EMC Formulas - Reverse engineering

EMC Formulas

Term Conversion in 50 Environment

Log

dBV to dBm

dBm dBV 107

dBA to dBm

dBm dBA 73

dBm to dBV

dBV dBm107

dBA to dBV

dBV dBA 34

dBm to dBA

dBA dBm 73

dBV to dBA

dBA dBV 34 Log Linear

Volts to dBm Amps to dBm

dBm 20 Log(Volts) 13 dBm 20 Log(Amps) 47

Watts to dBV

dBV 10 Log(watts) 137

Amps to dBV

dBV 20 Log(Amps) 154

Watts to dBA

dBA 10 Log(Watts) 103

Volts to dBA dBV to Watts

dBA 20 Log(Volts) 86

Log Linear

dBV 137

Watts 10 10

dBA to Watts

dBA103

Watts 10 10

dBm to Volts

dBm13

Volts 10 20

dBA to Volts

dBA86

Volts 10 20

dBm to Amps

dBm47

Amps 10 20

dBV to Amps

dBV 154

Amps 10 20

Linear

Volts to Watts

Amps to Watts Watts to Volts Amps to Volts

Watts Volts2 50

Watts Amps2 50 Volts Watts50 Volts Amps50

Watts to Amps

Amps Watts 50

Volts to Amps

Amps Volts 50

Unit Conversion

Log Linear

Watts to dBm Volts to dBV

dBm 10 LogWatts 30 dBV 20 logVolts120

Amps to dBA

dBA 20 logAmps120

to dB

dB 20 log

Used for the conversion of Voltage & Current

dBm to Watts dBV to Volts dBA to Amps dB to

Log Linear

dBm30

Watts 10 10

dBV 120

Volts 10 20

dBA120

Amps 10 20

dB

10 20

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Term Conversion / Ohms law

Log

dBV to dBm

dBm dBV 10 Log() 90

dBA to dBm

dBm dBA 10 Log() 90

dBm to dBV

dBV dBm10 Log() 90

dBA to dBV

dBV dBA 20 Log()

dBm to dBA

dBA dBm 10 Log() 90

dBV to dBA

dBA dBV 20 Log()

Linear

Find Watts Watts Amps2 , Watts Volts2

Find Volts Volts Amps , Volts Watts

Find Amps

Amps Watts , Amps Volts

dB Calculations

dB Watts

dB

10Log

Watts1 Watts2

dB Volts

dB

20Log

Volts1 Volts2

dB Amps

dB

20Log

Amps1 Amps2

New Watts w/dB

dB10Log(Wattsstart )

WattsNew 10

10

New Volts w/dB

Volts 10

dB

20

Log 20

(Voltsstart

)

New

New Amps w/dB

dB20Log( Ampsstart )

AmpsNew 10

20

dB Correction for distance change (antenna far field)

dB

20

Log

distance2 distance1

W V

W

V A

V

W

W

A

A

V

A

Volts Amps

W A2

V A Ohms Watts

W

V 2 V 2 A 2

W

Sine Wave

Voltage levels for a sine wave

Voltspeak

2

Voltsrms

2

VoltsAvg

Voltsrms

Voltspeak 2

2

2 VoltsAvg

Voltsavg

2

Voltspeak

2

2

VoltsAvg

Voltspeakpeak 2 Voltspeak

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w/ Impedance of air = 377 dBV/m to dBm/m2 dBm/ m2 dBV / m 115.8 dBm/m2 to dBV/m dBV / m dBm/ m2 115.8 dBA/m to dBV/m dBV / m dBA/ m 51.5 dBV/m to dBA/m dBA/ m dBV / m 51.5 dBA/m to dBpT dBpT dBA/ m 2 dBpT to dBA/m dBA/ m dBpT 2

Watts/m2 to V/m V/m to Watts/m2

Radiated Field

V / m Watts/ m2 377

V2

Watts/ m2 m 377

dBV/m to V/m

dBV / m120

V / m 10 20

V/m to dBV/m

dBV / m 20 Log(V m) 120

New V/m with dB

V / m 10

dB20Log 20

(V

mstart

)

new

Current Injection

Power needed for BCI probe (50) for given Insertion loss(IL(dB))

IL10LOGVolts2

50

Watts 10

10

Watts

10

IL10LOG Amps250 10

ILdBA73

Watts 10 10

Power needed for BCI probe or EM Clamp (150) for given Insertion loss(IL(dB))

IL10LOG

Volts2

150

Watts 10

10

Watts

10

IL10LOG Amps2150 10

Conducted current measurement using a current probe. Where reading is in dBV and probe factor is dB or

dBA dBV dB

dBA dBV 20 Log()

Interpolation values on a graph w/ Log of frequency This equation works for finding all points on a test curve where test limit is sloping (i.e. DO 160F BCI testing)

valuenew

Log Log

freqnew freqlower

frequpper freqlower

valueupper valuelower

Valuelower

Power needed for TEM Cell

Watts V m Height 0.52

(50) Power needed for GTEM Cell

Watts V m SpectrualHeight2 1.08

(50) Wave length ()

[meters] 300 MHz

1 4

[meters]

75 MHz

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Period

VSWR

Time(s) 1 Hz 1

Hz

Time(s)

VSWR given Fwd/Rev power

1 VSWR

1

Wattsrev Wattsfwd

Wattsrev Wattsfwd

VSWR given Return Loss (RL)

RL(dB)

VSWR

1

10

20 RL( dB)

1 10 20

VSWR Given Impedance (Z)

ZO>ZL

VSWR O L

ZL>ZO

VSWR L O

VSWR given reflection coefficient () VSWR 1 1

Reflection Coefficient () WattsRev WattsFwd load Amp load Amp VSWR1 VSWR 1

RL(dB)

10 20

Return Loss (RL) in dB

RL(dB) 20 LogVSWR1 VSWR 1

RL( dB)

10

Log

Wattsfwd Wattsrev

RL(dB) 20 Log

Transmission Loss (TL) in dB

TL(dB)

10

Log

Wattsfwd Wattsfwd Wattsrev

TL(dB) 10 Log 1 2

TL(dB)

10

Log1

10

RL(dB) 20

2

TL(dB)

10

Log1

VSWR VSWR

1 1

2

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Antenna Equations

Far Field Distance Dipole & Log-periodic antenna

FarField 2

Horn antenna FarField 2 apeture2

Far Field Equations

Gain over isotropic

GaindBi

GainNumeric 10 10

GaindBi 10 Log(Gainnumeric)

GainNumeric

Meters

V

2

m

30 Watts

GaindBi

10

Log

Meters

V

2

m

30 Watts

GaindBi 20 Log(MHz) AF 29.79

Antenna Factor (AF) AF 20 Log(MHz) GaindBi 29.79

AF 20 Log(MHz) 10 Log(Gainnumeric) 29.79

Find Antenna Spot size, Beam Width and Distance

Spot meters

2 Distancemeters

tan

Angle3dB 2

Distancemeters

2

Spot meters tan Angle3dB

2

Angle3dB

2

tan

1

2

Spotmeters Distance

Field Strength

V / m 30Watts Gainnumeric Meters

V /m

GaindBi

30Watts10 10 Meters

Watts V m meters2

30 Gainnumeric

Watts V m meters2 GaindBi 30 10 10

Power needed if gain remains constant (in Far Field) using same antenna and changing field level or test distance.

For Field Change

V

2

WattsNew WattsOld

m New

V

2

mOld

For Distance Change

WattsNew

WattsOld

MetersNew 2 MetersOld 2

Power for given Amplitude Modulation %

Wattspeak WattsCW 1 % 0.012

Wattsavg

WattsCW

2 % 0.012

2

Wattsavg

Wattspeak 2 % 0.012 2 1 % 0.012

Power for given Pulse Modulation Duty Cycle %

Wattspeak

Wattsavg % 0.01

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Useful conversions

1 in = 0.0254 m 1 ft = 0.3048 m 1 yd = 0.9144 m 1 in2 = 0.00064516 m2 1 ft2 = 0.092903 m2 1 yd2 = 0.83612736 m2 1 in3 = 0.000016387064 m3 1 ft3 = 0.028316846 m3 1 yd3 = 0.764554858 m3 1 lb = 0.45359237 kg 1 psi. = 6,894.7573 Pa (Pascal)

1 hp = 550 ftlb/sec = 745.6999 Watts

C = (F-32)/1.8

1,000,000,000,000,000,000,000,000 = 1024

yotta

Y

1,000,000,000,000,000,000,000 = 1021

zetta

Z

1,000,000,000,000,000,000 1018

exa

E

1,000,000,000,000,000 = 1015

peta

P

1,000,000,000,000 = 1012

tera

T

1,000,000,000 = 109

giga

G

1,000,000 = 106

mega

M

1,000 = 103

kilo

k

100 = 102

hecto

h

0.01 = 10-2

centi

c

0.001 = 10-3

milli

m

0.000001 = 10-6

micro

0.000000001 = 10-9

nano

n

0. 000000000001 = 10-12

pico

p

0. 000000000000001 = 10-15

femto

f

0. 000000000000000001 = 10-18

atto

a

0. 000000000000000000001 = 10-21

zepto

z

0. 000000000000000000000001 = 10-24

yocto

y

Resistor Color Codes

A B C D

DA C B

1st

2nd

(A) (B)

00

11

22

33

44

55

66

77

88

99

Gold

Silver

No color

Multiplier (C)

1

10

100 103 104 105 106 107 108 109

0.1

0.01

Tolerance (D) 1% 2% 3% 4%

5% 10% 20%

Color

Black Brown

Red Orange Yellow Green

Blue Violet Gray White

Capacitor Color Codes

E A B C D

Disc Cap

E A B C D

Ceramic Cap

White=EIA Code Black=Military Code Color=Old EIA

Classification

A B D C

Mica Cap

Mult iplier (C)

1 10 100 1000

0.01 0.1

Color Codes for Ceramic Caps

Tolerance

(D)

Temp Coef

Abo Below ppm/C

ve 10pf

(E)

10pf

20 2.0

0

1

-30

2

-80

3

-150

4

-220

5

0.5

-330

6

-470

7

-750

8 0.25

30

10 1.0

500

Color

Black Brown

Red Orange Yellow Green

Blue Violet Gray White

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