Concept of Negative Feedback

In a feedback system, a signal that is proportional to the output is fed back to the input. It may happen unintentionally or be done intentionally. When the feedback signal adds to the input signal, it is called positive feedback, and when the input signal gets subtracted from the feedback signal, it becomes negative feedback.

Positive feedback is mostly used for the realization of oscillators, whereas negative feedback is used to stabilize the gain of amplifiers against a variation in transistor parameters, supply voltage, and temperature etc.The study in this chapter is limited to negative feedback only, which is primarily used to improve any one of the four types of amplifiers given in the next section, such that the amplifiers become as close to ideal as possible. However, certain conditions are required that help achieve the objective. For example, a primary amplifier is needed to have a very high gain in the forward direction, minimum reverse transmission, which normally happens as a property of the transistors used. Appropriate negative feedback connection and minimum effect of loading due to the feedback network on the main amplifier circuit are also very important.

The above mentioned term appropriate negative feedback needs a bit of explanation. In the voltage and current amplifiers, variables at the input and output are the same, hence there is no problem as such while feeding a part of the output to input.

In this chapter, the theory and properties of singleview camera geometry are discussed. We consider theprinciple of image formation in optical cameras inthis case and apply it to relate thethree-dimensional (3-D) world with the image pointson a two-dimensional (2-D) plane.

11.1 | Pinhole camera

A mapping of a point in a 3-D coordinate space to apoint on a 2-D plane has been already discussed inthe previous chapter while explaining the canonicalconfiguration of a 2-D projective space. We relatethese concepts with respect to a pinhole camerabased imaging system. Consider a 3-D scene point, 𝑷, as shown in Fig. 11.1. The corresponding imagepoint, 𝒑′, is the point of intersection of theimage plane and the straight line from 𝑷 thatpasses through the center of the lens, 𝑂. In thesame analogy, consider the formation of an image infront of the camera center, where the correspondingimage plane is placed at the same distance as thesensor is placed behind the lens. In this case, theimages obtained on the image plane that is placed infront of the lens are of the same size as on thesensor, and there is a logical transformation ofcoordinates from point 𝒑′ to point 𝒑. Thus we maydirectly relate the scene point 𝑷 with the imagepoint 𝒑. This is a convenient way of handlingcoordinate system of image points by placing it infront of the camera in the same side of the viewingobjects.

12.1 INTRODUCTION [LO1]

There are in general two approaches to solving equilibrium problems in solid mechanics: Eulerian and Lagrangian. The first approach deals with vectors such as force and moments, and considers the static equilibrium and compatibility equations to solve the problems. In the second approach, scalars such as work and energy are used, and here solutions to problems are based on the principle of conservation of energy. There are many situations where the second approach is more advantageous, and here some powerful methods, such as the method of virtual work, based on this approach, are used.

Eulerian and Lagrangian approaches to solving solid mechanics problems are much more involved. However, here we have chosen to describe these in a simplified manner, which is suitable as a prologue to the present discussion on energy methods.

In mechanics, energy is defined as the capacity to do work, and this may exist in different forms. We are concerned here with elastic strain energy, which is a form of potential energy stored in a body on which some work is done by externally applied forces. Here it is assumed that the material remains elastic when work has been done so that all the energy is recoverable and no permanent deformation occurs. This means that strain energy U = work done. If the load is applied gradually in straining, the material load–extension graph is as shown in Figure 12.1, and we may write U = ½ Pδ.

The hatched portion of the load–extension graph represents the strain energy and the unhatched portion ABD represents the complementary energy that is utilized in some advanced energy methods of solution.

List of Experiments

• 1. Determine the energy band gap of N-type Germanium (Ge) semiconductor using the four-probe method.

• 2. Verify Stefan's fourth power law for black body radiation and determine the exponent of temperature.

• 3. Study of thermoelectricity: Determine thermopower of copper-constantan thermocouple.

• 4. Study the variation of magnetic field with distance along the axis of current-carrying coil and then estimate the radius of the coil.

• 5. Study of Carrey Foster bridge: Determine resistance per unit length of the bridge wire and of a given unknown resistance.

• 6. Determine specific charge (charge to mass ratio; e/m) for electron.

• 7. Study of tangent galvanometer: Determine reduction factor and horizontal component of the earth's magnetic field.

• 8. Determine the wavelength of sodium light using Newton's rings method.

• 9. Determine the concentration of sugar solution using half-shade polarimeter.

• 10. Determine the wavelength of spectral lines of mercury (for violet, green, yellow-1, and yellow-2) using plane transmission grating.

• 11. Determine the charge sensitivity and ballistic constant of a ballistic galvanometer.

• 12. Determine the wavelength of spectral lines of hydrogen and hence the value of Rydberg constant.

• 13. Draw the V-I characteristic of light-emitting diode (LED) and determine the value of Planck's constant.

Experiment 1: Band Gap of Semiconductor

Objective: To determine the energy band gap of n-type Ge-semiconductor using four-probe method.

Apparatus Used: The following apparatus are used in this experiment:

• 1. Probe arrangement (shown in Figure 14.1).

• 2. n-type Ge-crystal chip with nonconducting base.

• 3. Oven with temperature up to 200°C.

• 4. A constant current generator power supply.

• 5. Power source for the oven.

• 6. Thermometer.

Introduction

Classification, characteristics, and basic design methods of certain types of networks that perform filtering action on the basis of the frequency of signals are briefly discussed in this chapter. The filters, which used only passive elements, and known as passive filters, were the only kind of filters in earlier days. Passive filters are still in use in many specific cases but have been replaced by active filters (using at least one active device) in a majority of applications. One essential reason for the changeover from the passive filters to the active filters was the inability of the realization of practically feasible inductors in integrated circuit (IC) form over a large frequency range of operation. Hence, structures that replaced (simulated) inductors employing resistance, capacitance, and op-amp were synonymous with the active filters, and these were called active RC filters. The usage of op-amps is still dominant, but other active devices are also used in a big way.

Another important approach to analog filter realization has emerged in the form of switched capacitor (SC) circuits. An important feature of the SC circuits is that it uses only capacitors, op-amps, and electronic switches. Consequently, performance parameters of the circuit depend on capacitor ratios and switching frequency. It is to be noted that very small value capacitances can be used, resulting in consuming less chip area, and better practical results as capacitors in ratio form can be fabricated with much less tolerance.

Our lived experiences are punctuated by events that are sometimes a result of our purposeful intentions and at other times outcomes that happen by pure chance. Even at an abstract level, it is a very human endeavor to deduce meaning from seemingly random observations an exercise whose primary objective is to derive a causal structure in observed phenomena. In fact, our whole intellectual pursuit that differentiates us from other beings can be understood through our inner urge to discover the very purpose of our existence and the conditions that make this possible. This eternal play between chance episodes and purposeful volition manifests in diverse situations that I have labored to recreate through computer simulations of realistic events. This play has a dual role - first, it binds together the flow of our varied experiences and, second, it offers us a perspective to assimilate our understanding of events happening around us that affect us. In order to appreciate this play of chance and purpose, it is essential that students and readers have a conceptual grounding in the areas of probability, statistics, and stochastic processes. Therefore, several playful computer simulations and projects are interlaced with theoretical foundations and numerical examples - both solved and exercise problems. In this way, the presentation in this book remains true to its spirit of inviting thoughtful readers to the various aspects of this area of study.

Historical remark

The advent of a rigorous framework for studying probability and statistics dates back to the eighth century AD and is documented in the works of Al-Khalil, who was an Arab philologist. This branch of mathematics continues to be under development with major contributions from Soviet mathematician Andrey N. Kolmogorov, who developed the modern foundations of probability and statistical theory from a measure-theoretic standpoint in the twentieth century.

This chapter provides an insight to some of the generalimage transforms that offer an alternativerepresentation of images and videos. Few of theirproperties and applications are also discussed thatare related to image compression and reconstruction.Other forms of representation that depend on data,like principal component analysis and sparserepresentation, are provided as an extension tothese representations. Techniques of computing basisfunctions and dictionary learning are introduced inthis chapter.

2.1 Image transforms

Consider a continuous function, 𝑓(𝑥), inone-dimensional (1-D) space, where, 𝑥 ∈ ℝ. Considera set, B, of 1-D basis functions, whose functionalvalues may either be in real or in complex domain.This is represented as in Eq. 2.1.

NANO

The term “nano” is derived from a Greek word that means “dwarf” (small) and is represented by the symbol “n.” As a unit prefix, it signifies “one billionth,” denoting a factor of 10-9 or 0.000000001. It is primarily used with the metric system, as illustrated in Figures 8.1 and 8.2. For example, one nanometer is equal to 1 × 10-9 m, and one nanosecond is equal to

1 × 10-9 sec. It is frequently encountered in science and electronics, particularly for prefixing units of time and length.

HISTORY OF NANOTECHNOLOGY

The origin of nanotechnology is often attributed to American physicist Richard Feynman's speech, “There's Plenty of Room at the Bottom,” which he gave on December 29, 1959, at an American Physical Society conference at Caltech. A 1959 lecture by Richard Feynman served as the intellectual inspiration for the field of nanotechnology. The term “nanotechnology” was initially used in a conference in 1974 by a Japanese scientist by the name of Norio Taniguchi from Tokyo University of Science to describe semiconductor techniques with characteristic control on the order of a nanometer, such as thin film deposition and ion beam milling. According to his definition, “nanotechnology” is primarily the processing, separation, consolidation, and deformation of materials by a single atom or molecule.

Appendix A

Clustering is a task oforganizing objects into groups whose members aresimilar in some way. A cluster is a collection of objects thatare similar to each other, but dissimilar to theobjects belonging to other clusters. In other words,a cluster is a group of objects with loosely definedsimilarity among them, which may have the potentialto form a class. A class is a known group of objects thatare described by similar characteristics, andclassification isthe task of assigning a defined class to an object.Image segmentationis also a problem that is similar to clustering,where the clusters are formed by groups of pixelsthat are similar in some context. In imagesegmentation, homogeneous regions in an image may beclustered to derive segments in the image. Thesesegments represent clusters. An example of imagesegmentation is shown in Fig. 6.1, where theforeground is represented by mushroom and thebackground is represented by humus substance aroundit. In this case, the image is primarily clusteredinto two regions, which are shown by white solidcontour (foreground) and white dashed contour(background).

The main motivations of clustering techniques are asfollows.

• • To find representative samples of homogeneousgroups in the given data, which would reduce thedata transmission and storage requirements incertain applications. Here, the data isrepresented by a smaller set of representativesamples that capture the characteristics of totaldata.

• • To discover natural groups or categories inthe data, which may be used to describe the datasamples by their unknown properties.

• • To find relevant groups in the data, whichfacilitates to draw attention toward major groupsof the data in the distribution. These groups formthe major clusters in a given context, likesegments in an image.

• • To detect unusual data objects, which are theoutliers in the data, that deviate from thecollective characteristics of groups of data in agiven context.

In the previous chapter, we saw that compactness is a topological property. In this chapter, we shall discuss another important topological property, called connectedness. Vaguely speaking, a connected topological space means a space that is in one single piece. In other words, there is no separation possible for a connected space. The formal definition is given below.

9.1 Connected Spaces

As indicated by the definition, connectedness is a topological property since it is defined in terms of the open sets of X. Therefore, if X is a connected space, then any space that is homeomorphic to X is also connected (see Theorem 9.1.34).

Observe that a separation of a topological space X is a pair of open subsets U and V and U ∩ V = ∅, U ∪ V = X. Thus, it follows that U and V are complements of each other. Since U is open, V = X ∖ U is closed, and since V is open, its complement U = X ∖ V is closed. Alternately, a separation of X can be defined with respect to closed sets as follows.

INTRODUCTION

Classical mechanics is mainly based on Newton's laws of motion and gravitation. Initially, it was thought that Newton's second law of motion was valid and applicable at all speeds. But new experimental evidence showed that Newton's second law of motion is valid and applicable at low speeds and invalid when the object is moving at high speeds comparable to the velocity of light. This failure of classical mechanics led to the development of the special theory of relativity by young physicist Albert Einstein in 1905, which showed everything in the universe is relative and nothing is absolute. Relativity connects space and time, matter and energy, electricity and magnetism, which are useful and remarkable to our understanding of the physical universe.

The special theory of relativity is applicable to all branches of modern physics, high-energy physics, optics, quantum mechanics, semiconductor devices, atomic theory, nanotechnology, and many other branches of science and technology.

The theory of relativity has two parts: the special theory of relativity and the general theory of relativity. The special theory of relativity deals with the inertial frame of references, while the general theory of relativity deals with the accelerated frame of references. Some common technical terms that are frequently used in relativistic mechanics are as follows:

• 1. Particle:A particle is a tiny bit of matter with almost no linear dimensions and is considered to be located at a single place. Its mass and charge define it. Examples include the electron, proton, and photon, among others.

Remote sensing involves measurements on a targetwithout getting in contact with it and it comprisestechniques for collecting, storing, and processinggeoreferenced and geospatial data to extractvaluable information. In this context, data refer torepresentations stored in computer memory, which canbe manipulated using computers to derive meaningfulinsights. Remote sensing imaging systems primarilywork with georeferenced images, capturing Earth'ssurfaces, environment, atmosphere, etc. Theseimaging systems may be carried by satellites orairborne platforms like airplanes or drones. Forsatellite-based imaging, revolution of the satellitearound continuously rotating Earth allows periodiccapture of images over the same area. There are twomain types of imaging systems: passive and active.In passive systems, sensors detect reflected andemitted electromagnetic (EM) waves from Earth'ssurface, from mainly two types of energy sources,namely sunlight during the day and terrestrial heatat night. These sensors operate within specificspectral bands, converting energy into electricalsignals stored as two-dimension (2-D) images. Theprinciple is similar to optical cameras.Additionally, energy from Earth's thermal emissioncontributes to night time imaging, particularly inthe thermal infrared (IR) or far IR bands. Passiveremote sensing involves capturing images acrossvarious spectral bands, resulting in multispectraland hyperspectral images of specific regions onEarth.

In active imaging systems, microwave radar (RAdioDetection And Ranging) technology is utilized. Aradar transmitter emits a pulse of an EM wave with aspecific wavelength (in the microwave band). Whenthis pulse strikes a target, some of its energyreflects back to the radar antenna to which theradar receiver is connected. The receiver capturesinformation about the location and geometry of thetarget by recording the phase and amplitude of thereturned signal. By scanning the radar beam over anarea, an image of that region is formed. One of thelimitations of radar imaging is that, the size ofthe transmitting antenna is required to be large forobtaining images of high spatial resolution.

An artificial neural network (ANN) is a network ofneural nodes or perceptual nodes.1 In a feed forwardneural network, each node is fed with a weightedinput vector and the net sum of the weighted vectorsfrom several such nodes is passed through anonlinear function, whose response is the output ofthat node. The layers formed by the input nodes andthe output nodes are known as the input layer andthe output layer, respectively. The layers formed byother nodes are known as hidden layers. A network ofseveral such layers (along with input and outputlayers) forms an ANN, as shown in Fig. 9.1.2 Theconventional ANNs have very few hidden layers,usually not more than three. Using only one or twohidden layers is also common in many applications.In contrast, deep neuralarchitectures have relatively more numberof layers. Even more than 100 hidden layers is notuncommon. This is one of the distinguishedcharacteristics of deep neural networks (DNN) froman ordinary ANN.

The concepts used in deep neural computations aredecades older. In fact, they involve the same neuralnetwork computations as in a simple ANN model. Theseconcepts were introduced in 1980's and their basicprinciples still remain the same. However, a boom inusing deep architectures after almost three decadesof their proposition is mainly attributed to theadvancement in technology and science.

Key Concepts

• • Electricity scenario in India and the need for transition to green energy in the country

• • Indian pledge at CoP-26 at Glasgow and the targets of 2030

• • National solar mission and major initiatives that led to exponential growth in solar energy installation in India

• • Net-zero target of India and road map for achieving it

• • Major solar power projects in India

• • Various policies and government organizations involved in achieving the target of solar PV deployment in India

• • Changes required in the grid in view of massive deployment of variable and uncertain sources of electricity

Introduction

India is now the most populous country in the world, with almost 18% of the global population. Being a developing country and one of the major evolving economies, the electricity demand in the country is also growing. India ranked fifth in terms of installed capacity and third in terms of electricity produced, in 2018, in the world. India's annual per capita electricity consumption, although, is about 1122 kWh, which is much lower than the world average of 2674 kWh per year, but this number too is one of the fastest-growing. In the last decade the installed capacity of the Indian grid has increased by more than 200 GW. At this rate India is set to become the biggest electric load centre in the world by 2030 with about 1.5 billion people.

Being the most populous developing country, Indian response to the climate crisis is key to the success of sustainable development and the climate protection mission. India historically accounted for less than 5% of the global emissions.

Directed graphs, also known as digraphs are a fundamental structure in graph theory, where the relations between two vertices are allowed to be asymmetrical. An edge as we have known so far, has always signified a two-way relationship between two vertices. But in directed graphs, a directed edge has a designated direction in which you may go from say a to b but not always from b to a. This directionality introduces the concept of ordered pairs where each edge has a distinct starting point (source) and an ending point (target). Understanding their properties and behavior is crucial for solving problems related to reachability, hierarchy and optimization. This chapter explores the core concepts of directed graphs including their representation, traversal techniques and properties while also providing a succinct introduction to the world of networks.