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.

Analog electronic circuits are generally offered as a core subject during the third or fourth semester of the second year in a four-year course in the electronics and communication, instrumentation and control, and computer engineering branches. It is an important subject and may be slightly toned down in the electrical, civil, chemical, and information technology branches of engineering. Design of discrete and linear integrated circuits (ICs), digital electronic modules, and electronic instrumentation are some of the obvious areas where knowledge of microelectronic circuits becomes essential. Therefore, it becomes important for students at this level of study to be proficient in electronic circuit analysis and their usage in relevant areas.

There are many fine books on electronic (devices and) circuits. Many of them have combined “devices” and “circuits”; a good practice, but sometimes resulting in the book becoming bulky. The idea here is to provide a text that deals with the fundamentals of analog electronic circuits for those who already have a basic knowledge of electronic devices, like semiconductor diodes, bipolar junction transistors (BJTs), and metal oxide semiconductor transistors (MOSFETs), either as full subject or as an introductory subject. Serious effort has been made in preparing the text so that it is not only as study material for examinations but also emphasizes fundamental concepts without being overly voluminous.

Appendix B

Transistor Biasing

When transistors are used as switches, they operate either in cut off or in saturation mode. Whereas, when transistors are used to amplify small signals, a quiescent operating point is selected somewhere in the middle of the conduction range. The region of the location of a quiescent point depends on the kind of amplifier. For example, an amplifier may be used for maximum voltage and/or current gain, or high input resistance, or power gain. In some applications, an amplifier ought to consume minimum power, especially when it is used with a battery-operated device. After selecting the quiescent operating point, it is also required that it remains stable. If there is some change in the operating temperature or variation in supply voltage, the operating point may change its location. Variations due to the manufacturing tolerance in component values and in transistor parameters also affect the quiescent point. Irrespective of the reason, it is required that the quiescent point should remain located within specified limits.

Three amplifier configurations are commonly used while employing either BJT or FET amplification. The configuration depends on the terminals, out of the three, that is common to the input and the output of the amplifier. These configurations are studied on the basis of their characteristics, such as voltage gain, current gain, input and output resistance, and bandwidth, i.e., the frequency range within which the amplifier operates without any significant reduction in the output waveform. The operating frequency range becomes limited as the voltage gain drops at low and high operating frequencies. Hence, the study of frequency response becomes important.

Introduction

A current mirror is a transistor-based circuit that the current level is controlled in an adjacent transistor, and the adjacent transistor essentially acts as a current source. Such circuits are now considered a commonly used building block in a number of analog integrated circuits (IC). Operational amplifiers, operational transconductance amplifiers, and biasing networks are examples of such circuits that essentially use current mirrors. Analog IC implementation techniques such as current-mode and switched-current circuits use current mirrors as basic circuit elements.

A significant advantage associated with the current mirrors is that they act as a near-ideal current source while fabricated using transistors and can replace large-value passive resistances in analog circuits, saving large chip area.

The later part of the chapter discusses another important analog circuit, namely, differential amplifier. As the name suggests, differential amplifiers amplify the difference between two signals that are applied to their two inputs. In addition to the differential amplification, it is also required that differential amplifiers suppress unwanted signal, which is present on the two input signals in the form of a common-mode signal. A differential amplifier is a particularly very useful and essential part of operational amplifiers. A differential pair is the basic building block of a differential amplifier that comprises of two transistors in a special form of connection.

In this chapter, the coupling of IBMs with turbulence and wall models is discussed to provide the reader with a guideline to apply these methods to high Reynolds number flows. In fact, is this context, the small thickness of the flow boundary layer, combined with the impossibility to benefit from a wall-normal mesh refinement, challenges the use of IBMs unless additional models are used at the wall.

The possibility to resort to adaptive wall refinement is presented, although it is also shown that it can be combined only with RANS models.