Evaluation of Magnetic Resonance Amplifier (MRA) Institute for Advanced Studies / EarthTech International, Inc. 4030 Braker Lane, Austin TX 78759 512-346-3848 H. E. Puthoff and Scott Little 20 January 1995 Abstract: An MRA device provided by Joel McClain and Norman Wooten was tested for power efficiency. The MRA is essentially a power converter, driven by an audio frequency AC voltage and producing a DC output. Our tests included meter measurements, made in the manner employed by McClain and Wooten, and digital oscilloscope measurements, which provided high-resolution recording of input voltage and current traces. Our meter measurements duplicated the results reported by McClain and Wooten which would appear to indicate over-unity (>100% efficiency) performance at certain frequencies, but only because the reactive behavior of the system is not properly taken into account by this measurement procedure. The digital oscilloscope measurements, which correctly account for the effects of circuit reactance, yielded a nearly constant 50% efficiency at all frequencies. Introduction: The MRA device we tested consisted of a piezoelectric transducer connected in series with the primary of a specially-constructed, hand-wound transformer. The transformer has a ferrite core and the secondary is connected to a full-wave bridge whose output is connected to a load. McClain and Wooten computed AC input power by determining an equivalent resistance R of the MRA, and then substituting that value R, and the closed-circuit MRA input voltage V, into V^2/R to calculate an input power. They determined this equivalent resistance by substituting a decade resistance box in place of the MRA to find the resistance that would yield the same connected-circuit driving voltage. (Such a procedure is appropriate for purely resistive loads.) In their most recent tests McClain and Wooten used a small DC motor as a load for the MRA. We used the motor initially to confirm proper operation of our MRA testbed, but replaced it with a 130 ohm resistor to eliminate commutation noise for the tests described below. We also attached a 30,000 microfarad filter capacitor across the load resistor to smooth out the DC to ensure accurate measurement with common digital meters. We used two Micronta 22-185A meters, one in series with the load to measure current, and one connected across the load and the other meter to measure total voltage delivered to the load and current meter. Total output power is the product of these two quantities. To generate the 34 kHz signal needed to drive the MRA we used a TEK FG504 Signal Generator amplified with a Pioneer H100, a modern solid-state 160-watt audio power amplifier without output transformers. To duplicate the performance of McClain and Wooten's Radio Shack MPA-45, 35-watt amplifier, we had to add series L (34 microhenries) and R (11.68 ohms) to our amplifier. Without the series R we only observed a 0.10 volt droop when driving the MRA at resonance (McClain and Wooten's amplifier exhibited a 1.58 volt droop under this loading). Without the series L the anomalous effects were still present but substantially lower in magnitude than those observed by McClain and Wooten. With our amplifier thus modified by the addition of these elements, we have duplicated the McClain-Wooten driver amplifier setup precisely. We used a LeCroy ScopeStation 140 100MHz digital oscilloscope with simultaneous sampling on 2 channels to measure MRA input voltage and current. Current was sensed as the voltage drop across the 11.68 ohm resistor placed in series with the amplifier output. This resistor was made by placing two 22 ohm, 2 watt carbon comp resistors in parallel to provide the desired resistance with a minimal inductance. Procedure: We conducted a series of measurements at different frequencies. At all times the MRA was connected to the 130 ohm load resistor. At each frequency we made the following measurements with the MRA connected to the AC signal source: f source frequency (measured with a Fluke 87) VinMRA voltage across the source terminals with the MRA connected (Fluke 87) Vout DC voltage across the 130 ohm load resistor and current meter (Micronta) Iout DC current through the 130 ohm load resistor (Micronta) Vin digital recording of the input voltage trace covering about 4 cycles (LeCroy) Iin digital recording of the input current trace simultaneous with Vin (LeCroy) At each frequency we also disconnected the MRA and measured: Vopen the open circuit voltage of the source (Fluke 87) We then connected a decade resistance box across the source terminals and by trial-and-error determined: Requiv the resistance required to produce the same driving voltage as with the MRA connected Results: The following table shows these measured quantities for four different frequencies, beginning at resonance and then decreasing. 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 The first entry in the table is at resonance and is characterized by the highest Vout value. The second entry has Vout at approximately 85% of the maximum value as suggested by McClain and Wooten. The digital data for Vin and Iin are not presented in this table in the interest of brevity. The several pages of digital data generated for each line in this table are, however, available upon request. The next table shows the results of the power calculations, both by the V^2/Requiv method used by McClain and Wooten, and by the averaging of Vin times Iin using the digitized data. Also tabulated are efficiency figures for each method (i.e., output power divided by input power). f DC output V^2/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 The figures in columns 2 - 4 are in watts. The last two columns contain ratios. The column labeled "Mc-W eff" is the power efficiency calculated by dividing the DC output by the McClain- Wooten input power V^2/Requiv. Discussion: The second row in the table shows the condition that McClain and Wooten interpreted as over-unity performance (e.g., an efficiency of 5.36). The problem lies in the value of 1900 ohms for Requiv. This value was obtained because of the small voltage change between open- and closed-circuit conditions (24.04 to 23.84) measured at that frequency. Note that at even lower frequencies, the source voltage was observed to actually increase above the open circuit voltage when the MRA was connected...a condition that McClain and Wooten also observed but did not attempt to analyze. At first glance this could be interpreted as evidence that the MRA was now feeding power to the source. However, this behavior is exactly what is predicted by classical AC circuit analysis when a load with a net capacitive reactance is driven by a source that has a net inductive reactance. Since the MRA is essentially a series LC circuit, at frequencies below resonance it will exhibit a net capacitive reactance. The audio amplifier used by McClain and Wooten has an output transformer which, at the MRA operating frequency (substantially higher than the middle of the audio range), will exhibit a noticeable inductive reactance in its output impedance. With such a combination of reactances one cannot, using only the magnitudes of voltage and current, determine the actual power being transferred to the MRA device. In particular, the Requiv method fails as one detunes from resonance because it ignores the effect of reactance. Such reactance creates a phase shift between voltage and current, a fact well-known in the electric power industry as "power factor." For example, if both voltage and current are sinusoids, true power is given by V*I*cos(A) where A is the phase angle between the voltage and current waveforms. An equivalent method, which is more general because it is applicable to any waveform, is to average the product of the voltage and current waveforms over an integer number of cycles. This is the method we used to obtain the values in the second table in the column "avg Vin*Iin". Conclusion Based on the results of our experimentation and analysis we find that the MRA device provided by McClain and Wooten does not produce over-unity-efficiency results. The MRA circuit behaves instead as one would expect of a loaded transformer with a series capacitor in the primary circuit. When the MRA is detuned from resonance to frequencies slightly below resonance, the observed changes may give the impression that the MRA then draws unusually little power from the source while nonetheless maintaining a healthy output. This impression is false. True power measurements show that the MRA continues to draw about twice as much power from the source as it delivers to the load.