Report of Tests on Joseph Newman's Device

5. Uncertainty Estimates

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5.1 Introduction

In this section, the primary sources of measurement uncertainty are identified and their magnitudes are estimated. Two different kinds of uncertainty limits are discussed. One is an offset and the other is variations in the repeatability of the measurements which are represented as random errors. The sign convention used is that a positive offset produces a measured result which is larger than the true value of the parameter while a negative offset produces a measured result which is smaller than the true value. The


basis for the estimation of the offsets is described below. The limits for random variation, designated "+/-", are bounds which will include almost all repeated measurements. The following five measurements are evaluated: the input power using the sampling wattmeter; the input power using the analog-multiplier wattmeter; the output power using the active attenuator; the output power using the thermal element; and the output power using the BI-200 load.

5.2 Uncertainty and Offset in Input Power Measurements

The input power was measured using the sampling wattmeter and the analog-multiplier wattmeter. The primary sources of measurement error and their estimated magnitudes are listed in Table 5.

The low-pass filter introduces error because the higher frequency components of the power are measured with a consistent offset. As discussed in section 4.2, this error is such that the input power is consistently underestimated. The data support an estimate of -3% for this error.

The power dissipated in the voltage divider is between 0.1 and 0.2 watt depending upon the voltage level used. The percentage of the input power represented by this quantity depends on the load and the condition of the tape on the commutator. For this reason, this error was identified as being partially a systematic offset and partially a random error.

Table 5

Estimated offsets and uncertainties in input power measurement


Low-pass filter   -3% -3%

Power dissipated in the voltage divider   +3%+/-2% +3%+/-2%

Scale factor calibration   +/-0.4% +/-0.2%

Frequency response of the voltage divider   +/-0.2% +/-0.2%

Voltage dependence of the voltage divider   +/-0.2% +/-0.2%

Averaging duration errors   +/-1.0% +/-1.0%

Frequency response of the current shunt   +/-0.2% +/-0.2%

Amplitude dependence of the current shunt   +/-0.2% +/-0.2%

Induced signals   +/-1.0% +/-1.0%

The calibration of the scale factors for both the sampling wattmeter and the analog wattmeter was performed by applying known signals from a commercially


available calibrator to the input terminals of the instruments. The values listed are the residual errors which were not accounted for in the calibration of the devices. It can be seen from Table 5 that the error due to this source was small compared to errors arising from other sources. This observation underscores the fact that a knowledge of the scale factors is necessary, but not sufficient, for a reliable measurement.

As noted in section 2.3, the calibration of the voltage divider indicated that variations in its frequency response are less than +/-2% up to 5000 hertz. Because the bandwidth over which significant power is drawn is smaller than 500 hertz, a smaller error is estimated.

As a portion of the voltage divider calibration, the voltage dependence of its response was measured. These measurements indicated that the divider ratio changed by less than 0.1% as the voltage was increased from 300 volts to 1000 volts and was maintained at 1000 volts for five minutes.

To determine the average power, one must average over exactly one or an integral number of cycles or must average over a very large number of cycles so that the effect of any fractional cycle is negligible. The averaging duration error was estimated by noting the variation of successive measurements taken within a few minutes of each other. Since the averaging intervals are uncorrelated with the operation of the device, a major contributor to the difference in successive readings can be attributed to the averaging error. The measurement results obtained support an estimate of +/-1% for this uncertainty.

The current shunt was a 100-ohm, non-inductive resistor. The stray capacitance is below the value which would affect the measured value of the input power by more than 0.2%.

As a portion of the calibration of the system, the amplitude dependence of the response of the current shunt was measured. The data obtained indicated that, over the range from 1 to 50 milliamperes, the response did not change by as much as 0.2%.

By use of appropriate grounding and shielding techniques, the induced signals, or "noise", did not contribute more than 1% of the measured input power. As will be seen in section 5.3, "noise" was a more significant factor in the output measurement.

5.3 Uncertainty and Offsets in Output Power Measurement

The output power was measured using an active attenuator, a thermal element, and a special resistive load called the BI-200. The estimated uncertainties for each of these measurement approaches are listed in Table 6.

The power dependence of the various loads was measured using a commercially available calibration source. No resistance value changed by as much as 0.6% from very low power to the maximum power measured in these tests.

The active attenuator was connected by short, shielded leads to the load. These shielded leads combined with a shielded attenuator and operation at relatively high voltage made this device less sensitive to induced signals


than other approaches. It is possible that the induced signal contribution is even smaller than estimated, but the short-term instability of the device under test makes it difficult to demonstrate that a smaller effect has been achieved. During some of the tests using the thermal element, the input to the thermal element was shorted and the device still indicated a power which was 3% to 8% of that which was measured without the short, indicating that this effect always gives rise to a measured value which is larger than the true value. That measurement is the basis for the induced signal offset and associated uncertainty estimates. The induced signal component using the BI-200 200 load results from the fact that during one polarity reversal of the commutator (and not both) the ground is disconnected from the coil before the battery is disconnected. In this situation, the coil has 400,000 ohms rather than 200,000 ohms in parallel with it. This contribution, will always yield a measured value of the output power which is larger than the true value. From photographs of the waveform and from comparison measurements, it is estimated that the offset is about 10% with an uncertainty of +/-5%.

Table 6

Estimated offsets and uncertainties in the output power measurements


Power dependence of the load +/-0.6% +/-0.6% +/-0.6%
Induced signals +/-2% +5+/-3% +10+/-5%
Averaging duration errors +/-1% +/-1% +/-1%
Scale factor errors +/-0.6% +/-0.6% +/-0.2%
Frequency response of loads +/-0.3% +/-0.3% +/-0.3%

The considerations which contributed to the assignment of averaging duration errors and scale factor errors are the same as those for input error measurement. In addition, an in situ check of the thermal element and the active attenuator was performed by applying a known voltage to the resistive load with the device-under-test disconnected. Each measurement system agreed with the input value to within 1%.

The contribution of the frequency response of the loads was estimated from comparisons of the direct current and 50-hertz calibration of the systems. These data showed that the frequency dependence was less than 0.3%.

5.4. Offset and Uncertainty in Efficiency Determination

Adding the systematic offsets and calculating the square root of the sum of the squares of the random errors provides an estimate of +/-2.5% for the uncertainty of the measurement of the input power for each instrument. Using the same approach to calculate the output offset and uncertainty yields an estimate of +/-2.5% for the active attenuator, +5%+/-3% for the thermal element, and +10%+/-5% for the BI-200. To estimate the uncertainty in the efficiency determination, the square root of the sum of the squares of the random


components of the input and output uncertainties is computed and added to any net offset. In this way, the following offsets and uncertainties in the efficiency determination are obtained:

It should be emphasized that the uncorrected values of the efficiency in Table 1 obtained using the thermal element and the BI-200 are larger than the true values of the efficiency.


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