Further, the frequency for which this occurs is
and the maximum stored potential energy occurs at this frequency.
I low can such a system he buiii and the AC force magnification be used to mechanical advantage? Testa described] nst such a system, ill 1919. which can he driven by either a centrifugal pump or by a reciprocating pitmp. See Figure 4. which is taken from Testa's series "My Inventions". The mechanism. an air powered jack-hammer, functions by means of the introduction of a nonlinear element — the "escape ports".
In the mechanical apparatus illustrated, an attempt is made to convey an idea of the electrical operations os closefyits practicable. The reciprocating and centrifugal pumps, respectively, represent an alternating and a direct cwrent generator. The water lakes the place of I he electric fluid The cylinder with its elastically restrained piston represents the condenser The inertia of the moving parti corresponds to the self-induction of the electric circuit and the wide ports around the cylinder, through which the fluid can escape, perform the function ofthe air-gap The operation of this apparatus will now he readily understood. Suppose first that the water is admitted to the cylinder from the centrifugal pump, this corresponding to the action of a continuous current generator As the fluid is forced into the Cylinder, the piston moves upward until the ports are uncovered, when a great quantity of the fluid rushes out. suddenly reducing the pressure so that the force of the compressed spring asserts itself and sends Ihe piston down, closing the ports, whereupon these operations are repeated in as rapid succession as it may be desired Each lime I he system, comprising the piston, rod. weights and adjustable spring, receives a Mow,
Turning to (lie electrical case, we consider the analog of the mcchanical oscillalor. A series resonant RLC circuit driven by a stnewave generator has the same analysis as above, with X —>J and F—> V(uj). At resonance, the magnification, given by Equation (21), again ascends to M = Q and the voltage across the capacitance increases to
The -j indicates that the capacitor voltage ism lagging phase quadrature with the source voltage. The
it quivers at its own rate which is determined by the inertia ofthe moving parts and the pliability of the spring exactly as in the electrical system the period of the circuit is determined by the self-induction and capacity. If instead of the centrifugal, the reciprocating pump ix employed, the operation is the same in principle except thai the periodic impulses of the pump impose certain limitations. The greatest energy oj movement will be obtained when synchronism i,\ maintained between the pump impulses and iha natural oscillations of the system.
It is not difficult to see the path in Testa's thoughts leading to a mechanical conception of human energy: "Wherever there is life, there is a mass moved by a force."32
and Electrical Oscillator voltage across the inductance rises to
and is in leading phase quadrature with Ihe source voltage. The current is limited only by the circuit resistance. At resonance, the current through the circuit rises until the voltage across the resistive loss is equal to the source voltage.
This simple circuit was a source of deep frustration to Edison because voltmeter readings taken wound the loop did noi obey Kirchoffs law! As a result, he issued the famous warning, Take Warning! Alternating currents are dangerous! They are fit only for powering the electric chair The only similarity between an AC and a DC lighting system is that they both started from the same coal pite.33
Ronald Scott, Dean of Engineering at Northeast-em University has observed,
One of the reasons that Edison mistrusted alternating currents was that he didn't really understand them ...it wasn 7 until the work of Steinmetz at the General Electric Company that a good method for solving AC circuits became available. In 1/197. complex algebra and phasors were applied to electric circuits in a classical paper by Steinmetz. and since that time no one has had any excuse for not understanding AC circuits. 34
The series resonant RLC circuit has been called "a voltage amplifier ' or "a voltage magnifier" by many of the old electrical engineering texts. (See Ryder,35 for example.) The dual network (the parallel or "anti-resonant" circuit) has been called a "current magnifier". In both cases, the magnification, M = Q.
The electrical analog of Tesla's jack hammer oscillator is found by introducing an electrical nonlinear clement in place of the escape ports - the spark gap. When a spark gap is set across the circuit, the capacitor charges up to the gap breakdown and RF filiations occur as long as ihe plasma arc across ihe gap conducts. (Contrary to many erroneous discussions of spark gap transmitters, the spark docs not create the RF oscillations!)
Consider the push button "oscillator" shown in Figure 5. If the button is held down, current will Row and magnetic energy will be stored in the magnetic field ofthe coil. When the button is released, none of this energy can return to the battery, instead, as ihe magnetic field collapses, the current induced in the circuil will charge up Ihe electrical potential energy stored in the capacitor. Energy, of course, will be dissipated in the resistive losses.
This interplay of kinetic energy and potential en ergy will occur at a fixed rate known as the natural resonant frequency ofthe system. The situation is not unlike a child on a swing, the pendulum in a grandfather's clock, or the torsional oscillator (or flywheel) in an old-fashioned pocket watch. In these mechanicai oscillators the frequency may be maintained with considerable precision. However, a supply of energy must be periodically imparted to the system, at the right time in the cycle, to overcome the resistive damping. Otherwise the motion will simply ring down at the resonant frequency. In a watch, the energy was stored in a mainspring and periodically released to the flywheel through the use of a nonlinear mechanism called a ratchet and pawl.
In Figure 5, the energy exchange back and forth in the LC tank circuit provides an electrical flywheel for oscillations, but we need a creature the likes of Maxwell's demon to stand at the push button and press the button synchronously with the oscillations, in order to introduce enough energy each cycle to overcome the resistive losses.
Ryder notes that what is needed is a nonlinear device such asa vacuum tube:
The tube will operate at a synchronous switch, supplying dc power in pulses (of length 28 ¡)to the resonant LC circuil. in synchronism with the voltage across the load After supplying a pulse
of energy. the switch disconnects the energy source from the had, and the energy in the load continues to oscillate at the resonant frequency. The action is comparable to thai of a pendu lum. driven hy short mcrgy pulses, and swing Ingfreely at us own rah for most tif the cyvte. " This type of operation occurs lor class C amplili ers.
The Early Tesla Transformer - Coupled Lumped Oscillations
Coupled mechanical oscillators have been treated inconsiderable detail in many books. They are the counterpart to the tuned lumped coupled coils which describe Tesla coils during the duration of the primary spark. Since we have written many articles and an entire book on this (complete with software), we will refer the reader to the literature. A well written and lucid treatment of lossless lumped coupled luned coils is presented by Finkelstein. Smythe includes losses, But, neither author recognizes the importance of sparfc duration, and both miss the slow-wave distributed resonator mode of the helical secondary.
TCTUTOR has a useful discussion of the whole topic. The bottom line on all this is that lossles;. luned lumped coupled coils, assuming infinite spark duration, have a magnification given by
This can be greatly improved upon by following the disclosures patented by Tesla in 1897 - operate the secondary as a quarter wave helical resonator, not a lumped coupled coil. The voltage rise will then be by VSWR, not lumped circuit Q. A true Testa Coil is a distributed resonator.
Transmission line resonance transformers utilize wave interference phenomena for the build up of extremely high voltage standing wave modes. It has long been recognised that RF resonance transformers possess the following capabilities:
1) high voltage generation (tens of megavolts, limited only by the electrical breakdown of the electrode geometry and surrounding dielectric medium)
2) high efficiency (limited only by these copper losses of the structure and RF dielectric losses oHhe primary capacitance)
3) high peak power perfonnance (hundreds of megawatts per discharge)
4) high repetition rate, heavy duty cycle operation (hundreds of kilowatts of continuous average power processed)
5) broadband speclra (generated via high voltage RF discharge).
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It seems like the efforts to find the best alternative energy sources are seriously being looked into by lots of countries including most US cities. One proof is the signing of the Kyoto Treaty. The main aim of the concerned group and individuals is to lessen the greenhouse gases and pollutants.