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Electronics are mainly the study of direct current and voltage of relatively small magnitude. The word "electronics" came from electron which is a tiny particle of atom. Electricity is not a thing but a phenomena. Electricity means the flow of electrons. Although the electricity is an older concept , it is fundamentally related to Modern physics, especially quantum mechanics which is very hard to grasp. An electron can be regarded as a set of events grouped together by particular relation. Every piece of matter occupies some space and exist in time as it passes through a set of those events which identify it. Among these events two form an interval called timelike interval. Quantum mechanics treats electron as a wave and we can only say that electron tends to exist at some place. We have only statistical knowledge about electron 's existence. Given some experiment which we can perform , sometime s we will find the electron and sometimes we do not. That is to say, if we perform the experiment many many times and calculate the probability, it will match the value predicted by theory. All these are best left for discussion about quantum mechanics. We will focus on electrical circuit theory here. Electronics circuits are quite ubiquitous now. They are inside the Television and radio, they are inside computers, refrigerators, cell phones and even they are the basic components of artificial satellites. One of the greatest revolutions in electronics engineering was the invention of transistors which lead the discovery of radio and lots of other electronic machines like computers.
In analysis of ac circuit , sine wave is too important signal that carry power and energy. The power can be calculated using calculus. The way to calculate average power of sine wave is to take integral of sine wave over a period T and divide the result by the period. Integration is a process to calculate infinite sum.


  rms value
So in the process of calculating the average power we have actually computed infinite sum of the product of the values of voltage and very small time. All kinds of integration involve this process of adding infinite number of small quantities.

Almost every circuit relies on the principle of ohm's law. The law says voltage and current are proportional to each other. There is a proportionality constant between them, which is known as resistance of branch of the circuit in question. Resistance is a linear element of electronic circuits. Surprisingly, capacitor and inductor are linear element also. All the resistors , inductors and capacitors are passive elements of circuit. They absorb energy supplied by the active elements of circuits , like voltage or current sources. They have linearity property. By linearity you can assume that a small change in the input will produce a small change in the output of an element of the circuits. That is why R-L_C circuit can be linear circuit because both R, L and C are linear elements. Capacitor and inductor are linear elements because th sir current voltage relationship is describe d by differential operator which is a linear operator. To know more about linearity you can give a quick look here. It will play a vital role in all of the fields of physics and engineering. I forgot to give the definition of circuit, which means any closed path across which current flows. Where there is no circuit there will be no current flowing. Based on on this definition we can infer that electrical engineering is a game of two wires. Every circuit with combination of resistor, capacitors and inductors can be modeled with linear differential equation. The solution to the equation gives the response of the system. There are various techniques for solving dc and ac circuits. One of those used in solving dc circuit is node analysis. In a node of a complex circuit KVL(kirchoff's voltage law) is applied. Then we can solve the equation for various voltages or current. Every circuit can be described by a mathematical equation. We can solve for currents or voltages for some circuits when the initial conditions are known (in case of differential equation).

Semiconductor

Semiconductor falls in the middle way between the conductors and insulators. The insulators are those materials in which the energy gap between the valence band and conduction band is very high to overcome. On the contrary the energy gap between the valence band and conduction band is very small in conductors. Let me explain a little bit about the band theory of solid. Every atom has electrons which occupy some energy level corresponding to their orbit. In conductor when an atom comes in contact with another atom electrons can share atomic orbitals with each other. This causes an overlap of orbital energy and creates separate energy levels in material. In metal electron can move easily from valence band to non-occupied conduction band as the gap energy is infinitesimally less. In case of insulator there is a large gap, which on application of external electric field can not be easily disintegrated. For details about the band theory of solid another study is needed. In case of semiconductor the gap is small. These are intrinsic semiconductors. But semiconductor can be made to have special electrical properties when they are doped with some materials. This doping turns them into n-type or p-type extrinsic semiconductors which are widely used to make diode, transistors, ICs. Transistors are three terminal device which are widely known as n-p-n or p-n-p transistors

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Transistors are very useful semiconductor device which can either act like an amplifier or a switch. As seen the figure, we can conclude that transistor is a non-linear device. The voltage(collector-emitter) versus collector-emitter current I(c) relationship is non-linear for each value of the gate current I(b). When acting as an amplifier it can amplify weak signal applied to its terminal. On the other hand it can act like a current controlled switch. The operating point is properly chosen for the specific task to be performed by the transistor. Thee operating point is chosen by biasing the transistor in the correct region in a diagram describing current (gate)-voltage(collector) relationships of the transistor. Its actually a graph (two dimensional) that denotes three operating regions of transistor namely active, cut-off and saturation mode. As seen from the curve the collector current increases rapidly in the saturation region. For if we increase base current, the collector current also increases and becomes maximum at zero collector emitter voltage. Beyond that, collector current no longer increases and transistor is said to be fully on.


Fig: Transistor voltages
In both transistors (npn, pnp), the emitter current is the sum of collector and base current. The junction voltages are the collector to emitter , collector to base and emitter to base emitter voltages. These are the internal voltages of transistor.

Fig: Transistor characteristics equations

When there is no bias voltage {V(BB) = 0 } the the base and emitter will be in reverse biased and a little current will flow due to base junction voltage V(BE) - by equation (EEB). The base -emitter current is approximately zero and there will be no collector current . This makes the collector emitter voltage maximum. The region is indicated in the graph as the region below the x-axis. In order to get distortion-less output transistor is always operated in the active region which is indicated as the non-shaded region in the graph. Then the transistor is said to be acting as an amplifier. How transistor works is still a mystery. It was never really designed to serve specific purpose rather it was a solution designed to find specific problem. What is happening inside transistor is some weird stuffs obeying the rules of the quantum world. Schrodinger's equation perfectly describes the probabilistic behavior of atoms and electron inside them. Quantum revolution began when Max plank came up with a strange but realistic idea that energy is discrete and proportional to the frequency of radiation. Energy comes as lumps. Energy is composed of discrete packets called quanta. For example light consists of discrete or separate packets of energy when it is emitted or absorbed. I deliberately mentioned emission and absorption because there seems to be no existence of light in between emission and absorption. The problem is more philosophical than physical, which is better left at the moment.

In Plank equation, there is a proportionality constant between energy and frequency , which is known as planks constant (h). Plank equation was actually devised to solve a problem. He actually played a trick mathematically and came to conclusion that energy must be discretized. At some point the energy cannot be dived further into smaller chunks. So any hot object does not emit infinite amount of energy and does not violate energy conservation principle. Energy are transferred as parcels. If we have a perio di c process with frequency v, we have access to energy of multiples of hv (hv, 2hv, 3hv, ..). We can not have fractional energy of hv. In this way, Plank created the first revolution to quantum mechanics. The value of plank constant is excessively small and thus justifies the behavior of the quantum reality. The objects in classical world does not show wave characteristic because the wave lengths associated with them are very small. De Broglie showed the relationship between wavelength and momentum by his famous equation: Lamda(λ) = p/h. This equation represent wave-particle duality.

On the other hand diode is two terminal device and act as a rectifier. That means it lets the current flow in one direction. A very well known application of diode is the use of it in rectifier circuit which convert an ac supply voltage to a dc voltage source. Like transistor , diode is also a non-linear device. Lets us review a rectifier circuit which will give us a clear concept about filter and some circuit theory.


Fig: Full-wave rectifier

In the diagram given above, a circuit of full wave rectifier circuit is shown. I suppose all you have already been familiar with rectifier circuit. For those who have not , I can say two things. The first one is that rectifier circuit can be built with or without using a capacitor and half wave rectifier converts only the positive portion of the ac signal into pulsating signal. So the output becomes unidirectional dc but not more uniform than the full wave rectifier as shown, which convert both negative and positive portion of a cycle of ac signal into pulsating signal. The second is that there is two types of dc voltage: one is pulsating and other one is uniform. AC means only alternating current. The mechanism of the full wave rectifier circuit is already apparent up to the portion before the capacitive branch. That is the portion of the circuit to the left of the capacitor C. When the ac signal voltage is positive it flows through diode D1 and D2 and when the ac signal is negative if flows through D3 and D4 , making the signal positive all the time across the capacitor, hence the resistor because it is in parallel with the capacitor. But the the output is still not uniform and for better performance smooth dc voltage is required. That is why the capacitor is added in parallel with a resistor. The capacitor makes the output of diode bridge to be an almost uniform dc output. We see that the capacitor charges to a peak value then it discharges again to maintain a steady voltage. There stills seems to be some ripples in the output because the value of capacitance and resistance is not ideal in this case for the smoothing out the voltage. This smoothing out depends on the time constant. We can think of this capacitor and resistor combination as a low pass filter, which blocks high frequency component from a circuit. DC signal connotes a zero frequency signal or the time period is infinity. Here the ac signal's frequency component is removed by the capacitor connected filter. That's why we get almost an uniform dc signal as if there is no pulsating present in the output(ideal rectifier). But how does the filter work? That is the question which begs the study of Fourier analysis

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Power Electronics

Power electronics is concerned with controlling and switching power devices. It is a circuit that can be configured to motors, generators and other power devices. In switching circuit SCR(silicon controlled rectifier) is used to control the flow of current in one direction. It is also known as thyristor. It acts like a diode. But unlike diode, it has three terminal or leads. It has four layers of p or n-type materials connected with each other. Three terminals are known as gate , anode and cathode. When gate pulse is applied in the gate terminal current flows from anode to cathode. Anode acts as negative terminal and cathode as a positive terminal when there are connected together in a circuit. Electrons flow from anode to cathode although the convention of electricity flow is the opposite of actual flow of electrons. Oscillators and ac/dc converters falls in the scope of power electronics. Oscillators are used to create alternating current or voltage. Basic components of the oscillator circuits are the feedback circuit connected with input and output of an amplifier. The feedback circuit provides a means to sustain oscillation. The total phase shift provided by the feedback loop must be 360 to create a complete cycle of oscillation.

A typical oscillator circuit using RC network is given below:

Fig: Basic RC network circuit

The above circuit is a basic oscillator circuit. Firstly a oscillating sine wave has 360 phase shift in one complete cycle, which is a priori condition. A pure sine wave lag itself by 360 over one complete cycle. So our goal is to create a circuit that can produce such phase shift of 360 degree. The three RC networks provide a phase shift of 180 degree, which can be done by choosing correct value R and C. Then the amplifier inverts the signal by producing an additional 180 degree phase shift. So we have a 180+180 = 360 + 0 = 0 (mod 360) degree phase shift. In modular arithmetic, 360 and 0 are equivalent modulo 360 because their difference is divisible by 360. Modular arithmetic is a branch of number theory, which deals with all numbers that are equal to some integer multiples of another number added to another number. All such numbers form a particular finite set. The oscillation should continue like this so that the voltage does not decay out. The feedback loop accomplish this by feeding the output to the input of RC branch. If there were no feedback after a certain time of one period the oscillation would stop. Feedback ensures that after one cycle has stopped the next cycle automatically start. Thus it is called feedback loop which is the core idea behind oscillator circuit. The frequency of the oscillation is determined by the value of R and C also. In addition, the total loop gain must be unity so the amplifier must have a gain that is inverse of the feedback gain. There is a formula for that. It is so simple that I have not given here explicitly.


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