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Some years ago I had written a book directed to anyone who designs electronic and electric circuits. Engineers, technicians, teachers, students and hobbyists took a real benefit from that book. The original book is now out of print, being available only used issues. Since the book is very useful, the author decided to review the old edition, add new content and so create a new book for anyone who need a fast access to formulas, tables and calculations when designing his projects or solving a problem. The author, who has himself designed multitudes of projects and circuits during his life, publishing many books and hundreds of articles in electronics magazines and teaching electronics, has collected an assortment of all basic information necessary for calculations needed when designing new projects or solving a problem. More part of these formulas and calculations is now in the author´s site. The site also has versions in Portuguese and in Spanish. In the site the reader will also find practical examples in projects or articles where many of the formulas shown in this book are used. When starting a project or solving a problem the main difficulty the designer or student founds is how to locate the desired information. This information is normally spread over a large number of resources, such as books, handbooks, Internet, and magazine articles. Although many of us who are experienced in electronics have in mind the principal formulas, we sometimes have trouble with the forgotten constant, multiplication factor or exponent. Finding these values is sometimes difficult depending of the circumstances, such as where you are at the time, or the amount of resources at your disposal.
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Handbook of Electronics Formulas and Calculations - Volume 2
Electricity and Basic Electronics
Newton C. Braga
São Paulo - 2016
Institute NCB
www.newtoncbraga.com
HANDBOOK OF ELECTRONICS FORMULAS AND CALCULATIONS – vol.2Author: Newton C. BragaSão Paulo - Brazil – 2016
key-words: Electronic, formulas, calculations, electricity, mechatronics, engineering
Copyright by
INSTITUTO NEWTON C BRAGA
2ª edition
All rights reserved. No part of this book shall be reproduced, stored in a retrieval system, or transmitted by any means, electronic, mechanical, photocopying, recording, or otherwise, without written permission from the publisher. No patent liability is assumed with taken in the preparation of this book, the author, the publisher or saller assume no responsibility for erros or omissions. Neither is any liability assumed for damages resulting from the use of information containes hereing.
Officer responsible: Newton C. Braga
Design and Coordination: Renato Paiotti
INSTITUTE NEWTON C. BRAGA
http://www.newtoncbraga.com
Preface
BRIDGES
128. WHEATSTONE BRIDGE
129. WIEN BRIDGE
130. RESONANCE BRIDGE
131. MAXWELL BRIDGE
132. SCHERING BRIDGE
133. OWEN BRIDGE
134. HAY BRIDGE
OPERATIONAL AMPLIFIERS
135. NON-INVERTING OP. AMP.
136. INVERTING OP. AMP.
137. VOLTAGE FOLLOWER
138. SUMMING OP. AMP.
139. SUBTRACTION OP. AMP.
140. DIFFERENTIATION USING OP. AMP.
141. INTEGRATION USING OP. AMP.
142. LOGARITHMIC OP. AMP.
143. VOLTAGE SOURCE
144. CONSTANT CURRENT SOURCE - Op. Amp
145. CONSTANT CURRENT SOURCE - Op. Amp.
146. ABSOLUTE VALUE AMPLIFIER - Op. Amp.
147. VOLTIMETER USING Op. Amp.
148. SQUARE WAVE OSCILLATOR - Op. Amp.
149. WIEN BRIDGE OSCILLATOR USING Op. Amp.
150. BANDPASS AMPLIFIER USING Op. Amp.
151. NOTCH FILTER - Op. Amp.
152. LOW-PASS FILTER - Op. Amp.
153. HIGH-PASS FILTER - Op. Amp.
154. BUTTERWORTH FILTER - Op. Amp.
155. SERIES VOLTAGE REGULATOR (one transistor)
156. PARALLEL VOLTAGE REGULADOR
INTEGRATED VOLTAGE REGULATORS
157. VOLTAGE REGULATORS
158. CURRENT REGULATOR
159. Calculating a voltage regulator
Digital Circuits
160. Binary to Decimal Conversion
161. BYTE TO DECIMAL CONVERSION
162. BCD to Decimal Conversion
163. HEXADECIMAL TO DECIMAL CONVERSION
164. Decimal-to-Binary Conversion
165. DECIMAL TO HEXADECIMAL
Logic Functions
166. AND Gate
167. NAND Gate
168. OR Gate
169. NOR Gate
170. Exclusive-OR
171. Inverter
172. Binary Addition
173. Binary Subtraction
174. Binary Multiplication
175. Binary Division
The Postulates of Boolean Algebra
176. Laws of Tautology
177. Laws of Commutation
178. The Laws of Association
179. Laws of Distribution
180. Laws of Absorption
181. Laws of Universe Class
182. The Laws of Null Class
183. Laws of Complementation
184. Laws of Contraposition
185. Law of Double Negation
186. Laws of Expansion
187. Laws of Duality
Boolean Relationships
188. Idempoint
189. Commutative
190. Associative
191. Boolean Relationship - Distributive
192. Absortion
193. Demorgan Theorem
Miscelaneous
194. Instantaneous Values of Sine Waves
195. Inches to Millimeters
196. Millimeters to Decimal Inches
Temperature Conversions
197. Degrees Celsius (C), Degrees Fahrenheit (F), Degrees Kelvin (K) and Degrees Reamur
Sound and Acoustics
198. Sound Wavelength
199. Velocity of Longitudinal Sound Waves
200. Sound Interval
201. Sound Pressure
202. Sound Pressure Level
203. Sound Intensity
204. Interference (Beat)
205. Doppler Effect
Loudspeaker Crossover Networks
206. Simple Crossover Network for Tweeter (6dB/octave)
207. 6 dB Octave Crossover Network II
208. Two-Channel 12 dB/Octave Loudspeaker Crossover
209. Two-Channel 18 dB/octave PI-Crossover Network
210. Crossover and Design Frequencies for 3-way Networks
211. Three-Channel 6 dB/Octave Crossover (Series)
212. Three-Chanell 6dB/Octave Crossover (Parallel)
213. Three-Channel 12 dB/Octave Crossover (Series)
214. Three- Channel 12 dB/Octave Crossover (Parallel)
215. Weeler’s Formula
Optoelectronics
216. Wavelength and Frequency for Light Radiation
217. Luminous Intensity and Flux
218. Luminous Density
219. Refraction
220.LEDs
221. Photocell
222. LDR or Photoresistor
223. Photodiode
224. Phototransistor
225. Stefan-Boltzmann’s Law
Mathematics
226. Differentiation Formulas
227. Integration Formulas
228. Tolerances
229. Fourier Transforms
Some years ago I had written a book directed to anyone who designs electronic and electric circuits. Engineers, technicians, teachers, students and hobbyists took a real benefit from that book. The original book is now out of print, being available only used issues. Since the book is very useful, the author decided to review the old edition, add new content and so create a new book for anyone who need a fast access to formulas, tables and calculations when designing his projects or solving a problem.
The author, who has himself designed multitudes of projects and circuits during his life, publishing many books and hundreds of articles in electronics magazines and teaching electronics, has collected an assortment of all basic information necessary for calculations needed when designing new projects or solving a problem.
More part of these formulas and calculations is now in the author´s site at www.newtoncbraga.com. The site also has versions in Portuguese (www.newtoncbraga.com.br) and in Spanish (www.incb.com.mx).
In the site the reader will also find practical examples in projects or articles where many of the formulas shown in this book are used.
When starting a project or solving a problem the main difficulty the designer or student founds is how to locate the desired information. This information is normally spread over a large number of resources, such as books, handbooks, Internet, and magazine articles.
Although many of us who are experienced in electronics have in mind the principal formulas, we sometimes have trouble with the forgotten constant, multiplication factor or exponent. Finding these values is sometimes difficult depending of the circumstances, such as where you are at the time or the amount of resources at your disposal.
By putting the principal formulas and tables in a unique place, a designer can find the desired information easier, and, more importantly, can take this information wherever he goes.
And with the aid of the new technologies, the information can be accessed by a tablet, Smartphone or a laptop, if you have the virtual version. This is the aim of this book.
But formulas and tables are not useful only when designing a new configuration. They are necessary when we need to know what happen when a specific working circuit is altered, for the electronic student doing homework or the researchers in other fields who work with electronic equipment.
The tables contain a large amount of important information, such as particular values of constants, physical properties of circuits and materials, and even calculated values that can´t be found without using complex or hard-to-do procedures.
Finally, we have laws and theorems describing the properties of circuits and devices, and procedures to be used in calculations, which are very important when doing practical works.
Most of the formulas and tables are accompanied by application examples. They are very important to show the reader how the calculations are made when using the given information. To avoid problems with incorrect results, in all formulas and applications the units to be used are indicated.
The formulas range from the simplest, where elementary arithmetic operations such as sum, subtraction, multiplication and division, are used, to the more complex that require some good working knowledge of algebraic and trigonometric functions, or even differential and integral calculus.
Although mathematics is an exact science, when some calculations are applied to other sciences and in “real-life” electronics, the results can be different from the expected. When making calculations involving electronic circuits, it is often said that “When working with electronics, practice and theory often disagree.”
This means that in many cases the results found in calculations will need some “adjustments” when applied to an actual application.
This fact is applicable even to the tolerances of the electronic components used in practical applications, plus the fact that many formulas are not exact, but empirical.
But why use an exact formula, including complex logarithms, trigonometric functions or differential equations, if we can get results good enough to make a circuit work by using a reduced formula?
In many stages of the design process, the results will depend on the tolerance of the components used.
This explains why in many cases we´ll not give the exact formula but an empirical formula, where the “complex part” of the calculations will be reduced to a constant, or even eliminated.
This means that this book is not an advanced resource for engineers or researches that need a very accurate result in their calculation. We can consider that in many cases the formulas are empiric, i.e. giving approximate results, but good enough to put a project to work.
About the units – the preference is the use of the decimal system or International Units System (SI - Système International d´Unités). Only in the cases where conversion formulas and tables are given will other units appear. The notations will be that recommended by NIST (National Institute of Standards and Technology), but in some cases, to make easier the use by reader less experienced with calculations, some “non-conventional” notations can be found.
Although the preferred symbol to indicate multiplication operations is the “x”, in some cases we also use the bullet (*) or even the point (.).
The tables were obtained from different sources – physics handbooks, engineering books, manufacturers and technical documentation were consulted. As for composition of materials, the calculation procedures can change from one manufacturer to another, so small differences in the tabulated values will be found if comparing to other resources.
Many tables were calculated by the author using software created to the task.
Using the book is very easy. The formulas are distributed in groups according to subject, and all the reader needs is a calculator (in your cellular or computer) and a piece of paper to work. A scientific calculator or math software in your computer, tablet or even Smartphone is recommended if trigonometric functions or logarithms are used.
The most important point of this introduction is that this Handbook can become an important tool for everyone who works with electricity and electronics – from students and hobbyists for researchers, teachers and engineers. Anyone in need of practical information or formulas and calculations as applied to electricity and electronics will find this book indispensable.
Newton C. Braga (2016)
P.S. The original version for this book is out of print and had another tittle. The version has new formulas and new examples consisting in a new book.
In this volume:
Bridges
Operational Amplifiers
Digital Electronics and logic
Voltage and Current Regulation
Thermometry and thermology
Sound and Acoustics
Optoelectronics
Light and Colour
Mathematics