To design any electrical circuit, eitherÂ analogÂ orÂ digital,Â electrical engineersÂ need to be able to predict the voltages and currents at all places within the circuit.Â Linear circuits, that is, circuits with the same input and output frequency, can be analyzed by hand using complex number theory. Other circuits can only be analyzed with specializedÂ software programsÂ or estimation techniques.
Have you ever wondered what happens when you flip a switch to turn on aÂ light,Â TV,Â vacuum cleanerorÂ computer? What does flipping that switch accomplish? In all of these cases, you are completing anÂ electric circuit, allowing a current, or flow of electrons, through the wires.
AnÂ electricÂ circuit is in many ways similar to your circulatory system. Your blood vessels, arteries, veins and capillaries are like the wires in a circuit. The blood vessels carry the flow ofÂ bloodÂ through your body. The wires in a circuit carry the electric current to various parts of an electrical or electronic system.
YourÂ heartÂ is the pump that drives the blood circulation in the body. It provides the force or pressure for blood to circulate. The blood circulating through the body supplies various organs, like your muscles,Â brainÂ and digestive system. AÂ batteryÂ or generator producesÂ voltageÂ -- the force that drives current through the circuit.
The diagram above shows a simple circuit of a flashlight with a battery at one end and a flashlight bulb at the other end. When the switch is off, a complete circuit will not exist, and there will be no current. When the switch is on, there will be a complete circuit and a flow of current resulting in the flashbulb emitting light.
Circuits can be huge power systems transmitting megawatts of power over a thousand miles -- or tiny microelectronic chips containing millions of transistors. This extraordinary shrinkage of electronic circuits made desktop computers possible. The new frontier promises to beÂ nanoelectronicÂ circuits with device sizes in the nanometers (one-billionth of a meter).
Power circuitsÂ transfer and control large amounts of electricity. Examples are power lines and residential and business wiring systems. The major components of power circuits are generators at one end and lighting systems,Â motors, heating systems or household appliances at the other end. In between are power lines,Â transformersÂ andÂ circuit breakers.
The blood flowing through your body doesn't get a free ride. The walls of the blood vessels impede the flow, and the smaller the blood vessel, the more the resistance to flow. Some of the pressure produced by your heart is just for pushing blood through blood vessels. As electrons move through wires, they bump intoÂ atoms. This impedes the flow of the electrons. The wire offersÂ resistanceÂ to the flow of the current. The amount of resistance depends on the material, diameter and length of the wire. The resistance increases as the diameter of the wire decreases. Resistance is in units ofÂ ohmsÂ
In aÂ series circuit, the same current flows through all the components. The total voltage across the circuit is the sum of the voltages across each component, and the total resistance is the sum of the resistances of each component. In this circuit, V = V1+V2+V3Â and R = R1+R2+R3. An example of a series circuit is a string ofÂ DiwaliÂ lights. If any one of theÂ bulbsÂ is missing or burned out, no current will flow and none of the lights will go on.
Parallel circuitsÂ are like the smallerÂ bloodÂ vessels that branch off from an artery and then connect to a vein to return blood to theÂ heart. Now think of two wires, each representing an artery and a vein, with some smaller wires connected between them. These smaller wires will have the same voltage applied to them, but different amounts of current flowing through them depending on the resistance of the individual wires.
An example of a parallel circuit is the wiring system of aÂ house. A single electric power source supplies all the lights and appliances with the same voltage. If one of the lights burns out, current can still flow through the rest of the lights andÂ appliances. However, if there is a short circuit, the voltage drops to almost zero, and the entire system goes down.
Circuits are generally very complex combinations of series and parallel circuits. The first circuits were very simple DC circuits. We'll look at the history of circuits and the difference between DC and AC.
History of Electrical Circuits
Japanese Prime Minister Junichiro Koizumi laughs as a balloon clings to him with a static electrical charge.Â
Early investigations ofÂ static electricityÂ go back hundreds of years. Static electricity is a transfer of electrons produced by friction, like when you rub a balloon across a sweater. A spark or very brief flow of current can occur when charged objects come into contact, but there is no continuous flow of current. In the absence of a continuous current, there is no useful application ofÂ electricity.
The invention of theÂ batteryÂ -- which could produce a continuous flow of current -- made possible the development of the first electric circuits. Alessandro Volta invented the first battery, the voltaic pile, in 1800. The very first circuits used a battery and electrodes immersed in a container ofÂ water. The flow of current through the water produced hydrogen and oxygen.
The first widespread application of electric circuits for practical use was for electric lighting. Shortly after Thomas Edison invented his incandescentÂ light bulb, he sought practical applications for it by developing an entire power generation and distribution system. The first such system in theÂ United StatesÂ was the Pearl Street Station in downtownÂ Manhattan. It provided a few square blocks of the city with electric power, primarily for illumination.
One classification of circuits has to do with the nature of the current flow. The earliest circuits were battery-powered, which made in a steady, constant current that always flowed in the same direction. This isÂ direct current, or DC. The use of DC continued through the time of the first electric power systems. A major problem with the DC system was that power stations could serve an area of only about a square mile because of power loss in the wires.
In electronic circuits, the distances and currents are very small, the currents and voltages in these circuits represent constantly changing phenomena, so the electrical representations, or analogs, are also constantly changing. The second reason is thatÂ radioÂ waves (like those used byÂ TVs,Â microwavesÂ andÂ cell phones) are high-frequency AC signals. The frequencies used for all types ofÂ wirelessÂ communication has steady advanced over the years, from the kilohertz (kHz) range in the early days of radio to the megahertz (MHz) and gigahertz (GHz) range today.
However, in some situations it is difficult to prevent adjacent inductors from influencing each other, as the magnetic field of one device couples with the windings of its neighbours. This influence is defined by the mutual inductance M. For example, if you have two inductors in series, there are two possible equivalent inductances depending on how the magnetic fields of both inductors influence each other.
When there are more than two inductors, the mutual inductance between each of them and the way the coils influence each other complicates the calculation. For a larger number of coils the total combined inductance is given by the sum of all mutual inductances between the various coils including the mutual inductance of each given coil with itself, which we term self-inductance or simply inductance. For three coils, there are six mutual inductancesÂ M12,Â M13,Â M23Â andÂ M21,Â M31Â andÂ M32. There are also the three self-inductances of the three coils:M11,Â M22Â andÂ M33.
By reciprocityÂ MijÂ =Â MjiÂ so that the last two groups can be combined. The first three terms represent the sum of the self-inductances of the various coils. The formula is easily extended to any number of series coils with mutual coupling. The method can be used to find the self-inductance of large coils of wire of any cross-sectional shape by computing the sum of the mutual inductance of each turn of wire in the coil with every other turn since in such a coil all turns are in series. Reversed so that M is negative, then the parallel inductance is nearly zero or the combination is almost non-inductive. We are assuming in the "tightly coupled" case M is very nearly equal to L. However, if the inductances are not equal and the coils are tightly coupled there can be near short circuit conditions and high circulating currents for both positive and negative values of M, which can cause problems.
More than 3 inductors becomes more complex and the mutual inductance of each inductor on each other inductor and their influence on each other must be considered. For three coils, there are three mutual inductancesÂ M12,Â M13Â andÂ M23. This is best handled by matrix methods and summing the terms of the inverse of theÂ LÂ matrix (3 by 3 in this case).