Handbook of Electronics Formulas and Calculations - Volume 1

Handbook of Electronics Formulas and Calculations - Volume 1

Electricity and Basic Electronics

Newton C. Braga

São Paulo - 2016

Institute NCB

www.newtoncbraga.com

leitor@newtoncbraga.com.br

HANDBOOK OF ELECTRONICS FORMULAS AND CALCULATIONS – vol.1

Author: Newton C. Braga

São 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

Índice

Preface

SI Unit rules and style conventions

Part 1 - DC Formulas

1. Units

2. Resistance of a conductor

3. Conductance

4. Conductance of a Length of Wire

5. Thermal Influence in the Resistance of a Cable

6. Ohm´s Law

7. Electric Power

8. Joule´s Law

9. Electric Energy

10. Electrolysis (Faraday´s Law)

11. Resistors in Series

12. Resistors in Parallel

13. Voltage Divider (resistive)

14. Loaded Voltage Divider (resistive)

15. First Kirchhoff´s Law

16. Second Kirchhoff´s Law

17. Capacitance

18. Planar Capacitor

19. Breakdown Voltage in a Capacitor

20. Energy Stored in a Capacitor

21. Capacitors in Parallel

22. Capacitors in Series

23. Magnetic Field of a Solenoid

24. Magnetic Induction inside a Solenoid

25. Inductance

26. Inductances in series

27. Inductances in Parallel

28. Mutual Inductance

Part 2 - AC Formulas

29. Frequency and Period

30. Cyclic or Angular Frequency

31. Average Value

32. RMS Value

33. Frequency & Wavelength

34. Capacitive Reatance

35. Inductive Reactance

36. Quality Factor (Factor-Q)

37. Ohm´s Law for AC Circuits

38. RL in Series

39. RC in Series

40. LC in Series

41. RLC in Series

42. RC in Parallel

43. LR in Parallel

44. LC in Parallel

45. Ressonance

46. Time Constant (RC Circuit)

47. Time Constant (LC)

48. Inductive Coupling Using Transformers

49. Direct Inductive Coupling

50. Ohmic Coupling

51. Capacitive Coupling

52. Low- Pass Filters

53. High Pass Filters

54. Band-Pass Filters

55. Differentiation

56. Integration

57. Noise

58. Bandwidth

59. Voltage Ratio in Transformers

60. Current Ratio in Transformers

61. Impedance Ratio in Transformers

62. Decibel

63. The Neper

64. Balanced T-Attenuator

65. Balanced π-Attenuator

66. Unbalanced T-Attenuator

67. Unbalanced π-Attenuator

68. Half-Wave Dipole

69. Folded Half-Wave Dipole

70. Range (VHF and upper signals)

71. Coaxial Cable

72. Two-Wire Balanced Line

73. Impedance Match or π-Network

Part 3 - Electronic Circuits

74. Semiconductor Diode

75. Half-Wave Rectifier

76. Full-Wave Rectifier

77. LC Filter Coefficient

78. RC Filter Coefficient

79. Ripple Factor

80. Filter Inductance

81. Filter Capacitance

82. Conventional Voltage Doubler

83. Cascade Voltage Doubler

84. Bridge Voltage Doubler

85. Full Wave Tripler

86. Cascade Voltage Tripler

87. Full-Wave Voltage Quadrupler

88. Zener Diode

89. Capacitive Voltage Divider

90. NTC

91. PTC

92. VARICAPS

Part 4 - TRANSISTORS

93. Transistor Static Current-Gain (Common Emitter)

94. Transistor Static Current Gain (Common Base Configuration)

95. Relationship between Alpha and Beta

96. Hybrid Parameters

97. Common Base

98. Common Emitter

99. Common Collector

Part 5 - Basic Quantities of Circuits Using Transistores

100. Short-Circuit Output

101. Open Circuit Output

102. Short-Circuit Input

103. Open-Circuit Input

104. Common-Base Configuration Usual Formulas

105. Common-Emitter Configurations Usual Formulas

106. Common Collector Usual Formulas

Part 6 - TRANSISTOR PRACTICAL FORMULAS

107. LOAD RESISTANCE

108. Base- Biasing Resistance

109. Automatic-Biasing Resistance

Part 7 - JUNCTION FIELD EFFECT TRANSISTOR-JFET AND THE MOS FIELD EFFECT TRANSISTOR (MOSFET)

110. Common Source

111 – Common Drain

112. Common Gate

113. UJT – Unujunction Transistor

114. SCR

115. TRIAC

Part 8 - OSCILLATORS

116. Astable Multivibrator

117. Neon-Lamp Oscillator

118. Phase Shift Oscillator

119. Wien Bridge Oscillator

120. Twin-T Oscillator

121. Hartley Oscillator

122. Colpitts Oscillator

123. CMOS Two-Gate Oscillator (I)

124. CMOS Two-Gate Oscillator (II)

125. CMOS Schmitt Trigger Oscillator

126. The Astable 555

127. Monostable 555

Preface

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 enorgh 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,