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#### Num7

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Many of the sources in the alt-sci underground relate that Philadelphia Experiment-type setups rely on a rotating (usually magnetic) field as the key mechanism for producing spacetime shifts. We should be able to accomplish this without the need for bulky, expensive 1940's electromechanical equipment such as synchro-motors and generators. Indeed, it can be done quite simply (at least the basic waveform control) using today's fast digital signal processing chips and software. For you hobbyists, however, there's also a relatively simple way to do it using analog circuitry built from readily-available parts.

First, we need an oscillator or wave function generator, which can be built using a few parts that you can buy from Radio Shack. (We are assuming audio frequencies in this discussion, up to about 10 KHz maximum.)

1) Using the example of the simplest periodic wave, the sine wave, the first step is to generate both the sine wave itself, and simultaneously, a cosine wave (a sine wave shifted in time by +/- 90 degrees with respect to the sine wave) at the same frequency.

2) These two waveforms must then be transmitted into an area together, with a 90 degree spatial separation between the antennas/coils/speakers/transducers. In other words, they're perpendicular or "orthogonal" to one another.

3) Across from each of the above, at the opposite side of the central focal point for all this transmitted wave energy, we need another transducer whose waveform is inverted or phase shifted 180 degrees from our sine and cosine waves, above.

Thus our 4 transducers' outputs form a "cross" with one transducer at each point of the cross, or "compass," in a horizontal plane:

the "North" one projects the reference sine wave;

the "South" projects an inverted sine wave;

the "East" projects a cosine wave;

the "West" projects an inverted cosine wave.

All four transducers are aimed at the central focal point which they surround.

Now what you must understand is that the above will only work if you have complete control over that 90 degree phase separation at each and every frequency of interest. If you decide to change the reference oscillator frequency, the cosine wave must "track" and maintain the quadrature (90 degree time-) relationship. If you want to do this with more complex waveforms, such as sawtooth or square or even white noise, this can be very problematic. Why? Well, how did you generate the cosine wave from the sine wave in the first place? Ah, there's the rub: If you didn't use a quadrature oscillator (which automatically does this for you), then you must have used a phase-shift circuit to do it. The problem with that is that phase-shifters do not and cannot shift each and every frequency across the audio spectrum by the same amount. It's just mathematically impossible, since the phase shift offered to any particular frequency is a function of capacitive reactance vs. resistance in the phaser: the good old electronics technician's formula Xc = 1/(2 PI F C), where R = Xc at the quadrature frequency. By definition, only ONE frequency will be shifted by 90 degrees for a given RC combination. So what do we do now? The answer is to use a differential phase-shifter, which is actually two separate phase-shifters, each of which are inputted with a copy of the audio signal we're interested in making quadrature. Yup, each of them suffers from the same problem as outlined above, BUT-- if we carefully tailor the values of the capacitors and resistors in them, we can engineer things such that the difference in phase shift between channel 1 and channel 2 will always be about 90 degrees! In other words, it doesn't matter that channel 1 of my phaser shifts 1 KHz waves by 270 degrees (-90) but only shifts 2 KHz waves by 225; channel 2 will shift the 2 KHz frequency by 315 or by 135 degrees-- the point is that the difference between 225 and 135 is 90 degrees, and that's what we want, a quadrature separation.

**A Differential Audio Phase Shifter for Rotating Field Generation**

Below I present a schematic diagram of 1 of two identical channels of a differential phase-shifter built with commonly-available quad op amps such as the LM324, the TL074, etc. It can also be built using 2 LM358 dual op amps per channel, or you can use 4 single 741's if necessary. Nothing is too critical here. Notice that below the schematic I've included a graph of frequency vs. phase shift (data from electronic simulation of my circuit), and that, above 10 Hz, the difference between channels is almost exactly 90 degrees on up to near 10 KHz. (Above and below those extremes the error increases unacceptably.)

Notice that this arrangement implies that we could use broadband "white" noise-- lowpass filtered a bit with a rolloff around 5 KHz, so it would really be "pink" noise-- as our signal source. Transmitting this type of noise in quadrature would mean that the central focal point would be surrounded by a rotating, multi-frequency standing wave, containing every frequency and amplitude (varying randomly) from 10 Hz to 5000 Hz. This might have application to measuring and quantifying absorption/reflection characteristics of, say, a human body standing at the focus or "zero-point" of the rotating "wave-cloud". But which way does it spin? You have complete control over that; simply reverse the phases of the cosine wave and its inverted twin, while leaving the sine wave as it was, and you will have reversed the direction of field rotation.