--- Addendum --- Error Analysis of MRA Test Results presented in report dated 20January 1995 Institute for Advanced Studies / EarthTech International, Inc. Scott Little and H. E. Puthoff 1 February 1995 Introduction: This analysis refers to MRA test results we presented in a separate report dated 20 January 1995. These results were based upon measured values of voltage, current, frequency and resistance. In this addendum, the magnitude of experiment error associated with these measurements is discussed and quantified. As will become evident below, the error analysis does not detract from our original conclusion, but rather strengthens it. Data: The tables below are reprinted from the original report: f (kHz) VinMRA Vopen Requiv Vout Iout 33.84 21.06 23.36 140 18.68 .1324 33.56 23.84 24.04 1900 15.02 .1068 33.34 24.20 24.10 negative 9.75 .0696 32.47 24.58 24.26 negative 5.28 .0377 f DC output V2/Requiv avg Vin*Iin Mc-W eff Vin*Iin eff 33.84 2.473 3.168 4.566 .78 .54 33.56 1.604 .299 3.265 5.36 .49 33.34 .679 negative 1.467 negative .46 32.47 .199 negative .401 negative .50 Analysis: The data in the second line in these tables is of particular interest. That is the frequency at which the input power determination suggested by McClain and Wooten yields an efficiency of 536% whereas our input power measurement yields an efficiency of only 49%. Let us examine the individual errors that contribute to the total error in our efficiency measurement (i.e. the 0.49 value that appears in the column labeled "Vin*Iin eff" in the second table). This value is the ratio of the DC output power (1.604 watts) to the AC input power (3.265 watts in the column labeled "avg Vin*Iin"). The DC output power value was obtained by multiplying Vout by Iout. Both of these measurements were taken with Micronta 22-185A digital multimeters. The Vout meter was connected across both the 130 ohm load resistor and the current meter so as to include the voltage drop across the current meter so that the power dissipated in that meter would be included in the DC output power determination. It should be noted that a small amount of power, not included in our original determination was dissipated in the Vout meter itself. This meter has a 10 megohm input resistance and, at the 15 volts present in the 2nd observation, was dissipating 22 microwatts. This should be added to the result of Vout*Iout to obtain the total output power. For the 2nd observation, this omission results in a 0.001% underestimation of the output power, an error that will be seen to be insignificant when compared to the errors in Vout and Iout which directly affect the DC output result. The mfgr's literature on the 22-185A meter indicates that our Vout measurement accuracy was +/- 0.8% relative and the Iout measurement accuracy was +/- 1.5% relative. These errors are independent so they add in quadrature to yield a +/- 1.7% uncertainty in the computed DC output (Vout*Iout). The errors in the avg Vin*Iin values are more difficult to characterize. The digital scope manufacturer's stated voltage measurement accuracy does not completely describe the errors that occur when two different waveforms are recorded by the scope and multiplied together. There is a finite amount of non-simultaneity (i.e. jitter) in the sampling of the two channels. When the two traces are multiplied together, the resulting error will be highly dependent on the actual waveforms being sampled. Therefore we elected to determine the error in the avg Vin*Iin value empirically. Ten sets of current and voltage waveforms were taken from the MRA device after it had been operating for about an hour to ensure thermal equilibrium. The operating conditions were similar to those in the second line of the data tables. The results of the Vin*Iin averaging for the ten sets were as follows: 3.26 3.24 3.25 3.20 3.20 3.29 3.16 3.24 3.18 3.27 The observed standard deviation in these values is +/-0.042 watts. This is 1.3% of the mean value. Combining (in quadrature) this error with the 1.7% error in the DC output power, we get a 2.1% relative error expected in our "Vin*Iin eff" values. That is, the 0.49 in line 2 should be interpreted as 0.49 +/- 0.01. Therefore, there is virtually zero chance that the conclusions presented in the original report were wrong due to experimental error. Our measured efficiency is 0.49 +/- 0.01. The McClain-Wooten value of 5.36 is 487 standard deviations away from our value. The probability of our reading being a chance observation, assuming that such readings exhibit a normal distribution, is astronomically small.