Introduction

In the early days, an operational amplifier (op-amp) was the only linear integrated circuit (IC) that was used in the design of linear IC circuits and systems. Typical applications of the op-amps were mathematical operations, such as summation, subtraction, integration, small signal amplification, and generating oscillations. Over the years, other devices, such as operational transconductance amplifiers, current conveyors, and so on, have also come into common use; still, it has not reduced the importance and areas of application of op-amps. Rather, it became possible to realize many more advanced functions with linear ICs and many applications coming under the domain of nonlinear applications with advances in the process technology and increased level of integration. Some of the more common nonlinear applications are precision rectifiers, voltage-level detectors, and Schmitt trigger circuits. The Schmitt trigger circuit itself is very popular in generating varieties of pulses and other waveforms like triangular waveforms. Some other nonlinear applications such as log and antilog amplifiers, analog multiplier, charge amplifier, and isolation amplifiers are discussed in brief; phase lock loop and its basic function are also included.

Precision Rectifiers

Conventional rectifiers work well for converting alternating supply to a pulsating one. Filters are normally used to remove ripples in the pulsating voltage to obtain dc. It is observed that these rectifiers have some limitations. One of the main limitations is that when a diode conducts during rectification, it has a voltage drop across its terminals, which is approximately 0.7 V. Hence, the ac voltage available for conversion to dc is reduced by that amount.

Wave optics is the branch of modern physics in which the nature of light and its propagation are studied.

Interference

When two waves of the same frequency, having a constant phase difference between them, and traveling in the same medium are allowed to superimpose each other, there is a modification in the intensity pattern. This phenomenon is known as interference of light.

When the resultant amplitude at certain points is the sum of the amplitudes of the two waves, this interference is known as constructive interference.

When the resultant amplitude at certain points is the difference of the amplitudes of the two waves, this interference is known as destructive interference, as shown in Figure 11.1.

COHERENT SOURCES

Two sources are said to be coherent if the waves emitted from them have a constant phase difference with time.

THEORY OF INTERFERENCE

Let us consider two coherent sources S1 and S2 that are equidistant from source S. Let a1 and a2 be the amplitudes of the waves originated from source S1 and S2, respectively, as shown in Figure 11.2. Then the displacement y1 from the source S is given by

where δ is the phase difference between the two waves.

Now, according to the law of superposition, the resultant wave is given by

Band Theory ofSolids

The band theory of solids is different from the others because the atoms are arranged very close to each other such that the energy levels of the outermost orbital electrons are affected. But the energy level of the innermost electrons is not affected by the neighboring atoms.

In general, if there is n number of atoms, then there will be n discrete energy levels in each energy band. In such a system of n number of atoms, the molecular orbitals are called energy bands shown in Figure 7.1.

CLASSIFICATION OF SOLIDS ON THE BASIS OF BAND THEORY

The solids can be classified on the basis of band theory. The parameter that differentiates the solids among insulator, conductor, and semiconductor is known as energy band gap and represented by (Eg), as shown in Figure 7.2. When the energy band gap (Eg) between conduction band and valence band is greater than 5 eV (electron-volt) then the solid is classified as insulator. When the energy band gap (E g)between conduction band and valence band is 0 eV (electron-volt), that is, overlapping of bands occurs then the solid is classified as conductor. When the energy band gap (Eg) between conduction band and valence band is approximately equals to 1 eV (electron-volt) then the solid is classified as semiconductors.

Introduction

Statistical mechanics bridges the gaps between the laws of thermodynamics and the internal structure of the matter. Some examples are as follows:

• 1. Assembly of atoms in gaseous or liquid helium.

• 2. Assembly of water molecules in solid, liquid, or vapor state.

• 3. Assembly of free electrons in metal.

The behavior of all these abovementioned assemblies is totally different in different phases. Therefore, it is most significant to relate the macroscopic behavior of the system to its microscopic structure.

In this mechanics, most probable behavior of assembly are studied instead of individual particle interactions or behavior.

The behavior of assembly that is repeated a maximum time is known as most probable behavior.

hase Space

Six coordinates can fully characterize the state of any system:

• 1. Three for describing the position x, y, z and three for momentum Px, Py, Pz.

• 2. The combined position and momentum space (x, y, z, Px, Py, Pz) is called phase space.

• 3. The momentum space represents the energy of state,

For a system of N particles, there exists 3N position coordinates and 3N momentum coordinates. A single particle in phase space is known as a phase point, and the space occupied by it is known as µ-space.

olume Element ofµ-Space

4. Consider a particle having the position and momentum coordinates in the range.

Introduction

Humans have had a lengthy history of understanding electricity and magnetism. The tangible characteristics of light have also been studied. But in contrast to optics, electricity and magnetism—now known as electromagnetics—have been believed to be governed by different physical laws. This makes sense because optical physics as it was previously understood by humans differs significantly from the physics of electricity and magnetism. For instance, the ancient Greeks and Asians were aware of lode stone between 600 and 400 BC. Since 200 BC, China has been using the compass. The Greeks described static energy as early as 400 BC. But these oddities had no real effect until the invention of telegraphy. The voltaic cell or galvanic cell was created by Luigi Galvani and Alesandro Volta in the late 1700s, which led to the development of telegraphy. It quickly became clear that information could be transmitted using just two wires attached to a voltaic cell. The development of telegraphy was therefore prompted by this potential by the early 1800s. To learn more about the characteristics of electricity and magnetism, Andre-Marie Ampere (1823) and Michael Faraday (1838) conducted tests. Ampere's law and Faraday's law are consequently called after them. In order to comprehend telegraphy better, Kirchhoff voltage and current rules were also established in 1845. The data transmission mechanism was not well comprehended despite these laws. The cause of the data transmission signal's distortion was unknown. The ideal signal would alternate between ones and zeros, but the digital signal quickly lost its shape along a data transmission line.

Operational Amplifiers: Introduction

An operational amplifier (op-amp) is a very prominent active device used in analog integrated circuit (IC) design. Prominence is due to the widespread and diverse areas of applications of the op-amps as its parameters are very close to ideal in a certain range of operating frequencies. Apart from basic arithmetic operations such as addition, multiplication, and integration, op-amps are also widely employed as amplifiers, wave shaping circuits, active filters, log/anti-logarithmic amplifiers, nonlinear function generators, and in analog-to digital and digital-to-analog conversion, and so on.

Figure 8.1(a) shows a pin connection diagram of the most commonly used type-741 op-amp; it needs a dual power supply, has two terminals for inverting and non-inverting inputs, one terminal for the output, and three terminals without any connections for simple applications. Dual op-amps and quad op-amp ICs with matching characteristics are also available.

Op-amp is essentially a high-gain differential amplifier (DA) that can be shown in its simplest form as represented in Figure 8.1(b). The output voltage of the op-amp is the difference between the two input voltages multiplied by the high-gain factor A, so the output voltage is expressed as:

The differential gain A is frequency dependent in a practical op-amp. Therefore, as a first approximation, it is represented by a single-pole roll-off model given below.

Key Concepts

• • The growing share of electricity in the energy sector

• • The connection of electricity and global warming

• • Important terms related to electricity

• • Conventional sources of electricity generation

• • Green and renewable sources of electricity generation

• • Smart grid

Introduction

Electricity is the fundamental driver for growth of the modern society. The availability of reliable electric supply is a priority for any residential, industrial, or commercial setup. With the rapid proliferation of digital appliances and the critical role they are playing in our daily life, the dependence on high-quality electric power supply has further increased manifold.

Electricity started as a source of energy for lighting, replacing oil and gas-based lamps. But at that time very few people would have realized that slowly this new source of energy will ‘capture’ the whole residential, industrial, and workplace setup. It is difficult to imagine our lives without electricity now – starting from heating our meals, washing and drying of our clothes, heating the water, keeping the house or office cool or hot to running all kinds of entertainment and communication appliances. This source of energy has turned into an omnipresent phenomenon in our lives. Electricity is the main driver behind technologies related to the Internet and communication also. A major part of the railways is already running on electricity, and the transition of road transport is also imminent in the near future.

Key Concepts

• • Three-D path for green energy transition

• • Operation and maintenance of solar PV power plants using digital technologies

• • Role of energy storage in the decarbonization of power grid

• • Microgrid, nanogrid, and vehicle to grid

• • Peer-to-peer energy trading

• • Latest trends in solar cell and module technology

• • Role of smart grid in enabling integration of solar and wind energy sources with the power grid

• • Wind-solar hybrid, floating solar, agro photovoltaics

• • Role of education, training, research and development in successful transition to green energy

Introduction

Rapid transition of the energy system with growing utilization of green and renewable sources has come up with a number of challenges and opportunities. This transition will continue and completely alter the whole energy network. These developments have come up at a time when a number of new and established technologies are available which need to be used and integrated in this changed network. Artificial intelligence (AI), ML, Big Data, cloud computing, blockchain, and so on are some of these important technologies.

Operation and maintenance of solar and wind plants and the role of AI, ML, Big Data and so on; peer-to-peer energy transactions and the role of blockchain in them; grid integration challenges and their solutions; off-grid applications with and without battery storage; handling of PV waste; and solar energy derivatives such as green hydrogen are the areas which are set to play very important roles in the successful transition to the green and distributed energy network.

Apart from these technologies, other important developments are underway, such as solar PV modules of higher efficiency with new technology and material, a new shape, a lesser effect on ambient temperature, requiring less water for cleaning, and so on.

Semiconductor Diodes

A semiconductor diode is a two-terminal device. Ideally, the diode behaves as a short circuit in one direction for current flow; it is called the forward direction, and the same diode behaves as an open circuit for the current flow in the opposite direction, which is called the reverse direction.

Ideal Silicon p–n Junction Diode

One of the most important characteristics of an ideal diode is that it behaves as an ideal switch, and the switching action is controlled by the direction of the current that flows in one direction only. Figure 1.1(a) shows a symbol for an ideal diode as a switch, where the arrow is in the forward direction. It also shows the positive direction of the current and voltage drop across the diode. Figure 1.1(b) shows the v, i characteristics of the ideal diode, which conducts only in one direction. The names assigned to the diode terminals are anode and cathode. The direction of the forward current in the diode is from the anode to the cathode inside the diode.

Fabricating an ideal diode in practice is not possible. Still, its idealized model in Figure 1.1(b) serves as a good approximation of a practical diode for basic analysis purposes.

At an early stage, diodes were realized using vacuum tubes with filament inside. However, now solid-state diodes are fabricated using semiconductors.

Introduction

Figure 10.1 shows a simple block diagram of a typical analog signal processing system. The first step in the development of an analog signal processing system is to divide the given specifications into analog and digital parts. Based on the advantages in VLSI technology, a variety of signal processing systems have been developed and will continue to be developed with the format of Figure 10.1. One such example is the advent of sampled data technique and MOS technology, which enabled the fabrication of a general signal processor. However, analog-sampled techniques moved onward from MOS technology toward CMOS technology, as it was highly suitable for combining analog and digital systems.

In most of the practical cases, input signals are of analog types like speech signals, sensor output, radar signals, and so on. The first block in Figure 10.1 is a pre-processing block, which usually consists of analog filters, sample and hold process, and an analog-to-digital converter (ADC). Depending on the nature of the input signal, the input block may require signal processing with strict speed and accurate specifications. After the conversion of analog signals to digital signals, the next block is mostly a microprocessor. The advantage of using a microprocessor is that its function can easily be controlled and modified. Post-processing is done in the final stage, wherein the signal is converted back to the analog form in most cases, and this stage uses digital-to-analog converter (DAC) and some filtering. Proper interfacing is required between the three building blocks of Figure 10.1; placement of the the inter facing is indicated symbolically by the arrow heads.

The climate change challenge, mainly reflected as global warming, has emerged as an existential crisis not only for humanity but for the planet itself. This challenge and the need for sustainable development are, therefore, the most talked about issues of recent times. Ensuring development without causing harm to nature is the basic idea behind sustainable development. In line with this principle, there is a need to review and reset the energy sector and make it more environment friendly.

The need for electrical energy is a basic requirement of modern society. But meeting this requirement has contributed a large part to the climate change also. Conventional methods of generating electricity have been major contributors to CO2 emissions. In order to rectify this, generating the required energy in an environment friendly way has to be implemented. The decarbonization of the electric energy system, therefore, is an integral part of reworking the electrical energy sector in the spirit of sustainable development.

India, over the years, has shown unwavering commitment to contributing towards attaining the sustainable development goals. The country has taken excellent steps in this area under the leadership of Hon’ble Prime Minister Shri Narendra Modi. A major boost to these efforts was announced in terms of the Panchamrit promises declared at the 26th Conference of Parties at Glasgow, UK. Making 50% of the total installed capacity based on non-fossil fuel sources, reducing the carbon emission intensity in its GDP by 45%, and the installation of 500 GW of green energy plants by 2030 are indicative targets of the national resolve.

Frequency Response

Some amplifier circuits employing either BJT or FET were analyzed in Chapter 2. Almost all the circuits contained blocking and bypass capacitors in addition to the biasing components, load resistance, and so on. However, these external capacitors and the internal parasitic capacitors of the transistor were considered absent during the analysis because either dc analysis was done or for the simplification in the analysis. There was no mention of the practical limit on the device parameters or on the components used. It does not mean that the obtained expressions for the voltage gain, current gain, and input and output resistance were wrong. These expressions are very important and relevant, and for most of the operations of amplifiers, these expressions are to be employed. However, there is something more, which is also very important, and that remains to be studied.

When the internal device capacitances or the intentionally connected capacitance or load impedance having reactive components are considered, the amplifier gain becomes a complex number, A–θ, instead of a real number. A significant point is that both the gain A and phase angle –θ depend on the input signal frequency, and the gain magnitude decreases at low and at comparatively high signal frequencies; amplification remains almost constant in the mid-frequency range. The frequency response characteristics of an amplifier are the plot of gain and phase with frequency.

Introduction

Communication through optical fiber is one of the remarkable discoveries of the twenty-first century that have brought a revolution in modern times. The transfer of information over long distances was earlier performed through copper wires and coaxial cables. The limitation of these devices, such as limited bandwidth, could not fulfill modern needs and hence were replaced by glass fiber. It was the effort of Alexander Graham Bell, who in 1880 used the light as a carrier of signal. Since the attenuation in the optical fibers was quite high, an attempt to minimize it was done to improve it, and today its features are so fantastic that optical communication through glass fiber with low loss has become a reality. A large number of advantages of optical fibers over the traditional wires and coaxial cables are not hidden now and have been accepted over the entire globe. Apart from their use in communication, optical fibers are widely used in other areas also. In a nutshell, we can therefore say that fiber optics is a backbone of communication infrastructure.

The optical fiber is a cylindrical waveguide system operating at optical frequency. It consists of a core at the center and a cladding outside the core. The core is generally a cylindrical dielectric glass, and cladding is the second dielectric cover usually of glass with a lower refractive index n2, as shown in Figure 13.1.

Introduction

Numerous microscopic events, including atomic stability, blackbody radiation, the photoelectric effect, and atomic spectroscopy, could not be explained by classical physics. When Max Planck presented the idea of the quantum of energy in 1900, it marked the first significant advancement. Only after positing that the energy exchange between radiation and its surroundings occurs in discrete, or quantized, amounts was he able to replicate the experimental findings in his attempts to understand the phenomenon of blackbody radiation. He claimed that an electromagnetic wave of frequency v and matter can only exchange energy in integer multiples of h, or what he termed a quantum's energy, where h is a fundamental constant known as Planck's constant. The concept of quantizing electromagnetic radiation proved to have far-reaching effects.

Blackbody radiation was correctly explained by Planck's hypothesis, which inspired fresh thinking and set off a wave of new findings that provided answers to the most pressing issues of the day.

Planck's quantum idea received a potent reinforcement from Einstein in 1905. Einstein realized that Planck's theory of the quantization of electromagnetic waves must also apply to light when attempting to comprehend the photoelectric effect. So, adopting Planck's methodology, he proposed that light itself is composed of discrete energy units (or minuscule particles) called photons, each of which has energy hv, which corresponds to the light's frequency.

Introduction

The word laser is an abbreviation for “light amplification by stimulated emission of radiation.” Historically, the laser is the outgrowth of maser, which means “microwave amplification by stimulated emission of radiation.” If the stimulated radiation lies in optical region, the device is called optical maser or laser. Laser beam is highly monochromatic, highly coherent, intense, and highly collimated with a small diversion.

Using ruby as the active material, T. H. Maiman invented the first laser system in 1960. Thus, it is known as Ruby Laser.

ABSORPTION, SPONTANEOUS EMISSION, AND STIMULATED EMISSION OF RADIATION

Absorption of Radiation:An atom has a number of quantized states. Initially, an atom is in ground state, that is, all its electrons possess lowest possible energy state. When energy is given to an atom, it goes to excited state, that is, its electron jumps to a higher energy state by absorbing a quantum of radiation or photon. This process is called the absorption of radiation shown in Figure 5.1.

If E1 and E2 are the energies of an electron in initial and final states and ν is the frequency of absorbed radiation, then

where h is Plank's constant. Thus, absorption is a stimulated process.

SPONTANEOUS EMISSION

An atom in an excited state remains for only about 10−8 sec. After staying 10−8 sec, the atom jumps automatically to a lower energy state, emitting a radiation. If initially an atom is in excited state, then it spontaneously jumps to ground state, emitting a photon of frequency ν, given by

Climate change, global warming, and shifting to sustainable ways of growth are major concerns of present times. Although these issues were identified many years ago, for a long time the exact nature of these phenomena and their impact were under debate. However, recent years have seen clearly visible and regularly occurring phenomena that confirm the adverse effects and grave threat of global warming and climate change.

It is noteworthy that 17 November 2023 was an important day for climate change, as on this day the average temperature of the earth exceeded by more than 2°C compared to the pre-industrial age temperature for the first time. The Copernicus Climate Change Service of the European Union (EU) has confirmed that in 2023 the average temperature of the earth's surface was 1.48°C higher than the temperature during the pre-industrialization days. In absolute terms also, the global emissions of CO2 are rising; in 2022, for example, these emissions were at least a billion tonnes higher than in 2019.

The Conference of Parties (CoP) is the supreme decision, making body under the United Nations Framework Convention on Climate Change (UNFCC). CoP is an important annual event initiated about 30 years ago. But the increasing interest of public, over the years, in the event shows that we have come a long way in understanding the adverse impacts of climate change. From sceptics doubting the very idea of climate change to it becoming the most debated topic in the world is a major change.

Sinusoidal Oscillations

The feedback amplifiers having negative feedback are likely to become unstable because of some unavoidable phase lag at the output due to the frequency-dependent nature of the primary amplifier gain or feedback network, or due to both. The feedback becomes positive if the additional phase lag becomes 180o at a certain frequency. If the loop gain becomes unity at any frequency, the amplifier starts oscillating at this frequency. This instability and consequent oscillations are undesirable in circuits used as amplifiers. However, practically, such oscillations are generated intentionally for widespread applications also. Hence, many schemes and approaches are in use to obtain oscillations for different frequency ranges. Such circuits are known as oscillators, or signal generators.

To understand this instability and the development of oscillations, intended or otherwise, consider the basic block diagram of a negative feedback amplifier shown in Figure 6.1. Here, vin is the input signal, the net input to the amplifier is ve, the voltage gain of the amplifier is (Av) , βff is the feedback factor, and vout is the output voltage.

The voltage gain of the feedback amplifier is (vout/vin ) = Av/(1 + βf Av). When the voltage gain Av and feedback factor βf are negative (or positive) and real constants, the feedback becomes negative. However, because of the frequency-dependent nature of the primary (and/or in feedback circuit) amplifier, the loop gain has an additional phase shift of 180o at some critical frequency ωo.