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:

4

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

5

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)

6

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

7

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)

8

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

9

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

10

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.

11

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)

12

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

13