are of i t e r e s t i t e r e s t i t h i s partictral thesis. A fairly concise discussion of digital filtering is given in Appendix C, along with the description of the filter actually used.
In all cases shown, there is only significant bias due to the spectral window at the lowest frequencies estimated by a given run.
Y Rat
The high speed of the A/D converter allows channels Bi and Ci to be sampled within 0.04 seconds after channel Ai. The digital output of the AID for channels Bi and C i are packed together to form one 20 bit word. The memory controller actually carries two additional \?lords past the end of the record.
The only change made was a three-way switch that allowed the motor (but not the electronics) of the recording unit to be turned on and off remotely. The computer software assumes that the character is the same as the previous output of the same vjhen channel. So I decided to build a converter that could handle all the equipment (using the ready-to-use 115V (60Hz) a1 power supplies to provide different DC voltages).
Since no switching transients could be tolerated, the inverter had to supply power during the course of the experiment. Past work on th i s f i e l d shows the necessity of adjusting power supply voltages and noise source temperature. It is then assumed t h a t e f f e c t of temperature fluctuations at the output of each noise source can be considered as a temperature coefficient of 1 inaar.
The resistance values indicated are the final values chosen t o s e t 31.1 output voltages t o -0 volts at the start of the experiment. Electrically insulated Ni-chroile wire is wound around the length of the box as a heating e l e ~ ~ e n t. The outer a1 urilinun~ box provides passive attenuation of the high frequency components from room temperature.
Let us assume that the recorded data are the actual values of the indicated temperature, plus a quantization noise (n(t)) due to o. If the normal changes in the actual voltage of the temperature indicator during one sampling period were large compared to one quantization level of the A/D. It is interesting that the power spectral density estimate from the temperature of the T1 noise source actually goes lower than the power spectral density calculated for the quantization noise.
At the point a digression will be made to discuss the thermal transfer function of the furnace used to control the temperatures of noise sources. We now have power spectral density estimates for room temperature and for the temperatures of each of the noise sources.
SPEC DENSITY
A great deal has been spent to reduce the temperature variations of the noise sources, however, no claims have been made that the temperature of the noise sources has actually been maintained for a long time. Briefly - before the s t a r t of long-term measurements an attempt has been made to measure these coefficients. Since the ten2peratures were measured with the same thermistor and amplifier on different occasions, the coefficients will refer to terms of the change in volts at the noise source, an amplification f t e r divided by the change in volts from the thermistor amplifier.
As the t o t a l t e s t period was of the order of a few hours, the d i f t of the noise sources must be recognized as an e r r o r. A1 although most of Sn(f) for the 6 noise sources are not very good approximations to A j f , Eq. It may prove useful if one tries to consider the possibility of linear trends in the noise source v o l t a g e , or the f a c t h a t e f i c i e n t time may not have been aggregated in terms of reaching the source to the free.
For a rough estimate of the accuracy we can expect in th i measurement method, consider the following. A reasonable method of estimating fo and k from estimating the power spectral density of a popcorn source would be to compare the spectral density t o an A/f curve. For noise source #2, the burst amplitude was estimated to be approximately 0.39 volts with 2 positive steps and 2 negative steps.
The povrer spectral density estimates (resul t i ncj from these modified data) are shown in Fig. Therefore, if we choose L < T At, less than 1% of the bursts will be shorter in duration than L samples. If we intend to use this data to remove the burst component from a noise source to improve o u spectral estimation, this is clear.
H o p i n g to see solae trace of the popcorn com~oncnt r/ith amplitude of about 0.1 v o l t, another histogram was plotted with h a h i o h e r. The spectral density estimates were somewhat smaller at the high-frequency end for the modified data, but larger at the low-frequency end than for the raw data estimates. Since uncorrelated processes added in the time domain produce a spectral density that is the sum of the individual spectral densities, it is clear that a nevi component with 1 arge 1 ow frequency spectral density has, in fact, been added.
In fact, if for some reason the estimate f a f o r s missing more plus than minus steps (for example) the estimate of the burst component would diverge. For example, if we T+ - T-, and we missed or got a step about once out of every 40 steps, then we would expect the average powder of the remaining burst component, if we subtracted.
