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In the previous post on the P-N junction, we looked at the formation of a P-N junction. The resulting device is called a diode.

The semiconductor diode is closest to the ideal diode. To study electronic devices made up of the P-N junctions, we look into their VI characteristics.

The VI characteristics of a device is simply a plot of the V vs I curve for the device. For instance, the resistor follows ohm’s law & hence, we obtain a liner VI characteristic for resistance.

The curve below shows the VI characteristics of an ideal & a real diode…

The curve in the first quadrant represents the diode in its forward bias. The diode starts conducting at the voltage V_c called the Cut In Voltage. This voltage is about 0.6 V for Silicon & 0.2 V for Germanium.

In case of the reverse bias, a small current flows. This current, independent of the applied voltage & present only due to the minority charge carries, is called the reverse saturation current.

In reverse bias, the external applied voltage breaks the covalent bonds in the junction region. This leads to the breakdown of the junction at a specific voltage called the breakdown voltage(V _b).

Notice that we only consider V_b in the real case. Hence, ideally, there should be almost no current in the reverse bias state, & hence, no breakdown of the junction.

The breakdown simply means that the diode now allows all the current to flow through it. It is just a malfunctioning of the diode & not the damage of the diode. The diode is otherwise supposed to allow current through just one direction & stop all the current in the other.

Further, two kinds of resistances exist in the diode corresponding to the direct & alternating currents respectively.

The diode can also behave as a capacitor, and even as a variable capacitor. There are two different ways of looking at a diode as a capacitor.

The current that flows through the diode depends upon the applied voltage & the temperature(& hence, the voltage due to the temperature). It is given by…

where I₀ is the reverse saturation current, e is the electronic charge, k is the Boltzmann constant, V the applied voltage & T is the temperature. The term kT/e is also called the voltage equivalent temperature. Also, η is a constant = 1 (for silicon)
& 2 (for germanium).

All other diodes like the Zener Diode, LED, etc are derived from the basic semiconductor diode with a few changes in their design & functions.

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Harmonics formed on waves are generated as component frequencies of a fundamental frequency of the wave.

The fundamental & the higher frequencies(harmonics) generate periodic signals from the original wave. And every periodic signal can be written as a sum of the variuos harmonics using the Fourier series.

Hence, to find the various harmonics using the fourier series, we can use…

nth harmonic : (a_ncosx+b_nsinx)

where,

&

where p is the number of unique values of the function y. The following example will make things a bit more clear…

Example : y is a function of x periodic with period 2pi. Some experimental values of y are given below calculated for certain values of x. Expand y to 2 harmonics.

Solution :

Clearly, in the above, p=6,

& We simply need to find:

1st harmonic + 2nd harmonic = (a₁cosx+b₁sinx) + (a₂cos2x+b₂sin2x)

So, all we need is a₁, b₁, a₂ &
b₂

for which we use the formula mentioned above:

&

where x_i=0, 60, 120… & so on.

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In the previous post, we looked at p & n type semiconductors. These are more useful when combined together to form something called the P-N junction.

The p-doped region has holes as its majority charge carriers & the n-doped region has free electrons as its mobile charge carriers. Hence, the holes & free electrons attract & eliminate each other. This process is called recombination.

Thus, due to the diffusion of the charge carriers, a potential difference gets established in the region of recombination. This potential is called the barrier potential or the space charge potential & the region is called the depletion region.

The device resulting from the p-n junction is called a p-n junction diode or simply, a diode. P-N junctions are also used in transistors & rectifiers.

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We looked at pure or intrinsic semiconductors in the previous post on Analog Electronics.

We can however, change the electrical properties of the pure semiconductors by adding certain impurities to their structure, a process called doping.

When doping semiconductors of groups 3 & 4, these impurities are usually elements of group 3(acceptors) or 5(donors).

This gives rise to two kinds of extrinsic semiconductors : ones having free electrons as their majority charge carriers(called n-type) & those which have holes as their majority charge carriers(called p-type).

Extrinsic semiconductors are used in many electrical devices. A more useful version of doped semiconductors is the p-n junction.

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Here are some important properties of the Laplace Transform F(s) being the Laplace transform of f(t).

Initial Value Theorem
Final Value Theorem
periodic with a period T

Above, F₁(s) is the Laplace transform of f(t) for the first cycle.

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In the previous post on Fourier Series, we looked at functions periodic with period 2pi. Now, we’ll take a look at Fourier series for functions having an arbitary period, lets say, some period 2L.

The general formulas we would need for finding the Fourier series are as follows…

The Series:

The Constants:

These apply when the period given in the question are [-L, L]. We would modify the limits of integration in the above depending on the given interval.

Further, for functions periodic with a period 2pi, we only need to put L=pi in the above formulas. You can find those formula here.

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We’ve often heard of terms like the Silicon Valley & the Silicon Economy. What do they really refer to?

All modern day electronics are build using a special class of materials called semiconductors. These materials have an electrical resistivity between a conductor & an insulator.

They are the foundations of all electronics which are computerized(computers, ipods, etc) & ones which use radio waves(radio, cell phones, etc), silicon being the heart of all these devices.

The elements like Silicon & Germanium having 4 valence electrons are elemental semiconductors. The 4 valence electrons can easily bond with 4 neighbouring electrons to give rise to a lattice structure with no free electrons(at zero temperature).

Since, there are no free electrons at zero temperature, Intrinsic(pure/elemental) Semiconductors behave as insulators at zero temperature.

Then how do they differ from insulators? Well, the difference is in terms of the energy gap between the valence & conduction bands.

This energy gap is zero in case of conductors, very high for insulators & very small for semi conductors(about 1 eV)

Hence, on increasing the temperature, the electrons in the valence band of the semiconductor gain energy & some of them get sufficient energy to move to the conduction band.

This is what happens physically inside the lattice. In terms of the energy bands, we could show this as follows…

These electrons leave behind empty spaces called holes. The holes appear to move in a direction opposite to that of the electron & hence, are the positive charge carriers of the semiconductor.

Hence, a semiconductor conducts only at high temperatures & the conduction is due to both electrons & holes, also, the electrons & holes are equal in number.

However, the conductivity of the semiconductors can be changed drastically by adding certain impurities to the semiconductor materials. This process is called doping & is explained in the next post.

Semiconductors find their major application in manufacturing transistors. The first transistor was made of Germanium. Germanium, in fact, would have more free electrons at a particular temperature than silicon. But Silicon is preferable as it can be used at extremely high temperatures.

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C++, as the name suggests is a superset of C. As a matter of fact, C++ can run most of C code while C cannot run C++ code. Here are the 10 major differences between C++ & C…

1. C follows the procedural programming paradigm while C++ is a multi-paradigm language(procedural as well as object oriented)

In case of C, importance is given to the steps or procedure of the program while C++ focuses on the data rather than the process.
Also, it is easier to implement/edit the code in case of C++ for the same reason.

2. In case of C, the data is not secured while the data is secured(hidden) in C++

This difference is due to specific OOP features like Data Hiding which are not present in C.

3. C is a low-level language while C++ is a middle-level language

C is regarded as a low-level language(difficult interpretation & less user friendly) while C++ has features of both low-level(concentration on whats going on in the machine hardware) & high-level languages(concentration on the program itself) & hence is regarded as a middle-level language.

4. C uses the top-down approach while C++ uses the bottom-up approach

In case of C, the program is formulated step by step, each step is processed into detail while in C++, the base elements are first formulated which then are linked together to give rise to larger systems.

5. C is function-driven while C++ is object-driven

Functions are the building blocks of a C program while objects are building blocks of a C++ program.

6. C++ supports function overloading while C does not

Overloading means two functions having the same name in the same program. This can be done only in C++ with the help of Polymorphism(an OOP feature)

7. We can use functions inside structures in C++ but not in C.

In case of C++, functions can be used inside a structure while structures cannot contain functions in C.

8. The NAMESPACE feature in C++ is absent in case of C

C++ uses NAMESPACE which avoid name collisions. For instance, two students enrolled in the same university cannot have the same roll number while two students in different universities might have the same roll number. The universities are two different namespace & hence contain the same roll number(identifier) but the same university(one namespace) cannot have two students with the same roll number(identifier)

9. The standard input & output functions differ in the two languages

C uses scanf & printf while C++ uses cin>> & cout<< as their respective input & output functions

10. C++ allows the use of reference variables while C does not

Reference variables allow two variable names to point to the same memory location. We cannot use these variables in C programming.

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This includes the basic signals, their properties & classification of signals based on these properties. To easily understand signals & systems, we would visualize signals as simple mathematical functions.

Continuous & Discrete Signals

Continuous signals & those defined over a set of real numbers(R) & discrete signals & those defined for discrete integers(I).

For instance, a signal(a function) having the domain [0,10] is continuous & one having the domain {1,2,3…10} is discrete.

A Continuous Signal can be converted to a Discrete Signal using an Analog-to-Digital Converter(ADC). The conversion consists of a process called sampling.

The sampling process simply samples out values of the signal at certain points seperated by an equal interval called the sampling period. In the above figure, the sampling period would be 3.

A common application of the above process is a Compact Disc(CD) which is simply a signal sampled at 44.1kHz & Quantized at 16 bits/2 bytes.

Analog & Digital Signals Analog Signals are continuous electric signals which arise from non-electric signals. The variable of the converted signal is analogous to the non-electric time varying signal & hence, they are called analog signals.

A good example is an audio signal. The image below shows the analog signal for a song called Gulon Mein…

A digital signal, unlike the analog signal, takes only two vales-HIGH or LOW, ON or OFF, 0 or 1, TRUE or FALSE, etc. All computers & other gadgets use digital signals to store information. (The term sometimes also refers to discrete time signals which can also take discrete values other than 0’s & 1’s)

Based on the above, we may infer that a analog signal is continuous signal & a digital signal is a discrete time signal.

Signals are also classified as…

We then have Deterministic & Random Signals.

A random signal takes random values & at a point on the signal, we cannot determine its value just before it or just after it. However, these values can be easily determined for a deterministic signal. Next Post in this Category >> Signal Operations

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Signal Operations are simply modifications to the time variable of the signal to generate new signals. These are pretty similar to the mathematical graphical tranformations from our good old Calculus text.

The three kinds of Signal Operations are Time Shifting, Time Scaling & Time Inversion(or Time Reversal)

Time Shifting is simply shifting th signal in time. When we add a constant to the time, we obtain the advanced signal, & when we decrease the time, we get the delayed signal.

Time Scaling is compressing or dilating the signal.

Time Inversion is simply flipping the signal about the y-axis.

The above operations makes it easy to express a large domain of signals based on the fundamental signals by operation upon the basic signals.

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