Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Browse subjects
  3. Engineering
  4. RF and microwave engineering
  5. Content listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1479 results in RF and microwave engineering

Page 26 of 74

  • 4 - Fundamental concepts of radar remote sensing

  • Wayne K. Hocking, University of Western Ontario, Jürgen Röttger, Robert D. Palmer, University of Oklahoma, Toru Sato, Kyoto University, Japan, Phillip B. Chilson, University of Oklahoma
  • Book:
    Atmospheric Radar
    Published online:
    25 November 2016
    Print publication:
    17 November 2016, pp 217-267

  • Summary

    Introduction

    Fundamentally, atmospheric radars are designed to transmit an electromagnetic (EM) wave and to observe the effects that the atmosphere has on the scattered wave. These interactions may take the form of bending of the radiowave path, or reflection and scattering. In the simplest case, a transmit antenna and a receive antenna are required, which may be located at separates sites. More complex systems might involve multiple receivers and even multiple transmitters. Most commonly in MST atmospheric work, the transmitter and receiver are co-located; in these cases, refraction of the ray paths is not generally significant. Reflection and scattering are the primary phenomena that need to be considered in MST studies.

    The radar targets in MST studies

    Atmospheric reflection and scattering occur due to the interaction of the EM wave with changes in the refractive index. As discussed in Chapter 3, these refractive-index changes may be caused by a variety of phenomena. We will quickly revisit some of these processes here, because they help us to understand the different modes of radar analysis that we will discuss. Of course, aircraft and missiles are perhaps the most obvious examples of targets that spring to mind when we talk of radar, but these are not the primary targets when it comes to atmospheric studies. One simple example that is relevant is water droplets embedded in the air. In this case, the refractive index inside the water droplets is very different to that of the surrounding air, so each water droplet may scatter a small amount of incident radiation. In this case, scatter from a large number of water droplets is required before a detectable scattered signal can be produced. Insects and birds contain water, so they too can act as radiowave scatters. Indeed some radars use insects as tracers of atmospheric motions. Another example is the ionized trail of plasma left behind when a meteoroid enters the atmosphere. Meteoroids are generally small grains of dust (with diameters from micrometers to centimeters, though larger ones can occur) which enter the atmosphere at high speed (typically 10 to 70 km/s), creating large levels of frictional heating and thereby ionizing the air around them. As a result, a long trail of plasma (typically a few km in length) exists behind the meteoroid, and this so-called “meteor trail” can reflect radiowaves.

  • 5 - Configuration of atmospheric radars – antennas, beam patterns, electronics, and calibration

  • Wayne K. Hocking, University of Western Ontario, Jürgen Röttger, Robert D. Palmer, University of Oklahoma, Toru Sato, Kyoto University, Japan, Phillip B. Chilson, University of Oklahoma
  • Book:
    Atmospheric Radar
    Published online:
    25 November 2016
    Print publication:
    17 November 2016, pp 268-336

  • Summary

    Introduction

    In earlier chapters, we have discussed radars in a general sense, and dealt with some of the techniques available to optimize signal detection. We have discussed the conceptual difference between CW and pulsed systems, and concepts like range resolution and sampling strategies. In this chapter, we will take a closer look at the electronics and engineering that is required to develop a radar, and the associated hardware. Key topics will include antennas, transmitters, receivers, and controllers. Some topics from the previous chapter may be repeated, but generally in greater detail.

    One thing that all radars have in common is a need for a transmit antenna and a receive antenna. These may or may not be located at separate sites. The transmitter transmits radiowaves through a transmitter antenna into the air, and receives echoes from a target, or from multiple targets, with the receiver antenna. When the transmitter and receiver are co-located, the radar is referred to as a “monostatic radar,” while the term “bistatic radar” refers to the case that the transmitter and receiver are physically separated. If two or more receivers which detect echoes from a common target are located at different places, the system is called a “multistatic radar.” The degree of separation can be an important factor as well – if the transmitter and receiver are within maybe a few wavelengths of each other, they may be referred to as either monostatic or bistatic, depending on the application, even though, in the strictest sense, they are bistatic/multistatic. An example is the so-called “spaced antenna method” for measuring winds, in which case there are multiple receiver antennas but the theoretical development is often done in a quasi-monostatic sense. Generally, if the separation between the transmitting and the receiving antennas can be neglected compared with the distance to the target, the system is considered as monostatic, although even then the meaning of “small” and “large” distances depends on the objectives of the experiment. Experiments requiring detailed phase information between receivers may need to be considered multistatic, whereas if no phase information is needed the same configuration might be considered as monostatic, for example.

  • 12 - Antenna Integration

  • Steven W. Ellingson, Virginia Polytechnic Institute and State University
  • Book:
    Radio Systems Engineering
    Published online:
    28 May 2018
    Print publication:
    06 October 2016, pp 363-396

  • Summary

    INTRODUCTION

    Chapter 2 provided an introduction to antenna fundamentals in which antennas were described as transducers of guided electrical signals to unguided electromagnetic waves, and vice versa. In Chapter 4, receive antennas were viewed as receptors of environmental noise, resulting in sensitivity-limiting electrical noise characterized in terms of antenna temperature. Intervening chapters have introduced methodology for analysis and design of radios which accounts for effective radiated power and sensitivity (Chapter 7), impedance matching (Chapter 9), and noise within a receiver (Chapter 11). We are now in a position to confront some antenna issues that were bypassed in Chapter 2, namely: How to most effectively integrate an antenna with radio electronics so as to achieve system-level design goals. In this chapter we address the topic of antenna integration so as to close this gap in our review of radio electronics, before moving on to the topics of receiver and transmitter design (Chapters 15 and 17, respectively).

    The organization of this chapter is as follows. In Section 12.2 we consider the manner in which an antenna contributes to the SNR achieved by a receiver, thereby limiting sensitivity. In Section 12.3 we consider VSWR and efficiency of power transfer in transmit operation. These considerations are closely related to the issue of impedance matching between antenna and transceiver, which is addressed in Section 12.4. The trend toward increasingly small antennas is considered, first in terms of the impedance-matching challenge, and then (in Section 12.5) in terms of practical limits on an antenna size. Section 12.6 gives a brief introduction to antenna tuners, a resurgent technology that facilitates improvements in the performance of radios that must cover large tuning ranges using antennas which are narrowband or electrically-small. This chapter concludes with an introduction to baluns (Section 12.7), which are needed to accomplish the common tasks of interfacing single-ended antennas to differential transceivers, and differential antennas to single-ended transceivers.

    RECEIVE PERFORMANCE

    Let us now quantify the role an antenna plays in the sensitivity of a radio receiver. This issue was previously addressed in Sections 7.4 and 7.5, and a review of those sections is recommended before engaging with this section. We begin by elaborating on the concepts presented in those sections and consider the implications for the design of antennas and the transmission lines and matching networks used to interface them to receivers.

  • 9 - Impedance Matching

  • Steven W. Ellingson, Virginia Polytechnic Institute and State University
  • Book:
    Radio Systems Engineering
    Published online:
    28 May 2018
    Print publication:
    06 October 2016, pp 259-284

  • Summary

    INTRODUCTION

    In Chapter 8 we noted the central role two-port theory plays in RF circuit design, and especially the role of reflection coefficients in determining the stability and gain of two-ports. Reflection coefficients were introduced as surrogates for source and load impedance (recall Equations (8.32) and (8.37)), facilitating the use of scattering parameters. In this chapter we consider impedance matching, which is the process of converting impedances (equivalently, embedded reflection coefficients) from a given value to some other value.

    Applications for impedance matching include (1) maximizing power transfer between twoports, (2) eliminating reflections (not the same thing!), and (3) converting from a given impedance to another impedance necessary for setting the stability and/or gain of a two-port. In each of these cases, the problem is essentially as shown in Figure 9.1: We wish to design a passive two-port that converts the output impedance of the source, ZS = RS + jXS, into the desired input impedance for the load, ZL = RL + jXL. Usually we would like to achieve this with a TPG as close to 1 as possible, and often there is a frequency span over which a minimum TPG which must be achieved. At the design frequency, the nominal embedded input impedance Zin of the matching two-port is either for maximum power transfer or ZS for reflectionless matching. Similarly, the nominal embedded output impedance Zout of the matching two-port is either or ZL at the design frequency.

    The organization of this chapter is as follows. In Section 9.2 we consider some rudimentary approaches to impedance matching, including resistive matching, transformer matching, and reactance canceling. Section 9.3 introduces narrowband matching using two discrete reactances in an “L” configuration, which is useful both as a standalone technique as well as a building block for more sophisticated techniques. Section 9.4 considers the issue of bandwidth, and introduces the concept of quality factor to provide some insight into how the bandwidth of matching circuits is determined and can be manipulated. In Section 9.5 we combine the concepts of previous sections to develop impedance matching circuits having bandwidth which can be wider or narrower than that obtained by using discrete two-reactance matching. Section 9.6 explains how to obtain differential versions of the single-ended circuits developed in earlier sections.

  • 16 - Frequency Synthesis

  • Steven W. Ellingson, Virginia Polytechnic Institute and State University
  • Book:
    Radio Systems Engineering
    Published online:
    28 May 2018
    Print publication:
    06 October 2016, pp 486-515

  • Summary

    INTRODUCTION

    Frequency synthesis is the generation of a periodic waveform having a specified frequency. Here we concern ourselves primarily with the generation of sinusoids, which are commonly required as LO signals in frequency conversion, and as carriers in analog modulations such as AM and FM. In this chapter we consider the synthesis of sinusoids using feedback oscillators (Sections 16.2–16.6), phase-locked loop synthesizers (Section 16.8), and direct digital synthesis (Section 16.9). The problem of phase noise and its effect on radio system performance is introduced in Section 16.4. Also, Section 16.10 summarizes additional considerations that arise in IC implementation of frequency synthesis devices.

    LC FEEDBACK OSCILLATORS

    In Section 8.5.1, it was noted that two-ports that are active and include internal feedback are prone to instability, and that one particular consequence of instability could be oscillation. In that context, oscillation was undesirable; now, however, let us consider how we might exploit this type of mechanism for frequency synthesis.

    The LC Resonator

    Let us begin with a well-known passive circuit that exhibits oscillatory behavior: The LC resonator, which is an inductor (the “L”) and a capacitor (the “C”) in parallel as shown in Figure 16.1. One first establishes a steady-state condition (Figure 16.1(a)) by applying a DC voltage source set to some non-zero value v0> 0, which charges the capacitor to a voltage of v0. At this point no current flows through the capacitor; subsequently, the voltage across the inductor is zero.

    Oscillation begins when the applied voltage is removed, as indicated in Figure 16.1(b). No longer constrained by the source voltage, the capacitor begins to equalize the charge between its plates by sending current through the inductor. The resulting current through the inductor creates a magnetic field which grows stronger the longer the current flows. The voltage v across the capacitor decreases because the net difference in charge across the plates is diminishing.

    Once the charge is evenly distributed between the plates of the capacitor (i.e., the capacitor is fully discharged), v = 0 (Figure 16.2(a)). However, the magnetic field that has built up in the inductor keeps the current flowing, and so the redistribution of charge across the capacitor plates continues. A short time later we have the situation shown in Figure 16.2(b): The voltage across the capacitor is negative and decreasing, the flow of current is decreasing, and the magnetic field of the inductor is decreasing.

  • 10 - Amplifiers

  • Steven W. Ellingson, Virginia Polytechnic Institute and State University
  • Book:
    Radio Systems Engineering
    Published online:
    28 May 2018
    Print publication:
    06 October 2016, pp 285-337

  • Summary

    INTRODUCTION

    The primary purpose of most amplifiers used in radio frequency systems is to increase signal magnitude. This is necessary in receivers because propagation path loss results in a signal arriving with voltage or current which is far too small to be digitized or directly demodulated. Amplification appears in transmitters when it is convenient to synthesize a signal at low power and amplify it, as opposed to synthesizing signals directly at the intended transmit power; the latter is difficult for all but very simple analog modulations.

    This chapter is organized as follows. Section 10.2 introduces the transistor, its use as a gain device, and provides a brief summary of transistor types and device technologies. The design of narrowband single-transistor amplifiers is introduced in four parts: biasing (Section 10.3), small-signal design to meet gain requirements (Section 10.4), designing for noise figure (Section 10.5), and designing for voltage standing wave ratio (Section 10.6). Section 10.7 presents a design example intended to demonstrate the principles of amplifier design as laid out in the previous sections. Section 10.8 introduces the concepts of multistage, differential, and broadband transistor amplifiers. Section 10.9 describes the implementation of transistor amplifiers as integrated circuits.

    TRANSISTORS AS AMPLIFIERS

    The fundamental building block of modern radio frequency amplifiers is the transistor. A transistor is a three-terminal semiconductor device in which the current between two terminals can be manipulated using the voltage or current at a third terminal. The application to RF design is most easily explained in the context of a particular device – for our purposes, the silicon (Si) bipolar junction transistor (BJT) is a good place to start.

    Bipolar Transistors

    A BJT is depicted in Figure 10.1. The three terminals of a BJT are known as the base, the collector, and the emitter. The associated terminal currents and voltages are as defined in Figure 10.1. The Si BJT comes in two varieties, known as “NPN” and “PNP,” referring to the geometry of semiconductor materials within the device. The NPN variant is somewhat more common in RF applications and is specifically considered here (and shown in Figure 10.1); the PNP variant is relatively easily understood once the NPN variant is mastered.

  • 6 - Digital Modulation

  • Steven W. Ellingson, Virginia Polytechnic Institute and State University
  • Book:
    Radio Systems Engineering
    Published online:
    28 May 2018
    Print publication:
    06 October 2016, pp 139-202

  • Summary

    INTRODUCTION

    In Section 5.1 we defined modulation as the representation of information in a form suitable for transmission. Digital modulation might be defined as the representation of information as a sequence of symbols drawn from a finite alphabet of possible symbols. This definition is not completely satisfactory, since it would seem to include a variety of techniques that many practitioners would consider to be analog modulations; these include continuous wave (CW) signaling (the use of an interruptible carrier to send Morse code). In Section 5.1 we settled on the notion that digital modulation also requires the information to be transmitted to be represented in digital (not merely discrete-time) form at some point in the modulation process, whereas this is not required in analog modulation.

    Overview of a Digital Communications Link and Organization of this Chapter

    With this definition in mind, Figure 6.1 shows an overview of a digital communications link. Here is the usual signal flow.

  • • The starting point of the link is source coding, which is the processing of data and/or digitized analog message signals – e.g., voice – in order to render the data in a form better-suited for digital modulation. A common goal in source coding is compression; that is, reduction of data rate so as to reduce the required bandwidth. Source coding is addressed in Section 6.2.

  • • Data are often encrypted for security. The principles of encryption are not specific to radio communications and so are not addressed further in this book.

  • • Channel coding is the processing of data with the goal of making them more robust to propagation channel impairments, including noise, multipath, and interference. Channel coding is addressed in Sections 6.13 (error control coding) and 6.14 (interleaving).

  • • At this point the data are processed by what is traditionally considered “modulation.” The result is an analog signal representing a discrete-time finite-alphabet message, and which is suitable for frequency conversion and amplification. It is this form of the signal that is ultimately transmitted to the other end of the link. Modulation is addressed in Sections 6.3, 6.4, and portions of Sections 6.10–6.12, 6.18 and 6.19.

  • Preface

  • Steven W. Ellingson, Virginia Polytechnic Institute and State University
  • Book:
    Radio Systems Engineering
    Published online:
    28 May 2018
    Print publication:
    06 October 2016, pp xxxix-xlii

  • Summary

    The topic of this book is the analysis and design of radio systems and their constituent subsytems and devices. Chapters 1–6 cover the basics of radio: antennas, propagation, noise, and modulation. Chapters 8–18 cover radio hardware: circuits, device technology where relevant, and the basics of digital signal processing. The intervening Chapter 7 (“Radio Link Analysis”) serves as the bridge between these two parts of the book by demonstrating how system-level characteristics lead to particular hardware characteristics, and vice versa. Appendix B serves as a summary of commonly-encountered radio systems in this context. Appendix A addresses modeling of path loss in terrestrial channels, building on the fundamentals presented in Chapter 3 (“Propagation”).

    This book presumes the reader is interested primarily in communications applications, however, most of the material is relevant to other applications of radio including navigation, radar, radio astronomy, geophysical remote sensing, and radio science.

    The use of the term “systems engineering” in the title of this book bears some explanation. In the parlance of communications engineers, the scope of this book is limited to considerations at the physical layer and below, with little coverage of issues at higher layers of the protocol stack. Further, some readers may judge that only Chapters 1, 7, and Appendix B (or maybe just Chapter 7) address systems engineering, in the sense of complete “end-to-end” system analysis and design. Nevertheless, the title “Radio Systems Engineering” seems appropriate because each topic – especially those in Chapters 8–18 – is presented in the context of system-level design, with extensive cross-referencing to associated topics in the first half of the book and to Chapter 7.

    Intended uses of this book This book is has been written with three possible uses in mind.

  • • Primary textbook in senior- and beginning graduate-level courses in radio systems engineering. This book can serve as a single textbook for a two–three semester course sequence. Associated courses typically have titles such as “radio communications systems,” “wireless engineering,” “wireless systems,” etc.

  • Appendix B - Characteristics of Some Common Radio Systems

  • Steven W. Ellingson, Virginia Polytechnic Institute and State University
  • Book:
    Radio Systems Engineering
    Published online:
    28 May 2018
    Print publication:
    06 October 2016, pp 583-595

  • Summary

    This appendix summarizes the technical characteristics of some commonly encountered radio systems. This summary is by no means comprehensive – the number of systems that could be addressed is simply too large. Also the information provided here is necessarily at a high level, with only the principal or defining details provided. Nevertheless this information should be useful as quick/initial reference, and as a guide in relating concepts described in the numbered chapters of this book to the technologies employed in practical radio systems.

    Here are a few things to keep in mind before beginning. First: Frequency bands, where given, are approximate. This is because there are typically variations between countries and/or between regions of the world. Second: In some cases additional information on the systems identified in this appendix can be found in the numbered chapters of the book. All such instances may not necessarily be pointed out, but the index of this book should be effective for locating the additional information. Of course for definitive technical information on these systems, the reader should consult the relevant standards documents.

    BROADCASTING

    Broadcasting is the delivery of audio, video, and/or data from a single transmitter to multiple receivers, primarily for purposes of entertainment and public information. Broadcasting has enormous historical significance as the original application of radio technology, and the legacy of technology developed for early broadcast radio is evident in modern radio systems of all types.

    A few of the most common terrestrial broadcast systems now in common operation are identified in Table B.1. Some additional details follow.

    It should be noted that modern broadcast FM is not simply FM-modulated audio. Modulated along with the audio are a number of subcarriers that permit stereo audio and a rudimentary data service. The subcarriers are essentially transparent to a minimal (monaural audio) receiver, but are easily recovered with a bit of additional signal processing.

    Modern broadcast AM and FM transmissions often include a digital overlay signal. The overlay consists of OFDM-modulated signals that lie adjacent to existing channel boundaries; see Figure B.1 for an example. In the USA, the In Band On Channel (IBOC) system (commonly known by the brand name “HD Radio”) is common. The digitally-modulated signal offers higher audio quality and additional content and data services for suitably-equipped receivers.

  • 2 - Antenna Fundamentals

  • Steven W. Ellingson, Virginia Polytechnic Institute and State University
  • Book:
    Radio Systems Engineering
    Published online:
    28 May 2018
    Print publication:
    06 October 2016, pp 16-59

  • Summary

    INTRODUCTION

    An antenna is the interface between a radio and the unguided electromagnetic wave that transfers information between radios. This chapter presents the fundamentals of antenna engineering. This chapter is organized as follows: Section 2.2 explains how antennas create radio waves, culminating in an equivalent circuit model for a transmitting antenna. Section 2.3 addresses the reception of radio waves, culminating in an equivalent circuit model for a receiving antenna. Sections 2.4 and 2.5 explain the principles of antenna pattern and polarization. Section 2.6 addresses the integration of antennas with radios; in particular impedance matching and baluns (this topic continues as the primary focus of Chapter 12). Sections 2.7– 2.12 describe classes of antennas most relevant to radio communications applications, including dipoles, monopoles, patches, beam antennas, reflector antennas, and arrays.

    CREATION OF RADIO WAVES

    The creation of a radio wave using an antenna is difficult to explain concisely in a completely rigorous manner. However, those aspects of the theory which are most relevant to radio systems engineering are relatively simple, and are presented here.We begin with a rudimentary physicsbased explanation, and conclude with a few key concepts that are sufficient for understanding the antennas described later in this chapter.

    Physical Origins of Radiation

    Here are the two essential concepts: First, a radio wave is a coupling of electric and magnetic fields that transfers power over a distance and which persists in the absence of its source. This is the phenomenon of propagation, which is the topic of Chapter 3. Second, the source of a radio wave is a time-varying current.

    To make sense of these concepts, let us briefly review some principles from undergraduatelevel electromagnetics. Initially, we shall use real-valued quantities, as opposed to phasors. Consider an electric charge which is concentrated at one point in space; i.e., a point charge. When this charge is stationary, it gives rise to an electric field E which is static. If the charge is allowed to move with a constant velocity – that is, at a constant speed and with unchanging direction – then we have a steady current J, which gives rise to a static magnetic field B.

  • 15 - Receivers

  • Steven W. Ellingson, Virginia Polytechnic Institute and State University
  • Book:
    Radio Systems Engineering
    Published online:
    28 May 2018
    Print publication:
    06 October 2016, pp 446-485

  • Summary

    INTRODUCTION

    We have now arrived at a point where we can reasonably consider the analysis and design of radio receivers. In Chapter 1, we considered two broad classes of radio receivers: those employing analog detection (Figure 1.10), used primarily with AM/ASK and FM/FSK modulations; and receivers employing analog-to-digital conversion (Figure 1.11), where the ADC output is subsequently processed digitally. In either case, the central problem in receiver design is to accept the signal provided by the antenna – a problem we addressed in Chapter 12 – and to deliver it to the analog detector or ADC with sufficient gain, sensitivity, selectivity, and linearity. Receivers by this definition are also sometimes referred to as downconverters, implying that frequency downconversion occurs; or tuners implying that the center frequency of the received bandpass is variable.

    We have already addressed the topic of analog detectors in Chapter 5, so this chapter begins with a discussion of the requirements and characteristics of ADCs (Section 15.2). In Section 15.3 we consider the central question of gain – how much is nominal, how little is adequate, and the relationship to sensitivity. Sections 15.4 and 15.5 address techniques and requirements for selectivity. Section 15.6 provides a summary of the principal receiver architectures. Section 15.7 elaborates on the problem of frequency planning in superheterodyne receivers. In Section 15.8 we revisit the question of gain, now in the context of the various receiver architectures, and summarize the principles of automatic gain control. This chapter concludes with suggestions for receiver design case studies (Section 15.9), intended to further demonstrate the practical aspects of modern receiver design.

    ANALOG-TO-DIGITAL CONVERSION

    An ADC is a device that converts a continuous-time analog signal into a sequence of discretetime digital values that approximate the input signal. After a brief introduction to ADC method of operation, the issues of sample rate versus bandwidth (Section 15.2.2) and quantization noise (Section 15.2.3) are discussed. Finally, we consider the characteristics and limitations of practical ADCs (Section 15.2.4).

    Method of Operation

    A simple model for analog-to-digital conversion is shown in Figure 15.1. This model consists of three parts: an analog sample and hold device (S/H), a quantizer, and a output word generator.

  • 4 - Noise

  • Steven W. Ellingson, Virginia Polytechnic Institute and State University
  • Book:
    Radio Systems Engineering
    Published online:
    28 May 2018
    Print publication:
    06 October 2016, pp 99-113

  • Summary

    INTRODUCTION

    As discussed in Chapter 1, it is noise which ultimately limits the sensitivity of a radio system. Noise is present in a variety of forms, both internal and external to the receiver. This chapter addresses the fundamentals of noise, beginning with some basic theory (Sections 4.2 and 4.3), and continuing with concepts pertaining to the characterization of internal noise (Section 4.4), and external noise (Section 4.5).

    THERMAL NOISE

    The atoms and electrons comprising any material experience random displacements with an associated kinetic energy that increases with physical temperature. In an electric circuit, the combined displacement of charge-carrying particles – electrons in particular – is observed as a current. The net difference in electrical potential over some distance can be interpreted as a voltage. The voltage and current resulting from random displacement of charged particles due to temperature is known as thermal noise. This specific noise mechanism is also known as Johnson Noise or Johnson–Nyquist Noise.

    Because the displacements of charged particles due to temperature are random, the resulting noise voltage and current waveforms can only be described statistically. The instantaneous magnitude of noise waveforms are found to well-modeled as a Gaussian distribution with zero mean. To determine the relevant characteristics of this distribution, let us consider the example of a resistor.

    Figure 4.1(a) shows a Thévenin equivalent circuit for a resistor, consisting of an opencircuit voltage vn in series with an ideal (noiseless) resistance R. vn represents the thermal noise generated by the resistor. To learn something about vn(t), we imagine this circuit being terminated by an ideal load resistor also having ideal resistance R as shown in Figure 4.1(b). The voltage across the load resistor in this circuit is vL(t) = vn(t)/2, whereas the current flowing through this resistor is iL(t) = vn(t)/2R. The power dissipated in the load resistor is therefore

    where is (by definition) the variance of the random variable vn(t).

Page 26 of 74