ECE 221 Electric Circuit Analysis I Chapter 3 SI Notation, Units, Unit Conversion Herbert G. Mayer,...
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Transcript of ECE 221 Electric Circuit Analysis I Chapter 3 SI Notation, Units, Unit Conversion Herbert G. Mayer,...
ECE 221Electric Circuit Analysis I
Chapter 3SI Notation, Units, Unit Conversion
Herbert G. Mayer, PSU & CCUTStatus 10/15/2014
Taken with permission from PSU Prof. Phillip WongFor use at Changchun University of Technology CCUT
Syllabus Scientific Engineering Notation Dimensions Physical Quantities Units
Scientific & Engineering Notation
Scientific notation is a compact method for expressing very small or very large numbers.Format:
3
ba 10
mantissa base
exponent• The mantissa conveys the
number’s value and accuracy
• The base and exponent define the scaling factor
Scientific Engineering
exponent multiple of 1 multiple of 3
mantissa -10 < a < 10 -1000 < a < 1000
Example:
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Number Scientific Engineering0.000001234567 1.23456710-6 1.23456710-6
0.00001234567 1.23456710-5 123.456710-3
0.0001234567 1.23456710-4 12.3456710-3
0.001234567 1.23456710-3 1.23456710-3
0.01234567 1.23456710-2 0.012345670.1234567 1.23456710-1 0.12345671.234567 1.234567 1.23456712.34567 1.23456710 12.34567123.4567 1.234567102 123.45671234.567 1.234567103 1.234567103
12345.67 1.234567104 12.34567103
123456.7 1.234567105 123.4567103
1234567 1.234567106 1.234567106
Describing Physical Quantities
A physical quantity has three components: Dimension (e.g., length, time, etc.) Magnitude (quantity) Unit (reference amount)
Example: 12.5 m
A measurement determines the number of multiples of a unit that are contained within a physical quantity
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length
magnitude
unit
Dimensions
Dimensions describe physical quantities
Dimensions are independent of units
Each dimension may have a variety of units
Dimensions are divided into two areas: Fundamental (e.g., Length L or Time t) Derived (e.g., Velocity = Length / Time)
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Units
Commonly used unit systems: Metric (decimal: meter, kilogram, second) Engineering System (US: foot, pound-force, second)
Système International d Unités (SI) is the adopted ′world standard, except United States
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SI Base Units Length: meter (m) Time: second (s) Mass: kilogram (kg) Electric current: ampere (A) Temperature: kelvin (K) Amount of substance: mole (mol) Luminous intensity: candela (cd)
SI Supplementary Units Plane angle: radian (rad) Solid angle: steradian (sr)
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SI Unit Prefixes
1024 yotta Y 10-1 deci d1021 zetta Z 10-2 centi c1018 exa E 10-3 milli m1015 peta P 10-6 micro 1012 tera T 10-9 nano n109 giga G 10-12 pico p106 mega M 10-15 femto f103 kilo k 10-18 atto a102 hecto h 10-21 zepto z101 deka da 10-24 yocto y
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Commonly used electrical engineering units
Resistance (ohm): MΩ kΩ Ω mΩ μΩ nΩ Inductance (henry): kH H mH μH nH pH Capacitance (farad): kF F mF μF nF pF fF aF Voltage (volt): MV kV V mV μV nV Current (ampere): MA kA A mA μA nA pA
fA Power (watt): MW kW W mW μW nW
pW Frequency (hertz): THz GHz MHz kHz Hz
mHz Wavelength (m): km m cm mm μm nm
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M→106, k→103, 1, m→10-3, →10-6, n→10-9, p→10-12, f→10-15
Example:0.01 F = ? pF
0.009 mV versus 40.5 V. Which one is bigger?→ (0.009 mV)(103 V/mV) = 9 V. 40.5 V is bigger.
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M k 1 m n p f
M 1 103 106 109 1012 1015 1018 1021
k 10-3 1 103 106 109 1012 1015 1018
1 10-6 10-3 1 103 106 109 1012 1015
m 10-9 10-6 10-3 1 103 106 109 1012
10-12 10-9 10-6 10-3 1 103 106 109
n 10-15 10-12 10-9 10-6 10-3 1 103 106
p 10-18 10-15 10-12 10-9 10-6 10-3 1 103
f 10-21 10-18 10-15 10-12 10-9 10-6 10-3 1
From ↓To →
Multipliers for SI Prefix Conversion
→ (0.01 F)(106 pF/F) = 10000 pF
Example: Frequency & Wavelength for EM Waves
Electromagnetic waves:
(n=10-9, M=106, G=109, T=1012, P=1015, E=1018)
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Name Frequency f Wavelength Radio 3 Hz – 300 GHz 100 Mm – 1 mm
Microwave 300 MHz – 300 GHz 1 m – 1 mm
Infrared 300 GHz – 405 THz 1 mm – 750 nm
Visible 405 THz – 790 THz 750 nm – 390 nm
Ultraviolet 790 THz – 30 PHz 400 nm – 10 nm
X-Ray 30 PHz – 30 EHz 10 nm – 0.01 nm
Gamma ray more than 30 EHz Less than 0.01 nm
f
c
Speed of light
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