The Db Concept
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Db Math Marco Zennaro Ermanno Pietrosemoli Goals
dB Math Marco Zennaro Ermanno Pietrosemoli Goals ‣ Electromagnetic waves carry power measured in milliwatts. ‣ Decibels (dB) use a relative logarithmic relationship to reduce multiplication to simple addition. ‣ You can simplify common radio calculations by using dBm instead of mW, and dB to represent variations of power. ‣ It is simpler to solve radio calculations in your head by using dB. 2 Power ‣ Any electromagnetic wave carries energy - we can feel that when we enjoy (or suffer from) the warmth of the sun. The amount of energy received in a certain amount of time is called power. ‣ The electric field is measured in V/m (volts per meter), the power contained within it is proportional to the square of the electric field: 2 P ~ E ‣ The unit of power is the watt (W). For wireless work, the milliwatt (mW) is usually a more convenient unit. 3 Gain and Loss ‣ If the amplitude of an electromagnetic wave increases, its power increases. This increase in power is called a gain. ‣ If the amplitude decreases, its power decreases. This decrease in power is called a loss. ‣ When designing communication links, you try to maximize the gains while minimizing any losses. 4 Intro to dB ‣ Decibels are a relative measurement unit unlike the absolute measurement of milliwatts. ‣ The decibel (dB) is 10 times the decimal logarithm of the ratio between two values of a variable. The calculation of decibels uses a logarithm to allow very large or very small relations to be represented with a conveniently small number. ‣ On the logarithmic scale, the reference cannot be zero because the log of zero does not exist! 5 Why do we use dB? ‣ Power does not fade in a linear manner, but inversely as the square of the distance. -
Spectrum Management Technical Handbook
NTIA TN 89-2 SPECTRUM MANAGEMENT TECHNICAL HANDBOOK TECHNICAL NOTE SERIES NTIA TECHNICAL NOTE 89-2 SPECTRUM MANAGEMENT TECHNICAL HANDBOOK l U.S. DEPARTMENT OF COMMERCE Robert A. Mosbacher, Secretary Alfred C. Sikes, Assistant Secretary for Communications and Information JULY 1989 ACKNOWLEDGEMENT NT IA acknowledges the efforts of Mark Schellhammer in the completion of Phase I of this handbook (Sections 1-3). Other portions will be added as resources are available. ABSTRACT This handbook is a compilation of the procedures, definitions, relationships and conversions essential to electromagnetic compatibility analysis. It is intended as a reference for NTIA engineers. KEY WORDS CONVERSION FACTORS COUPLING EQUATIONS DEFINITIONS ·TECHNICAL RELATIONSHIPS iii TABLE OF CONTENTS Subsection Page SECTION 1 TECHNICAL TERMS:DEFINITIONS AND NOTATION TERMS AND DEFINITIONS . .. .. 1-1 GLOSSARY OF STANDARD NOTATION . .. 1-13 SECTION 2 TECHNICAL RELATIONSHIPS AND CONVERSION FACTORS INTRODUCTION . .. .. .. 2-1 TRANSMISSION LOSS FOR RADIO LINKS . �. .. .. 2-1 Propagation Loss . .. .. .. 2-1 Transmission Loss ........................................ 2-2 Free-Space Basic Transmission Loss .......................... 2-2 Basic Transmission Loss .................................... 2-2 Loss Relative to Free-Space .................................. 2-2 System Loss . .. 2-3 ; Total Loss . .. .. 2-3 ANTENNA CHARACTERISTICS . .. 2-3 Antenna Directivity ........................................ 2-3 Antenna Gain and Efficiency .................................. 2-3 I -
Model HR-ADC1 Analog to Digital Audio Converter
HALF-RACK SERIES Model HR-ADC1 Analog to Digital Audio Converter • Broadcast Quality Analog to Digital Audio Conversion • Peak Metering with Selectable Hold or Peak Store Modes • Inputs: Balanced and Unbalanced Stereo Audio • Operation Up to 24 bits, 192 kHz • Output: AES/EBU, Coaxial S/PDIF, AES-3ID • Selectable Internally Generated Sample Rate and Bit Depth • External Sync Inputs: AES/EBU, Coaxial S/PDIF, AES-3ID • Front-Panel External Sync Enable Selector and Indicator • Adjustable Audio Input Gain Trim • Sample Rate, Bit Depth, External Sync Lock Indicators • Peak or Average Ballistic Metering with Selectable 0 dB Reference • Transformer Isolated AES/EBU Output The HR-ADC1 is an RDL HALF-RACK product, featuring an all metal chassis and the advanced circuitry for which RDL products are known. HALF-RACKs may be operated free-standing using the included feet or may be conveniently rack mounted using available rack-mount adapters. APPLICATION: The HR-ADC1 is a broadcast quality A/D converter that provides exceptional audio accuracy and clarity with any audio source or style. Superior analog performance fine tuned through audiophile listening practices produces very low distortion (0.0006%), exceedingly low noise (-135 dB) and remarkably flat frequency response (+/- 0.05 dB). This performance is coupled with unparalleled metering flexibility and programmability with average mastering level monitoring and peak value storage. With external sync capability plus front-panel settings up to 24 bits and up to 192 kHz sample rate, the HR-ADC1 is the single instrument needed for A/D conversion in demanding applications. The HR-ADC1 accepts balanced +4 dBu or unbalanced -10 dBV stereo audio through rear-panel XLR or RCA jacks or through a detachable terminal block. -
Audio Engineering Society Convention Paper
Audio Engineering Society Convention Paper Presented at the 128th Convention 2010 May 22–25 London, UK The papers at this Convention have been selected on the basis of a submitted abstract and extended precis that have been peer reviewed by at least two qualified anonymous reviewers. This convention paper has been reproduced from the author's advance manuscript, without editing, corrections, or consideration by the Review Board. The AES takes no responsibility for the contents. Additional papers may be obtained by sending request and remittance to Audio Engineering Society, 60 East 42nd Street, New York, New York 10165-2520, USA; also see www.aes.org. All rights reserved. Reproduction of this paper, or any portion thereof, is not permitted without direct permission from the Journal of the Audio Engineering Society. Loudness Normalization In The Age Of Portable Media Players Martin Wolters1, Harald Mundt1, and Jeffrey Riedmiller2 1 Dolby Germany GmbH, Nuremberg, Germany [email protected], [email protected] 2 Dolby Laboratories Inc., San Francisco, CA, USA [email protected] ABSTRACT In recent years, the increasing popularity of portable media devices among consumers has created new and unique audio challenges for content creators, distributors as well as device manufacturers. Many of the latest devices are capable of supporting a broad range of content types and media formats including those often associated with high quality (wider dynamic-range) experiences such as HDTV, Blu-ray or DVD. However, portable media devices are generally challenged in terms of maintaining consistent loudness and intelligibility across varying media and content types on either their internal speaker(s) and/or headphone outputs. -
Decibels, Phons, and Sones
Decibels, Phons, and Sones The rate at which sound energy reaches a Table 1: deciBel Ratings of Several Sounds given cross-sectional area is known as the Sound Source Intensity deciBel sound intensity. There is an abnormally Weakest Sound Heard 1 x 10-12 W/m2 0.0 large range of intensities over which Rustling Leaves 1 x 10-11 W/m2 10.0 humans can hear. Given the large range, it Quiet Library 1 x 10-9 W/m2 30.0 is common to express the sound intensity Average Home 1 x 10-7 W/m2 50.0 using a logarithmic scale known as the Normal Conversation 1 x 10-6 W/m2 60.0 decibel scale. By measuring the intensity -4 2 level of a given sound with a meter, the Phone Dial Tone 1 x 10 W/m 80.0 -3 2 deciBel rating can be determined. Truck Traffic 1 x 10 W/m 90.0 Intensity values and decibel ratings for Chainsaw, 1 m away 1 x 10-1 W/m2 110.0 several sound sources listed in Table 1. The decibel scale and the intensity values it is based on is an objective measure of a sound. While intensities and deciBels (dB) are measurable, the loudness of a sound is subjective. Sound loudness varies from person to person. Furthermore, sounds with equal intensities but different frequencies are perceived by the same person to have unequal loudness. For instance, a 60 dB sound with a frequency of 1000 Hz sounds louder than a 60 dB sound with a frequency of 500 Hz. -
Rockbox User Manual
The Rockbox Manual for Sansa Fuze+ rockbox.org October 1, 2013 2 Rockbox http://www.rockbox.org/ Open Source Jukebox Firmware Rockbox and this manual is the collaborative effort of the Rockbox team and its contributors. See the appendix for a complete list of contributors. c 2003-2013 The Rockbox Team and its contributors, c 2004 Christi Alice Scarborough, c 2003 José Maria Garcia-Valdecasas Bernal & Peter Schlenker. Version unknown-131001. Built using pdfLATEX. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sec- tions, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled “GNU Free Documentation License”. The Rockbox manual (version unknown-131001) Sansa Fuze+ Contents 3 Contents 1. Introduction 11 1.1. Welcome..................................... 11 1.2. Getting more help............................... 11 1.3. Naming conventions and marks........................ 12 2. Installation 13 2.1. Before Starting................................. 13 2.2. Installing Rockbox............................... 13 2.2.1. Automated Installation........................ 14 2.2.2. Manual Installation.......................... 15 2.2.3. Bootloader installation from Windows................ 16 2.2.4. Bootloader installation from Mac OS X and Linux......... 17 2.2.5. Finishing the install.......................... 17 2.2.6. Enabling Speech Support (optional)................. 17 2.3. Running Rockbox................................ 18 2.4. Updating Rockbox............................... 18 2.5. Uninstalling Rockbox............................. 18 2.5.1. Automatic Uninstallation....................... 18 2.5.2. Manual Uninstallation......................... 18 2.6. Troubleshooting................................. 18 3. Quick Start 20 3.1. -
Le Décibel ( Db ) Est Un Sous-Multiple Du Bel, Correspondant À 1 Dixième De Bel
Emploi du Décibel, unité relative ou unité absolue Le décibel ( dB ) est un sous-multiple du bel, correspondant à 1 dixième de bel. Nommé en l’honneur de l'inventeur Alexandre Graham Bell, le bel est unité de mesure logarithmique du rapport entre deux puissances, connue pour exprimer la puissance du son. Grandeur sans dimension en dehors du système international, le bel n'est pas l'unité la plus fréquente. Le décibel est plus couramment employé. Équivalent à 1/10 de bel, le décibel comme le bel, peut être utilisé dans les domaines de l’acoustique, de la physique, de l’électronique et est largement répandue dans l’ensemble des champs de l’ingénierie (fiabilité, inférence bayésienne, etc.). Cette unité est particulièrement pertinente dans les domaines où la perception humaine est mise en jeu, car la loi de Weber-Fechner stipule que la sensation ressentie varie comme le logarithme de l’excitation. où S est la sensation perçue, I l'intensité de la stimulation et k une constante. Histoire des bels et décibels Le bel (symbole B) est utilisé dans les télécommunications, l’électronique, l’acoustique ainsi que les mathématiques. Inventé par des ingénieurs des Laboratoires Bell pour mesurer l’atténuation du signal audio sur une distance d’un mile (1,6 km), longueur standard d’un câble de téléphone, il était appelé unité de « transmission » à l’origine, ou TU (Transmission unit ), mais fut renommé en 1923 ou 1924 en l’honneur du fondateur du laboratoire et pionnier des télécoms, Alexander Graham Bell . Définition, usage en unité relative Si on appelle X le rapport de deux puissances P1 et P0, la valeur de X en bel (B) s’écrit : On peut également exprimer X dans un sous multiple du bel, le décibel (dB) un décibel étant égal à un dixième de bel.: Si le rapport entre les deux puissances est de : 102 = 100, cela correspond à 2 bels ou 20 dB. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
A 449 MHZ MODULAR WIND PROFILER RADAR SYSTEM by BRADLEY JAMES LINDSETH B.S., Washington University in St
A 449 MHZ MODULAR WIND PROFILER RADAR SYSTEM by BRADLEY JAMES LINDSETH B.S., Washington University in St. Louis, 2002 M.S., Washington University in St. Louis, 2005 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirement for the degree of Doctor of Philosophy Department of Electrical, Computer, and Energy Engineering 2012 This thesis entitled: A 449 MHz Modular Wind Profiler Radar System written by Bradley James Lindseth has been approved for the Department of Electrical, Computer, and Energy Engineering Prof. Zoya Popović Dr. William O.J. Brown Date The final copy of this thesis has been examined by the signatories, and we Find that both the content and the form meet acceptable presentation standards Of scholarly work in the above mentioned discipline. Lindseth, Bradley James (Ph.D., Electrical Engineering) A 449 MHz Modular Wind Profiler Radar System Thesis directed by Professor Zoya Popović and Dr. William O.J. Brown This thesis presents the design of a 449 MHz radar for wind profiling, with a focus on modularity, antenna sidelobe reduction, and solid-state transmitter design. It is one of the first wind profiler radars to use low-cost LDMOS power amplifiers combined with spaced antennas. The system is portable and designed for 2-3 month deployments. The transmitter power amplifier consists of multiple 1-kW peak power modules which feed 54 antenna elements arranged in a hexagonal array, scalable directly to 126 elements. The power amplifier is operated in pulsed mode with a 10% duty cycle at 63% drain efficiency. -
The Decibel Scale R.C
The Decibel Scale R.C. Maher Fall 2014 It is often convenient to compare two quantities in an audio system using a proportionality ratio. For example, if a linear amplifier produces 2 volts (V) output amplitude when its input amplitude is 100 millivolts (mV), the voltage gain is expressed as the ratio of output/input: 2V/100mV = 20. As long as the two quantities being compared have the same units--volts in this case--the proportionality ratio is dimensionless. If the proportionality ratios of interest end up being very large or very small, such as 2x105 and 2.5x10-4, manipulating and interpreting the results can become rather unwieldy. In this situation it can be helpful to compress the numerical range by taking the logarithm of the ratio. It is customary to use a base-10 logarithm for this purpose. For example, 5 log10(2x10 ) = 5 + log10(2) = 5.301 and -4 log10(2.5x10 ) = -4 + log10(2.5) = -3.602 If the quantities in the proportionality ratio both have the units of power (e.g., 2 watts), or intensity (watts/m ), then the base-10 logarithm log10(power1/power0) is expressed with the unit bel (symbol: B), in honor of Alexander Graham Bell (1847 -1922). The decibel is a unit representing one tenth (deci-) of a bel. Therefore, a figure reported in decibels is ten times the value reported in bels. The expression for a proportionality ratio expressed in decibel units (symbol dB) is: 10 푝표푤푒푟1 10 Common Usage 푑퐵 ≡ ∙ 푙표푔 �푝표푤푒푟0� The power dissipated in a resistance R ohms can be expressed as V2/R, where V is the voltage across the resistor. -
Sox Examples
Signal Analysis Young Won Lim 2/17/18 Copyright (c) 2016 – 2018 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Please send corrections (or suggestions) to [email protected]. This document was produced by using LibreOffice. Young Won Lim 2/17/18 Based on Signal Processing with Free Software : Practical Experiments F. Auger Audio Signal Young Won Lim Analysis (1A) 3 2/17/18 Sox Examples Audio Signal Young Won Lim Analysis (1A) 4 2/17/18 soxi soxi s1.mp3 soxi s1.mp3 > s1_info.txt Input File Channels Sample Rate Precision Duration File Siz Bit Rate Sample Encoding Audio Signal Young Won Lim Analysis (1A) 5 2/17/18 Generating signals using sox sox -n s1.mp3 synth 3.5 sine 440 sox -n s2.wav synth 90000s sine 660:1000 sox -n s3.mp3 synth 1:20 triangle 440 sox -n s4.mp3 synth 1:20 trapezium 440 sox -V4 -n s5.mp3 synth 6 square 440 0 0 40 sox -n s6.mp3 synth 5 noise Audio Signal Young Won Lim Analysis (1A) 6 2/17/18 stat Sox s1.mp3 -n stat Sox s1.mp3 -n stat > s1_info_stat.txt Samples read Length (seconds) Scaled by Maximum amplitude Minimum amplitude Midline amplitude Mean norm Mean amplitude RMS amplitude Maximum delta Minimum delta Mean delta RMS delta Rough frequency Volume adjustment Audio Signal Young Won -
MT-230 One Technology Way • P
Mini Tutorial MT-230 One Technology Way • P. O. Box 9106 • Norwood, MA 02062-9106, U.S.A. • Tel: 781.329.4700 • Fax: 781.461.3113 • www.analog.com Because this headroom of the converter is continuously being Noise Considerations in High constrained, maintaining a very low noise spectral density of Speed Converter Signal Chains −150 dBFS/Hz and lower is challenging with each new design. This is why it is paramount that the designer recognize the by Rob Reeder Analog Devices, Inc. importance of the surrounding noise contributions within the entire signal chain solution. Admittedly, there are many noise principles. This tutorial IN THIS MINI TUTORIAL addresses two of these principles: noise bandwidth and the The most common outside noise sources and how they addition of noise sources. influence the total dynamic system performance of a high NOISE BANDWIDTH speed signal chain are described as well as some analog and Noise bandwidth is not the same as the typical −3 dB band- digital tricks that can be employed to further increase the width of an amplifier or filter cutoff point. The shape for noise signal-to-noise ratio (SNR) in your next design. takes on a different form (rectangular) which specifies the total integration of the bandwidth. This means making a slight INTRODUCTION adjustment in the noise calculation when considering the noise Designing in high speed analog signal chains can be challenging bandwidth contribution. with so many noise sources to consider. Whether the frequen- For a first-order system, for example a first-order low-pass cies are high speed (>10 MHz) or low speed, the converter filter, the noise bandwidth is 57% larger.