"Some of the most interesting effects in nature," he writes, "are cyclic or involve an oscillation. It is generally the case where sustained oscillations are observed that the result of an action is fed back to influence the further course of this action. In electrical devices sustained oscillations can occur only if the circuit includes some element that can function as a negative resistance, so that an increase in voltage across the element goes with a decrease in current through it [see illustration at right].

"Negatively sloping characteristics for alternating current and voltage can be generated either by inductances or capacitors, if their electrical characteristics depend on the magnitude of either the applied voltage or the current. An iron-cored choke coil can be made to react in this way. Many transformers also show the effect.

"In some respects a choke coil acts as the electrical counterpart of a flywheel, the inductance of the coil being analogous to the mass of the wheel. Similarly, the capacitor can function as an electrical spring, the capacity being analogous to the stiffness of the spring. When a choke coil and capacitor are interconnected, the combination exhibits the property of resonance, just as the balance wheel and hairspring of a watch tend to oscillate at a characteristic rate. Moreover, just as the rate of the watch can be altered by changing the mass of the wheel or the stiffness of the spring, so can the resonant frequency of the electrical circuit be adjusted by altering its inductance or capacity.

"The inductance of an iron-cored choke coil is related to the amount of magnetic flux that can be induced in the core by a current of given magnitude. For weak currents the amount of current in the coil and magnetism induced in the core are directly proportional. But the ability of the core to acquire magnetism is limited. The current can be increased to a point beyond which the magnetism fails to increase in proportion. At this point the core is said to be approaching saturation. Thereafter the inductance of the choke coil decreases as current in the winding increases.

"When a choke coil is connected to a capacitor of such size that the combination resonates at a frequency of, say, 55 cycles per second, and the circuit is connected to a source of alternating current with a frequency of 60 cycles per second, the relationship between the current and voltage varies as shown by the curve at bottom left in the accompanying illustration [right]. Initially the current increases in proportion to the voltage. Then, as the core approaches saturation, the inductance falls. Roughly speaking, this has the effect of tuning the resonant circuit closer to the frequency of the source, from 55 cycles toward 60 cycles. At resonance the circuit offers minimum resistance to the current. Consequently as resonance is approached the current increases and the voltage decreases. As the slope of the curve shows, this is a case of negative resistance (more precisely, in this special alternating-current example, negative impedance). Beyond resonance the voltage again increases with the current, and the slope of the curve reverses. Here it is assumed that the choke coil is connected in series with the capacitor, as shown at top left in the illustration. When the coil and capacitor are connected in parallel, the curve assumes the shape at bottom right in the illustration.

"If one now includes a component in the circuit that offers increasing resistance to the current when the current increases, the circuit will become unstable and oscillate. An ordinary tungsten filament incandescent lamp can be used as such a component. The resistance of these bulbs typically increases by a factor of 13 between 'off' and 'on.' To demonstrate the effect connect the primary winding of a transformer (used as a choke coil) in series with a condenser and an ordinary tungsten filament lamp. If all the values are properly adjusted, the lamp will flash on and off regularly every few seconds. The primary or input winding of a five-volt, 10-ampere filament transformer such as the Stancor No. P-6135 may be used as the choke coil. (The terminals of the secondary winding should be separated and taped.) A 100-watt incandescent lamp and a 12-microfarad paper capacitor (not electrolytic) are satisfactory. Inexpensive one- or two-microfarad surplus capacitors can be connected in parallel to make up the required 12 microfarads.

"It is convenient to be able to adjust the power-line voltage applied to the combination by some sort of variable autotransformer such as a Variac [see illustration below]. The flashing rate of the lamp will depend on the 60-cycle line voltage; indeed, it is a sensitive indication of small changes in line voltage. Beyond the range of approximately five volts (about optimum) the lamp will remain either fully on or permanently off. (When working with series-resonant circuits, remember that the voltage across both the choke coil and the capacitor can be several times greater than the line voltage. Observe the usual precautions.)

"A comparable circuit that is relatively insensitive to changes in line voltage can be made by connecting two choke-capacitor-lamp combinations in parallel and placing a single capacitor in series with one of the power leads [see diagram at left in illustration on right]. If the components on the two sides of the parallel combination are approximately the same, the lamps will flash alternately in the manner of a railroad crossing signal. Up to four of these series combinations have been connected in parallel so that-the bulbs flash in stable sequence. One combination has been in uninterrupted operation for nine years. The sequence of flashing is maintained by the relative resistance of the lamps. The most sensitive combination flashes first; then the current automatically switches to the lamp in the next most sensitive component and so on. By the time all the lamps have flashed on and off, the one that flashed first has cooled sufficiently to present the least resistance and therefore initiates another round of flashing. Incidentally, the transformers run abnormally warm but do not become dangerously hot.

"Two choke-capacitor-lamp circuits in parallel can be made to operate in other interesting ways, either by unbalancing one of the negative-resistance assemblies or by applying abnormally low voltage. If one of the capacitors is slightly larger than the other, for example, one of the bulbs will remain permanently lighted unless the circuit is disturbed. A brief disturbance can be introduced by connecting the unused secondary windings of the transformers by means of a quick-acting push button [see diagram at right in illustration above]. Each time the button is momentarily depressed, the lamp that is normally on will go off for a fixed interval and the one normally off will go on-an action similar to that of a vacuum tube flip-flop circuit. At the end of the interval the circuit will flop back to its normal state. If the two halves of the circuit are balanced but the line voltage is very low, spontaneous switching will not take place. If the push button is operated when the circuit is in this state, however, the existing situation will reverse itself. The bulb previously off will go on and the bulb previously on will go off and stay that way.

"Small electric motors of the universal type draw progressively less current as they accelerate to full speed. In effect their resistance increases with time. Hence they can be used in a circuit characterized by negative resistance to induce oscillation. A small motor connected in series with the choke coil and a capacitor of appropriate size will accordingly turn itself on and off periodically. It must be remembered that the performance of these devices is influenced by line voltage. The voltage must be adjusted with a device such as a Variac for optimum performance.

"The experiments just described are all based on the negative impedance that is characteristic of a nonlinear choke coil and capacitor, plus a lamp (or motor), connected in series. It can also be shown that oscillatory behavior can be expected when the choke coil and capacitor are connected in parallel. To demonstrate this phenomenon, the paralleled units are connected in series with a resistance that decreases with increased temperature. Some thermistors will work in this application. An amusing experiment, though one rather difficult to perform, uses for the resistor a hot dog, one of the numerous substances in which electrical resistance decreases as temperature increases.

"A fascinating version of the well-known floating-ring experiment can be based on the property of negative resistance. In the classical version of the experiment a loose-fitting aluminum ring is dropped over a vertical solenoid that is energized by alternating current. When the power is switched on, the ring is lifted into the air. The alternating magnetic field of the solenoid opposes the alternating magnetic field set up around the ring by currents induced in the ring by the magnetism of the solenoid. In some experiments an extension rod of wood is added to the top of the solenoid as a guide to prevent the ring from flying away from the apparatus. The ring, restrained by the stick, then floats in the air. If the coil of the solenoid is resonated by a suitable capacitor, the current in the coil drops when the ring rises, thereby allowing the ring to fall back. But in falling back the ring interacts electrically with the coil (shifts the current across the region of negative resistance) and the current increases, initiating another cycle. Thus without using breaker points or other mechanical switching devices the floating ring can be transformed into one that dances. A display unit of this type that was designed for operation from a 110-volt, 60-cycle power line used a core two feet long made of thin iron laminations one inch wide and stacked one inch thick [see illustration below] The core extended below a coil four inches long and wound with approximately 3,000 turns of No. 18 wire. The ring, which slid up and down the 14-inch length of core above the coil, was a one-inch length of aluminum tubing. An eight-microfarad capacitor is about right. The ring continuously jumps up and down the full two-foot length of the core. A more elaborate version of the apparatus that is less sensitive to changes in line voltage can also be made [see illustration below].

"Another interesting oscillatory effect is observed when an iron pendulum bob is suspended directly over a coil that is similarly connected in series with an appropriate capacitor and energized by alternating current. If conditions are right, the iron bob will vibrate above the coil. This experiment has been described in 'The Amateur Scientist' as a method of keeping a Foucault pendulum in motion without the use of an escapement mechanism, either electrical or mechanical [see 'The Amateur Scientist'; June, 1958].

"Interesting oscillators need not be electrical in nature. An automatic Cartesian diver provides an illustration. Normally this charming toy consists of a small inverted vial, filled partly with water and partly with air, that floats in a larger bottle of water. Pressure applied to a diaphragm that closes the top of the large bottle compresses the air above the water. This pressure is transmitted through the water to the air inside the small vial, compressing it. The consequent loss of buoyancy causes the vial (the "diver") to sink to the bottom of the larger bottle. Removal of pressure reverses the process, and the diver rises. If the size of the air bubble is carefully adjusted, the diver can be made so sensitive that it will respond to the small change produced by squeezing the glass wall of the outer bottle. The diver can be made automatic by including a small drop of some volatile liquid in the air bubble of the vial and then either warming the bottom of the outer bottle or cooling its top. In either case the diver will sink; as it descends into warmer water the bubble expands, increasing the buoyancy of the diver. This makes the diver rise, whereupon cooling initiates a new cycle. One can either cool the top of the outer bottle with a piece of ice or warm the bottom slightly by any convenient source of heat. (A 60-watt lamp bulb that has been coated with carbon in a smoking flame works well.) In every case the initial buoyancy of the diver must be adjusted until it is on the verge of sinking. This can be done easily by adding or removing a little air from the diver with a pipette bent into a hook at the lower end for reaching up into the diver. The diver can be a two-inch length of quarter-inch glass tubing and will be most stable if a small bulb is blown at the sealed end [see top illustration below]. Any one of a number of volatile liquids can be used in the air bubble. Ether works well but eventually dissolves in the surrounding water. Petroleum ether is preferable.

"The sustained motion of the diver is due in part to the appreciable time required for it to change temperature. If the heating and cooling were instantaneous, the diver would take a position at the center of the outer flask and stay there, because any tendency to rise would immediately be counteracted by decreasing buoyancy. By introducing a time delay what otherwise would be a depth regulator is converted into an oscillator or heat engine. It is often observed in scientific experiments that regulators or servo devices oscillate if a time delay is introduced into the system -that is, if there is a delay in forwarding a signal from the output to the input of the feedback system.

"It is interesting to observe in the case of the Cartesian diver moving in a region of nonuniform temperature that the size of the bubble increases as the diver moves down into a region where the water pressure is also increasing. That is to say, the volume increases rather than decreases with increasing pressure. This corresponds exactly to the increase in current that accompanies the decrease in voltage in electrical negative resistance. In most electrical situations current increases with voltage.

"Another delightful oscillator can be bought in toy stores or made at home. It consists of a small metal boat that is powered by a boiler equipped with a pair of tubes that act as jets at the stern. When a candle is placed under the boiler, one soon hears a putt-putt sound and the boat is driven steadily forward. The alternate formation and condensation of steam draws water into the boiler and shoots it out. If the top of the boiler is flexible, the sound is quite loud. At first thought it may seem amazing that sucking in water and then blowing it out could drive the boat steadily ahead rather than first pulling it back and then pushing it forward. Two effects account for the forward motion of the boat. First, water is drawn in from all directions at the stern but is ejected almost straight backward. This imparts a net forward component of momentum to the boat. The second effect is caused by the shape of the tubes. When water is shot out of an L-shaped tube, the bend is driven forward. The principle is demonstrated by Hero's aeolipile, the earliest known jet motor. When water or gas is drawn into an L-shaped tube, however, the tube is not pulled backward.

"All these oscillators require that some energy be fed from the output back to the input through a system that introduces time delay. Moreover, this signal must act in a direction that reinforces the output. Signals that are fed back in opposition to the output stabilize the system, and the result is known as negative feedback. Negative feedback is found in nature as well as in man-made devices such as high-fidelity amplifiers. In animals negative feedback helps to stabilize muscle action.

"Biologists can perform surgery on a jellyfish to display a system that has delay, amplification and feedback, and which transforms the animal into a biological oscillator. In a normal jellyfish a controlling impulse is discharged from a central control point into the nerve network that stimulates an over-all contraction of the jellyfish 'bell' to produce a swimming stroke. But consider what happens when the center of the jellyfish is excised and a point on the outer ring of the nerve network is stimulated. The impulse is transmitted around the ring in both directions, initiating muscle contraction until the opposing actions cancel on the other side of the bell. If a point on the ring is squeezed, the impulse is blocked. Stimulation to the right of this point will start an impulse propagating around to the right. If at some time before this impulse arrives back at the starting point the block has been removed, the impulse will be propagated past the starting point and go around for another trip. In fact, the wave of action will continue to travel around the ring for a week or more if the jellyfish is merely left sitting in a pan of sea water. The characteristic time delay in this case is represented by the interval required for the transmission of an impulse around the ring."

Bibliography

NEGATIVE RESISTANCE. R. Stuart Mackay in American Journal of Physics, Vol. 26, No. 2, pages 60-69; February, 1958.

The Society for Amateur Scientists (SAS) is a nonprofit research and educational organization dedicated to helping people enrich their lives by following their passion to take part in scientific adventures of all kinds.