EST Formulas

Transmission Lines

Transmission Line Input Impedance

Length Termination LC Equivalent

4l

Shorted Parallel Resonant

4l

Open Series Resonant

4l

Shorted L (Purely Inductive)

4l

Open C (Purely Capacitive)

4l

Shorted C (Purely Capacitive)

4l

Open L (Purely Inductive)

Parallel Wire

Characteristic Impedance (If no relative permittivity nor material specified, assume εr=1)

276 2logO

r

DZ

d

Conductance

2ln

GD

d

S/m, where conductivity, 1

Balanced 2-wire with Unequal Diameters

Characteristic Impedance

160coshO

r

Z N

where 2

1 2

1 2 2 1

1 4

2

d dDN

d d d d

d1 and d2 are conductor diameters (mm)

D is the conductor spacing (mm)

Coaxial Line

Characteristic Impedance (If no relative permittivity nor material specified, assume εr=1)

138logO

r

DZ

d

Conductance

2

ln

GD

d

S/m, where conductivity, 1

Microstrip Line Characteristic Impedance

87 5.98ln

0.81.41O

r

hZ

b c

h=PC board thickness

b=Track width

c=Track thickness

Attenuation Constant

,2 O

Neper

length

R

Z

Phase Coefficient

2,

p

radlength

LCV

Propagation Velocity

1p fV cV f

LC

where Vf is the velocity factor

c is the wave velocity (in fiber optics, 300x10^8m/s)

Reflected Power 2

ref incidentP P

Reflection Coefficient

1

1

ref L O

inc L O

P Z Z SWR

P Z Z SWR

Return Loss, (dB)

Re _ 20log L O

L O

Z Zturn Loss

Z Z

Standing Wave Ratio

1

1SWR

(for reactive load)

O L

L O

Z R

R Z (for resistive load; pick the larger value)

Voltage Standing Wave Ratio

max

min

inc ref

inc ref

V VVVSWR

V V V

Current Standing Wave Ratio

max

min

inc ref

inc ref

I IIISWR

I I I

SWR as a dB Value

20log( )dBSWR SWR

Power Output of the System

( ) ( ) ( ) ( )output dbm input dbm total dB total dBP P Gain Loss

Attenuator Loss, 10 log indB

out

PL

P

Characteristic Impedance of the required Quarterwave Matching Transformer

'O O LZ Z Z ohms

276 2

' log'

O

r

DZ

d for parallel wire line

138' log

'O

r

DZ

d for coaxial line

where D is the conductor spacing (mm)

d’ is the diameter of the transformer

Input Impedance of a Transmission Line

tanh

tanh

L Oin O

O L

Z Z lZ Z

Z Z l

where l is the length of the transmission line

ZY j , is the complex propagation constant 2

Oin

L

ZZ

Z for

4l

(lossless since equal to quarter wavelength)

Acoustics

Sound Pressure Level (SPL)

20log 10logO O

P ISPL

P I

P is the RMS sound pressure (N/m2)

PO is the reference sound pressure

= 2 x 10-5

N/m2

or Pascal

= 0.0002 microbar

= 2.089 lb/ft2

Sound Intensity Level (IL)

10log 20logL

O O

I PI SPL

I P

IO = reference sound intensity (W/m2)

= 10-12

W/m2

Sound Power Level (PWL)

10logO

WPWL

W

WO = reference sound intensity (W)

= 10-12

W

Sound Intensity

From a point source above ground level, 24

WI

r

From a source at ground level, 22

WI

r

Relation of Sound Pressure Level (SPL) and Sound Power Level (PWL)

For sound produced above ground level by an isotropic source

SPL = PWL – 20logr – 10.9

For sound produced at ground level

SPL = PWL – 20logr – 8

What frequency is 10 octaves above 30HZ? 1 10 1

110 _ 2 2(30)(2 )nth octave f r

Telephony

The number of cells required for a given area, A

Na

where A is the total area to be covered

a is the area of one cell

For hexagonal cells, 2

_ _3.464 circle inscribing hexa r

For a coverage area of radius r, 2A r

Time between Fades (t)

A cellphone used by a woman inside a traveling car operates at 825MHz. If the car is traveling at 90kph, find

the time between fades.

/2

light

Hz m s

ct

f v

Antenna Separation (S)

In cellular system, what antenna separation is required if the antenna height at the base station is 15m?

11

metersmeters

hS

Via-Net Loss (VNL)

A loss introduced to avoid singing and echo

_

_ _

_

0.20.2 0.4 0.4

circuit length

one way delay time

facility propagation

dB

lVNL t

v

Channel Capacity

By Shannon-Hartley Theorem

/sec3.32 log 1

bits

abs

SC BW

N

, for a standard telephone channel BW=3.1kHz

Average Traffic per Cell (A)

_

#_ _ min_ /

#_ _in Erlangs

subscribers ave phoneUse dayA

of cells

Co-channel Interference Reduction Factor (CIRF or q)

_ _ 2_ _

_

separation bet cochannel cells

cell radius

Dq

R

Frequency Reuse Factor or Frequency Reuse Patterns (K) 2

3

qK

Let us say q=4.6, then K=7. This means that the total voice channels, say 395 channels, should be divided by 7.

So, the number of voice channels per cell is 57.

Fiber Optics

Units of Light Wavelengths

101 10A m

61 10micron m

Optical fiber communication 14 1510 10 Hz

Infrared (long distance communications) 6770 10nm nm

Visible Light (short distance communications) 390 770nm nm

Ultraviolet 10 390nm nm

Maximum Bit rate

_ ( sec.)

max( )

1

5rise time nano

MbpsBt

Resultant Dispersion

22 2

imd md wgdt t t t

Δtimd is the intermodal dispersion

Δtmd is the material dispersion

Δtwgd is the waveguide dispersion

Note: for single-mode the Δtimd = 0

Rise Time

The time required for the leading edge a pulse to rise from 10 percent to 90 percent of its final value. It is

proportionate to the time constant and is a measure of the steepness of the wavefront.

If Δt is in nanoseconds/km then in the received pulse,

_ ( sec) ( sec) ( sec/ ) max_ _ ( )( )rise time nano w nano nano km of fiber kmt t t L

where tw is the pulse width

Δt is the pulse spreading constant (nanoseconds/km)

( sec/ ) max_ _ ( )( )nano km of fiber kmt L is the total pulse spread, ΔT

If Δt is in nanoseconds then in the received pulse,

r wt t t

where Δt is the resultant dispersion (nanoseconds)

Mode of Propagation

Refers to the number of pathways

Single Mode

V-number (the normalized frequency fN of cutoff)

V k a NA

where 2

kc

_

2

core diameterda

Multimode – refer to handout for the various V-numbers for the

different optical fiber configurations

Number of Modes a Fiber can Support 2

210.5

2

coreN

d NAM f

Maximum Allowable Diameter of the Core

max( )

0.383corer

NA

where dmax = 2rmax

Critical Radius of Curvature (as in constant-radius bends in handling)

3

3

4

cladding

critical

nr

NA

System Rise Time, SYS 2 2 2

( sec ) 1.1nano ondsSYS S D C

S is the source rise time (nanoseconds)

D is the detector rise time (nanoseconds)

C is the cable rise time (nanoseconds)

Fastest Rise time to faithfully pass a specified BW

(sec)

0.35r

Hz

tBW

Composite Rise time of the Output of Amplifier/Oscillator/etc 2 2

( ) ( ) ( )1.1r output r input r amplifiert t t

Note if the tr of the amplifier is not given, use the Fastest Rise time as its value

Snell’s Law, the law of refraction

sin sincore inc clad reflectedn n

Index Profiles

Representation of the refractive index of the core, core claddingn n

Step Index

sin inNA , where 2 2

(max)sin in core claddingn n

with (max)in as the acceptance angle or the acceptance cone half-angle

which is the maximum angle in which light rays may strike the air fiber

interface and still propagate down the fiber with a response that is no

greater than 10dB down from the peak value.

Graded Index

sin cNA , where sincladding

c

core

n

n

with c as the critical angle which is the minimum angle of incidence at

which a light ray may strike the interface of two media and result in an

angle of refraction of 90° or greater.

Photon Energy,

( ) 'p Joules planck s

hcE h f

Total Loss

( ) /T dB dB km kmL D

where α is the attenuation constant

Dispersion Factor

/

1

5s km

Mbps km

dR D

where R is the maximum data rate

D is the length of the fiber optic cable

Data and Digital Communications

Hamming Bits

For FEC, it is the # of bits in the Hamming code that must be added to the character before transmission

2 1n m n

where n is the # of Hamming bits

m is the number of data bits

Note: do this by trial and error, substituting different values of n until the relationship holds. The least n value

that satisfies the relationship is the number of hamming bits.

Information Theory

The mathematical theory of data comm. and storage founded by Claude

E. Shannon

Nyquist Frequency

log2sampling anaf f

Hartley Law

The information capacity of a noiseless or ideal channel

22 logbps HzC BW n

where n is the number of coding levels (n=2 for binary, n=8 for octal,

n=10 for decimal, etc.)

Shannon-Hartley Theorem

The information capacity of a noisy or practical channel

3.32 log 1bps

abs

SC BW

N

PCM Code Number of Bits (a.k.a. Folded Binary Code)

PCM code is a sign-magnitude code where the MSB is the sign bit and the remaining bits are magnitude bits.

2 1n

absDR

where n is the number of PCM bits excluding sign bit

DR is the absolute value of the Dynamic Range

Dynamic Range

max max

min

abs

V VDR

V resolution

20logdB absDR DR

Total # of Bits Sent before a Collision is Detected by Transmitting Stations

1

bps cable

p

K f lengthV

PROBLEM

Calculate the transmitted data stream for the following data and CRC generating polynomials:

7 5 4 2 1 0G x x x x x x x , the data message

5 4 1 0P x x x x x , the generator polynomial function

Steps to find the transmitted data stream:

1. Multiply G(x) by the # of bits in the CRC code. The number of bits in the CRC code corresponds to the

highest exponent of P(x).

Product: 5 7 5 4 2 1 0x x x x x x x

2. Divide G(x) by P(x)

Quotient:

Remainder:

3. Discard the quotient

4. Truncate the remainder to 16 bits

5. Add to the message as the block check sequence (BCS)

6. Result is the transmitted data

Waveguide

Rectangular Waveguide

Cut-off wavelength 2 2

2o

m n

a b

where m is the # of half-wave patterns in the “a” dimension

n is the # of half-wave patterns in the “b” dimension

a is the width

b is the length

Cut-off frequency, c

o

cf

Note: The dominant mode in rectangular waveguides is the 10TE where a=2b. It is also the default.

Circular Waveguide

Cut-off wavelength

2o

r

kr

where r is the internal radius of the waveguide

(kr) is the solution of the Bessel Function

Cut-off frequency, c

o

cf

Note: The dominant mode in circular waveguides is the 11TE where (kr) = 1.84. It is also the default but not

mostly used.

Typical Operating Frequency

0.7operating

cff

RADAR

Pulse Repetition Time, _

_ unitless

Pulse WidthPRT

Duty Cycle

Average Power, Ave peakP P DR

where DR is the Duty Ratio or Duty Cycle

Pulse Repetition Rate, 1

PRRPRT

RADAR Range

_

42

min(4 ) 2

round tripT P O

R

c tP A SARange

P

PT is the transmitted power2

4 OP

AA

, is the antenna gain

S is the cross-sectional area of the target

AO is the captured area of an antenna

PRmin is the detected signal level in W

Multiplexing

AM: Philippine Standard - *131 channels in the country

531 _ 1 9carrierf kHz Channel X kHz

Example:

Channel 6 has a carrier frequency of 576 KHz

FM: Philippine Standard

88.1 _ 20 1 0.2carrierf MHz Channel X MHz

Example:

Channel 206 has a carrier frequency of 89.1 MHz

CCITT’s Recommendation for Loading Multichannel FDM Systems

15 10logavP N when N>240

1 4logavP N when 12≤N≤240 where N is the number of voice band channels

For FDM systems with 75% speech loading and 25% data/telegraph loading and N>240

11 10logrmsP N

PROBLEM

Let us consider a frequency range of 405.0125 MHz to 405.0875 MHz and a 25 KHz channeling plan.

Determine the center frequency of the second channel from the lower limit.

p. 366

2

25405.0125 25 405.05

2 2c L

BW kHzf f BW MHz kHz MHz

The Carrier Frequency given the Channel in FDM, 112 4carrierf Channel kHz

The Carrier Frequency given the Group Number in FDM, _ 312 48 #carrier groupf Group

Satellite Communications

Bit Energy in Joules per Bit

tb

b

PE

f where Pt is the total carrier power or the total transmit power (Watts)

fb is the bit rate in (bps)

Bit Energy in dBW

10log

1

b

b dBW

EE

Watt

Effective Radiated Power, ERP

_dBW dBT dBW

ERP P Fixed Loss Gain

where 10log

1

T

T dBW

PP

Watt

is the total carrier power or the total transmit power (dBW)

Satellite Range

The required distance from an earth station so that uplink/downlink path losses can be computed

2 2 2cos sinkmd R h R R

where β is the angle of elevation or the azimuth angle

R = 6 371 km (3 960 mi), the Earth’s radius

h is the satellite height

FOR GEO satellites, h = 35 855 km (22 300 mi)

Free Space Path Loss (Either Downlink or Uplink)

92.4 20log 20logdB km GHzL d f

Received Signal Strength or Received Power (dBm)

R dBm T dBm T dBi P dB R dBiP P G L G

where 310log

1 10

T

T dBm

PP

x Watts

is the total carrier power or the total transmit power (dBm)

T dBi

G and R dBi

G are antenna gains

Effective Isotropic Radiated Power

/ ( ) ( )Watts T R Watts T unitlessEIRP P G

/ ( ) ( )dBW T R dBW T dBEIRP P G

where PT/R is the power radiated from(in tx) or to(in rx) an antenna

GT is the antenna power gain

Problem

A satellite earth receiving installation with a figure of merit of 20dB is used as a ground terminal to receive a

signal from a satellite at a distance of 38, 000 km. The satellite has a tx power of 50W and an antenna gain of 40

dB. Assuming negligible losses between satellite Tx and its antenna, calculate the C/N at the Rx for a BW of 1

MHz using 12 GHz frequency. (Boltzmann’s constant is equal to -228.6 dBW)

_ 228.6of Merit PdBW

CdB EIRP Figure L

N

50

10log 40 20 92.4 20log38000 20log12 228.6 1001

C WdB dB

N W

Note:

The Earth’s escape velocity is roughly 25, 000 mph. All satellites have orbital velocities less than this.

Satellite Height (measured from Earth’s surface) 2 2

3_ 24

EarthEarth surface Earth

gT Rh R

where T is the satellite

period

Satellite Velocity in Orbit

11

_

4 10,sat

Earth Earth surface

x mvsR h

Satellite Period in seconds

__ ' _2 Earth Earth surfacefrom Earth s center

sat sat

R hdT

v v

Uplink Frequency

_ _ _ &2.225uplink downlink the difference between UP DOWNf f GHz

Microwave

Correction Factor for Earth’s Radius 1

0.0055771 0.04665 sNeR

k eR

where Ns is the surface refractivity

Fade Margin a.k.a. “Fudge Factor”

It is a multi-path loss and represents the system’s terrain sensitivity. It considers the non-ideal and the less

predictable characteristics of radio wave propagation.

By Barnett-Vignant Reliability Equation,

( _ tan ) _ Re30log 60log 6 10log 1 70km path dis ce GHz System liabilityFM d a b f R

where the roughness factor a = 1 (average terrain) – typical value

= 4 (smooth terrain) – over water

= 0.25 (very rough terrain) – mountainous region

the climate characteristics b = 0.25 (average climate) – typical value

= 0.5 (hot and humid) – coastal areas

= 0.125 (very dry and non-reflective areas) – mountainous regions

Diversity Operation – increases system’s reliability by increasing availability,

increases SNR and reduces depth of fade in combined output

1. Frequency Diversity – uses 2 transmitters and 2 receivers with each pair

tuned to a different frequency with usually 2-3% separation.

2. Space Diversity – uses 2 or more antennas spaced many wavelengths

apart, usually 100 and 200 λ apart

_ ' _3_

_

effective Earth s radiusRAntenna Separation

path length

in meters

effectiveR kR where

R = 6 371 km (3 960 mi), the Earth’s radius

K is 4/3 for normal propagation (Correction factor)

3. Polarization Diversity – is used with space diversity, a single RF carrier

is propagated with 2 electromagnetic polarizations – vertical and

horizontal.

Fresnel Zone

Is one of the conical zones between the tx and rx due to cancellation of some portions of the wavefront by other

portions that travel different distances.

Fresnel Zone

1 2

( )

17.3km km

n km

GHz Total km

nd dR

f d , for 1

st Fresnel Zone n=1

Fresnel Zone Optimum Clearance from Obstacle

1( )0.6clearance kmHeight R

Beamwidth of the Passive Repeater

58.7 wavelength

ftL

where wavelength

c

f

Lft is the effective linear dimension in feet

Television and Facsimile

NTSC Standards for Interlaced Raster

1 Field = 262.5 lines = 242.5 active = 1/60 seconds

2 Fields = 1 Frame

1 Frame = 525 lines = 485 active = 1/30 second

4 Fields = 1 NTSC Superframe = 1/15 second

NTSC Standards for Synchronization

Details of Horizontal Blanking

Period Time, μsec

Total Line (H) 63.5

H Blanking 0.15H-0.18H or 9.5-11.5

H sync pulse 0.08H or 4.75 + 0.5

Front Porch 0.02H or 1.27 (minimum)

Back Porch 0.06H or 3.81 (minimum)

Visible Line Time 52 - 54

Details of Vertical Blanking

Period Time

Total Field 1/60 seconds

V Blanking 0.0008-0.0013 seconds

Each V sync pulse 27.35 μsec

Total of six V sync pulse 3H = 190.5 μsec

Each equalizing pulse 0.04H = 2.54 μsec

Each serration 0.07H = 4.4 μsec

Visible field time 0.015-0.016 seconds

Y = 0.30R + 0.59G + 0.11B

I = 0.60R – 0.28G -0.32B

Q = 0.21R – 0.52G + 0.31B, where R,G and B are video voltages that provide picture information

Aspect Ratio

TV – 4:3

HDTV – 16:9

Common Formula:

The Video Frequency Response corresponding to a given Horizontal Resolution

1 1

2

Horizontalresponse

H S

Nf

T T

where Nhorizontal is the number of horizontal resolution lines

TH = 63.5 μsec (NTSC standard) is the horizontal line synchronization time

TS = 10 μsec (NTSC standard) is the line suppression period

Another Formula:

The Video Frequency Response corresponding to a given Horizontal Resolution

Frequency Modulation

Image Frequency Rejection Ratio, IFRR

2 21IFRR Q

where si s

s si

f f

f f , fsi is the image frequency

fs is signal frequency

fi is the intermediate frequency

Q is the Quality factor

Image Frequency, fsi

It is any frequency other than the selected radio frequency carrier that, if allowed to enter a receiver and mix

with the local oscillator will produce a cross-product frequency that is equal to the intermediate frequency.

2fsi fs fi

Note: for 2 uncoupled tuned circuit, 2

TIFRR IFRR

2

20logTIFRR IFRR

Signal-to-Noise Power Ratio

120log

i n

S

N

Phase Deviation

noisen

signal

V

V

PM FM

Maximum phase deviation, Δф or

Modulation Index, m 1 modk V 2 mod

mod

k V

f

Maximum frequency deviation, δ 1 mod modk V f 2 modk V

PM modulation index (also called Phase Deviation)

1 modm k V where k1 is the deviation sensitivity of PM (rad/volt)

Vmod is the peak modulating voltage

FM modulation index (also called Phase Deviation)

2 mod

mod mod

k Vm

f f

where δ is the maximum frequency deviation

k2 is the deviation sensitivity of FM (rad/sec)

fmod is the modulating signal frequency

max_ var min_ var_ 2 iation iationcarrier swing f f

RMS Voltage, mod

2rms

VV

Bandwidth by Carson’s Rule, 2 mBW f

Operating Frequency at a given Temperature

T O O Of f kf T T

where fo is the operating frequency at reference temperature To

k temperature coefficient per degree centigrade

Percent Modulation for FM and PM

max

% 100%actM x

Deviation Ratio for FM and PM

max

(max)

100%m

DR xf

Note: Typical FM values are δmax = 75kHz, fmodulating=15kHz, and the allowable DR of commercial FM

broadcast = 5.

Input Frequency,2

capture

input free running

ff f

Capture Range, _ _2CR free running input First Lockedf f f

Lock Range, _ _2LR input Last Locked free runningf f f

NOTES:

There is NO negative frequency. Take the difference that yields a POSITIVE answer.

Lock range - The range of frequencies over which a phase-locked loop will remain locked on. The related

tracking, or hold-in, range refers to how much the loop frequency can deviate from the center frequency, and is

one-half the lock range.

Capture range - The range of frequencies over which a phase-locked loop can detect a signal on the input and

respond to it. This is sometimes called the lock-in range.

Amplitude Modulation

AM modulation index

max_ mod _ max min

max_ _ max min

ulating signal

carrier signal

V V Vm

V V V

where Vmax is the maximum peak-to-peak voltage swing of AM wave

Vmin is the minimum peak-to-peak voltage swing of AM wave

Total Modulation Index 2 2 2 2

1 2 3T nm m m m m

Percent Modulation

%mod 100%ulation mx

Center Frequency, fO

O O LOf f f

where _ lim2

LO lower it

BWf f

fLO is the local oscillator frequency

fCO is the carrier oscillator frequency

fLL lower limit frequency

Bandwidth of AM wave

mod2AM ulatingBW f

Note: In the case of multiple data, choose the highest modulating frequency.

Efficiency

_ / _ modoutput w o ulation

source

P

P

where _ / _modsource dissipation output w o ulationP P P

Total Transmitted Power 2 2

_ _ 1 12 2

T carrier total sideband power carrier carrier carrier

m mP P P P P P

where 2 22

_ _ _ _2

SB ctotal sideband power upper sideband lower sideband

V VmP P P

R R

2

2

cccarrier

load

VP

R

2

_ _4

cupper sideband lower sideband

m PP P

Noise

Noise Power

,BoltzmannN k T BW Watts

RMS Noise Voltage

4Tn TV kT BW R where 1 2T nR R R R for series

1 2

1 1 1 1

T nR R R R for parallel

Total RMS Noise Voltage for Resistors in SERIES 2 2 2

( ) (1) (2) (3)n Total n n nV V V V where Vn(1) is the RMS Noise Voltage of the 1st resistor and so on

Noise Factor, input

output

S

NNF

S

N

Noise Factor by Friis’ Formula

321

1 1 2

11 NFNFNF NF

G G G

Noise Factor

1eq

antenna

RNF

R

Equivalent Noise Resistance, Req

32

1 2 2 2

1 1 2

eq

RRR R

A A A

321

1 1 2

eq

RRR R

G G G

Overall Noise Figure, 10logdBF NF

Equivalent Noise Temperature

1equivalent OT T NF where To = 290K

Noise Density, power

O

NN

BW

Noise Density in dBW, ( ) 10log1

OO dBW

NN

Watt

RMS Shot Noise Current for a Diode in Amperes

2n e dcI q I BW where qe is the charge of an electron (CONST 23)

Idc is the direct diode current

Noise Bandwidth,1

4noiseBW

RC

Noise Measurements

Antenna

Effective Isotropic Radiated Power, 2.14dB dBEIRP ERP dB

Antenna Efficiency

100% 100%radiated radiation

T radiation d

P Rx x

P R R

where PT is the total power supplied to the antenna

Rd is the antenna ohmic resistance

Total radiation dR R R is the total antenna resistance

Parabolic Antenna

Power Gain 2

2 metersDG k

k=0.54

7.5 20log 20logdB ft GHzG D f

Power Gain in Terms of Beamwidth 2

20310logdBG

where Dft = dish diameter in feet

fGHz = operating frequency

Beamwidth in degrees

70

metersD

, between half power points

2O , between nulls

where Dm = mouth diameter in meters

Helical Antenna

Power Gain 2

15D NS

G

Beamwidth

52

D NS

where D = helix diameter

S = pitch between turns

λ = wavelength

N = number of turns

Electric Field Strength in Volts/meter

30,T TP G V

mR where PT is the radiated power (Watts)

GT is the antenna power gain (GT=1 for isotropic antenna)

R is the distance from the antenna (meters)

Reflection Coupling Factor

2

'4

meters

m

l DA

where D’ is the diameter of the parabolic antenna

A is the antenna effective area in square meters

Radio Wave Propagation

Refractive Index of the Ionosphere

2

sin 811

sin

i

r Hz

Nn

f

where N is the number of electrons per m3

F is the frequency of the radio wave in Hz

Critical Frequency

The highest frequency that will be returned down to Earth by that layer after having been beamed vertically

straight upward

maxcos 9c if MUF N

where Nmax is the maximum number of free electrons per m3

Maximum Useable Frequency

The highest frequency wherein the signal is able to return back to Earth when beamed at a certain angle other

than vertical incidence

cos

c

i

fMUF

Optimum Working Frequency (Frequency of Optimum Transmission or Optimum Useable Frequency)

The best frequency used to operate a sky-wave link and provides the most stable link

Pyramidal Horn

Power Gain 2

7.5dB

DG

where D

Horizontal Beamwidth,

_

80

pyramidal hornwidth

0.85OWF MUF

Power Density in Watts/m2

24

T TP GERP

A r where PT is the radiated power (Watts)

GT is the antenna power gain (GT=1 for isotropic antenna)

Radio Horizon Distance (Maximum Radio Range)

( ) ( ) ( )17 17km t m r md h h

Note that the radio horizon distance is longer than the geometric (visual) horizon by 15% due to refraction

phenomenon.