Multi-Dimensional Circuits

Kenneth Strickfaden created special effects for classic Hollywood films using Inductive Discharge
Kenneth Strickfaden created special effects for classic Hollywood films using Inductive Discharge

Switched mode power circuits are an efficient means of generating high voltage output from a low voltage source. The operating principle behind these cicuits is quite remarkable. Every so often (generally, many thousands of times per second) a bundle of stored electric energy flashes from one state, or condition, into something entirely different. During those brief moments, an instantaneous acceleration of charge occurs in the output circuit.

The flash is sometimes called a radiant event; the conventional term is inductive discharge. Curiously, the normal rules of electric conduction are suspended during these events. Under normal conditions, such as when batteries or capacitors are discharged, the source voltage gradually declines until equilibrium is reached. At equilibrium (that is, when the voltage potential in circuit components is the same) electric current does not flow. This behavior is well-known and often described in terms of a mathematical relation known as Ohm’s Law.

The discharge of an inductor behaves quite differently. In this case, the source voltage rises spontaneously, as high as it needs to, until the potential in other parts of the circuit is overcome. This voltage rise, repeated many times in rapid succession, results in step-charging an attached capacitor higher and higher. Have you ever used an electronic camera flash, and heard a faint sound that quickly rises in pitch? That is the sound of a capacitor being step-charged to several hundred volts.

The reason the output circuit behaves differently, is because the new variable of time, or more accurately time compression, has been added to the system. When viewed on an oscilloscope, it becomes clear that pulses in the input circuit are time-compressed in the output circuit. This compression squeezes each pulse in the time dimension, which results in a corresponding voltage rise. The pulses become shorter and shorter, and the voltage rises higher and higher, as the potential in other components is overcome.

In a mathematical analysis, the output circuit would be modeled as a higher-order equation (as compared to the input) due to the added variable of time-compression. The combination is therefore a multi-dimensional circuit.

We are interested in multi-dimensional circuits because they present a unique opportunity to engineer an important natural phenomenon. During inductive discharge, the energy transformation is like a material phase change, as from the liquid state to a vapor. And just like the vapor-compression cycle in a common heat pump, the output circuit is capable of absorbing energy from the environment, through the action of inductive discharge.

In a conventional design the net energy gain is relatively small, and obscured by losses associated with other parts of the circuit. But the principle is valid, and a properly designed and tuned system is capable of greater efficiency, by absorbing energy from the environment to offset the inevitable losses.

A more detailed discussion follows…

There are several basic forms of the switched mode power supply, but the most interesting and useful is the flyback converter. This type of circuit, based on a principle discovered by Tesla over 100 years ago, is the basis for most high voltage power supplies. The flyback converter includes two different circuits which are electrically isolated from each other. The input stage is typically powered by a low-voltage DC supply, which can be a battery or a rectified AC source. The DC supply is applied to a coil or inductor for a brief time, and then interrupted by means of an electronic switch. The result is a series of pulses, coursing through the input circuit.

The output circuit is linked to the input by means of a second inductor in close proximty to the first. There is no electrical connection; the two circuits are connected only by the space surrounding the two inductors. It is through the medium of space, that energy is transferred between the input stage and the output stage. In the output circuit, a surge of current “flies back” after the input current is switched off.

Here is the critical point: The behavior of electric currents in the input and output stages are completely different. The input stage obeys the normal laws of electric conduction. An electric current is established by means of a voltage potential across the source. The voltage potential is relatively constant across the DC source, while the current passing through the inductor increases from zero to a maximum value depending upon the resistance of the inductor. As the current increases, a magnetic field is created around the inductor. There are no surprises here.

The output stage behaves quite differently. At the moment the DC supply is switched off, the magnetic field collapses, resulting in a sudden surge of electric current in the output stage. But this current does not obey the normal laws. The voltage potential is variable, and depends a great deal upon the geometry of the inductor and the speed of the switch. Back in Tesla’s day, the switch was mechanical, and comprised of a series of contacts rotated at extremely high speed. In modern times, the switch is generally a solid state device called a Power MOSFET.

Depending upon the design and materials used in the output stage, the voltage potential can easily rise to many hundreds of volts in a very short time. A fast switching diode captures the high voltage pulse in a condenser. Unless some provision is made to extract charge from the condenser, the voltage potential will jump higher and higher on each cycle of operation, which is generally many thousand cycles per second. The voltage in the output stage will rise as high as it needs to, to overcome the previous charge captured in the condenser. It is not uncommon, for an explosive failure of the condensor to occur under these conditions.

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