2.0 Engineering Formulas

2.1 Tuned Circuits
2.2 Active Circuits
2.3 Transmission Lines
2.4 Noise
2.5 Modulation
2.6 Electromagnetic Radiation
2.7 Satellites
2.8 Video
2.9 Fiber Optics
2.10 Information Theory
2.11 Codecs
2.12 Nyquist Channels
2.13 Digital Filters
2.14 Electro-Mechanics

 

 

Recommended Unit Prefixes

Exponent

Prefix

Symbol

1012

Tetra
T

109

Giga

G

106

Mega

M

103

Kilo

k

10-3

milli

m

10-6

micro

m

10-9

nano

n

10-12

pico

P

10-15

femto

F

10-18

atto

a

 

2.1 Tuned Circuits

 

Reactance

 

Series RLC

 

 

 

 

 

 

Parallel RLC

 

Transformers

 

2.2 Active Circuits

 

2.2.1 Differential Pairs

 

Schematic

 

Tail Current

 

Collector  Current

 

AC Output Voltage

 

Differential Gain

                               

 

Common Mode Gain

 

Input Impedance

 

Offset Voltage

 

Input Offset Currents

 

Common Mode Rejection Ratio

 

2.2.2 Basic Op Amps

 

 

General Circuit

 

 

 

 

 

 

Differential Amplifier

 

 

 

 

 

Noninverting Amplifier

 

 

 

Inverting Amplifier

 

 

 

Power Bandwidth

 

Corner Frequency

 

Feedback Fraction

 

Slew Rate

 

 

Initial Slope of a Sine Wave

 

 

 

Feedback

                             

Non-Inverting Voltage Feedback

Inverting Voltage Feedback

 

Non-Inverting Current Feedback

Inverting Current Feedback

 

OpAmp Feedback Formulas

Quantity

Noninverting Voltage Feedback

Inverting Voltage Feedback

Noninverting Current Feedback

Inverting Current Feedback

Voltage Gain

 

 

 

Transresistance

 

 

 

Transconductance

 

 

 

Current Gain

 

 

 

Input Impedance

Output Impedance

Distortion

Output Offset

Upper Critical Frequency

 

2.3 Transmission Line Formulas

 

Transmission Line Equation

 

A Solution to the Transmission Line Equation

 

Propagation Coefficient

 

Attenuation Coefficient

 

 

Phase Shift Coefficient

 

 

Characteristic Impedance

 

 

Approximations

 

Impedance Along a Transmission Line

 

Impedance Along a Lossless Transmission Line

 

Phase Velocity

 

Lossless Transmission Line

 

Distortionless Transmission Line

 

Skin Depth

 

Permittivity

 

Permeability

 

for most transmission line dielectrics:

 

Intrinsic Impedance

 

For tables of permeability, permittivity, and conductivity, please see the section on Constants.

2.3.1 Practical Cables

Twin Lead Cable

 

 

 

 

 

 

 

 

 

Design Equations

 

Coaxial Cable

 

Design Equations

 

2.4 Noise

 

Definitions

 

Johnson Noise

 

RMS Noise Voltage

 

Equivalent noise temperature

 

Tuned circuit noise bandwidth

 

 

Noise Ratio

 

Noise Figure (dB)

 

Friiss’ Formula

 

Shot Noise

 

2.5 Modulation

 

Definitions

 

2.5.1 AM

 

Defining Equation

 

Bandwidth

 

Modulation Index

 

Total Power

 

2.5.2 FM

Defining Equation

 

Modulation Index

 

Bandwidth [Carson’s Rule]

 

Bessel’s functions of the 1st kind and order p

 

Side Frequency Magnitude

 

FM Power Distribution

 

Noise

 

2.6 Electromagnetic Radiation

 

Designation

Frequency

Wavelength

EHF

30 - 300 GHz

1 cm - 1 mm

SHF

3 - 30 GHZ

10 cm - 1 cm

UHF

300 - 3000 MHz

1 m - 10 cm

VHF

30 - 300 MHZ

10 m - 1 m

HF

3 - 30 MHZ

100 m - 10 m

MF

300 - 3000 KHz

1 km - 100 m

LF

30 - 300 KHz

10 km - 1 km

VLF

3 - 30 KHz

100 km - 10 km

ULF

300 - 3000 Hz

1000 km - 100 km

SLF

30 - 300 Hz

10 Mm - 1 Mm

ELF

3 - 30 Hz

100 Mm - 10 Mm

 

Definitions

 

2.6.1 Antennas

Definitions

 

Electric field radiated from an antenna

 

Isotropic Radiator Wave Front Density

 

Non-Isotropic Radiator Wave Front Density

 

Effective Area

 

 

Received Power

 

Elementary Dipole

 

2.6.2 Arrays

Definitions

 

 

Elements Driven In-Phase

 

 

 

Phase Shift Between Elements

 

 

Array Factor [General Form]

 

 

 

Broadside Array

 

 

 

 

Broadside Array

 

Radiation Pattern

 

 

 

 

 

 

End Fire Array

 

 

 

End Fire Array

 

Radiation Patterns

 

 

 

Definitions

 

 

Helical Antenna

 

Flared Horn (single plane)

 

2.6.3 Tropospheric Propagation

Electric field intensity for vertically polarized surface waves:

 

Field Strength at Unit Distance

 

 

 

 

 

Geometry for the Flat Earth Approximation

 

The received signal, is modified by the presence of the ground reflected wave, and the increase (and decrease) in signal voltage is given by:

 

Received Field Strength

 

Radio Horizon Distance

 

2.6.4 Ionospheric Propagation

Definitions

 

Critical Frequency

 

Maximum Usable Frequency

 

2.9.5 Waveguides

Definitions

 

TE10 Mode

 

Wavelength Relationship

 

Cutoff Wavelength

 

Phase Velocity

 

Group Velocity

 

 

TE Wave Impedance

 

 TM Wave Impedance

 

Maximum Power [Rectangular guide, air dielectric, TE mode]

 

Lossy Dielectric Characteristic Impedance

 

Loss-Less Dielectric Characteristic Impedance [most]

 

2.7 Satellites

 

Band

Uplink [GHz]

Downlink [GHz]

Comments

L

.821 - .825

.866 - .870

MSAT

C

5.9 – 6.4

3.7 – 4.2

Fixed ground stations

X

7.9 – 8.6

7.25 – 7.75

Military mobile radio

Ku

14 – 14.5

11.7 – 12.2

Broadcast and fixed point

Ka

27 – 30

30 – 31

17 – 20

20 – 21

 

V/Q

50 – 51

40 – 41

41 – 43

Broadcast and fixed point

V

54 – 58

59 – 64

54 – 58

59 – 64

Inter-satellite

 

 

Definitions

 

Acceleration due to Gravity

 

Centrifugal Acceleration

 

Satellite Velocity [circular Orbit]

 

 

Uplink C/N

 

 

Downlink C/N

 

2.8 Video

 

World Television Formats [1]

 

System Code

Parameter

M (N)

B

C

G (H)

I

D K (K’)

L

Lines per picture

525 (625)

625

625

625

625

625

625

Field Frequency [Hz]

60 (50)

50

50

50

50

50

50

Line Frequency [HZ]

15734 (15625)

15625

15625

15625

15625

15625

15625

Video Bandwidth [MHz]

4.2

5

5

5

5.5

6

6

Channel Bandwidth [MHz]

6

7

7

8

8

8

8

Audio above Video [MHz]

4.5

5.5

5.5

5.5

6

6.5

6.5

Vestigial Sideband Width [MHz]

.75

.75

.75

.75 (1.25)

1.25

.75 (1.25)

1.25

Video Modulation Polarity

-

-

+

-

-

-

+

Audio Modulation

fm±25 KHz

fm±50 KHz

am

fm±50 KHz

fm±50 KHz

fm±50 KHz

am

FM Preemphasis [mSec]

75

50

 

50

50

50

 

 

Bandwidth Comparisons

 

Selected Country List

Country

Color

Code

Australia

PAL

B

Brazil

PAL

M

Canada

NTSC

M

China

PAL

D

France

SECAM

L

Germany [West]

PAL

B G

Germany [East]

SECAM

B G

Hong Kong

PAL

I

Japan

NTSC

M

Switzerland

PAL

B G

United Kingdom

PAL

I

USA

NTSC

M

USSR [former]

SECAM

D K

 

Luminance

 

NTSC Chroma

 

PAL Chroma

 

Chromance Signal Vector Diagram

 

CIE 1931 Chromaticity Diagram [2]

 

2.9 Fiber Optics

 

Definitions

 

Wavelength

 

Velocity

 

Index of Refraction

 

Snell’s Law

 

Critical Angle

 

Acceptance Angle

 

Numerical Aperture

 

Normalized Frequency

 

Number of Modes

 

Dispersion

 

Modal Dispersion [Multimode Fiber]

 

Modal Dispersion [GRIN Fiber]

 

Chromatic Dispersion

 

Wavegioude Dispersion

 

Total Dispersion

 

Maximum Bit Rate

 

2.10 Information Theory

 

Definitions

 

Information and Entropy

 

Shannon-Hartley Theorem

 

2.10.1 Packet Theory

Stop and Wait ARQ

 

Go Back N ARQ

                        for N > 2a+1

   for N < 2a+1

 

Selective Repeat ARQ

                              for N > 2a+1

                       for N < 2a+1

 

Pure ALOHA

 

 

 

 

Slotted ALOHA

 

 

 

ALOHA Thoughput

 

 

2.11 Codecs

 

 

Definitions

 

 

Aliasing Noise

 

 

 

 

 

 

 

Aliasing S/N

 

 

 

 

 

Quantizing Noise

 

 

 

A-Law

 

m-Law

 

Progression

 

Digitization

 

2.12 Nyquist Channels

 

Class

Channel Response

Channel

Name

Impulse

Notation f[d]

Radix

1

1

Ideal LPF

1

2

1

Cosine

1,1

3

2

Raised

Cosine

1,2,1

5

3

 

2,1,-1

5

4

Sine

1,0,-1

3

5

 

1,0,-2,0,1

5

 

2.12.1 Ideal LPF

 

Frequency Response

 

 

 

 

Impulse Response

 

 

2.12.2 Cosine Channel

 

Frequency Response

 

 

 

Impulse Response

 

 

2.12.3 Raised Cosine Channel

 

Frequency Response

 

 

 

Impulse Response

 

 

2.12.4 Sine Channel

 

Frequency Response

 

 

 

Impulse Response

 

 

2.13 Digital Filters

 

Transfer Function

 

 

 

 

 

Impulse Invariant Mapping

 

 

 

 

 

Bilinear Mapping

 

2.14 Electro-Mechanics

 

Definitions

 

Torque

 

Angular Acceleration

 

Shaft Geometry

 

Inertial [Disc or Solid Shaft]

 

Inertial [Hollow Shaft]

 

Mass

 

Gear Ratio

 

Motor Torque

 

Total Required Torque

 

Load Inertia

 

Reflected Load Inertia

 

Power

 



[1]               Video Techniques, Gordon White

[2]               Television Engineering Handbook, K. Blair Benson, ed., FIG. 2-10