EMC Formulas

EMC Formulas

Term Conversion in 50? Environment

Log

Linear

dB?V to dBm

dBm ? dB?V ? 107

dB?A to dBm

dBm ? dB?A ? 73

Volts to Watts

Watts ?

dBm to dB?V

dB?V ? dBm ? 107

Amps to Watts

Watts ? Amps2 ? 50

dB?A to dB?V

dB?V ? dB?A ? 34

Watts to Volts

Volts ? Watts ? 50

dBm to dB?A

dB?A ? dBm ? 73

Amps to Volts

Volts ? Amps ? 50

dB?V to dB?A

dB?A ? dB?V ? 34

Watts to Amps

Amps ?

Volts to Amps

Amps ?

Log ? Linear

Volts to dBm

dBm ? 20 ? Log(Volts) ? 13

Amps to dBm

dBm ? 20 ? Log( Amps) ? 47

Watts to dB?V

dB?V ? 10 ? Log(watts) ? 137

Amps to dB?V

dB?V ? 20 ? Log( Amps) ? 154

Watts to dB?A

dB?A ? 10 ? Log(Watts) ? 103

Volts to dB?A

dB?A ? 20 ? Log(Volts) ? 86

Log ? Linear

? dB?V ?137 ?

?

?

10

?

?

dB?V to Watts

Watts ? 10

dB?A to Watts

Watts ? 10?

dBm to Volts

dB?A to Volts

dBm to Amps

dB?V to Amps

Volts2

50

Watts

50

Volts

50

Unit Conversion

Log ? Linear

Watts to dBm

dBm ? 10 ? Log?Watts? ? 30

Volts to dB?V

dB?V ? 20 ? log?Volts? ? 120

Amps to dB?A

dB?A ? 20 ? log? Amps? ? 120

dB? ? 20 ? log???

Used for the conversion of Voltage & Current

? to dB?

? dB?A?103 ?

?

?

10

?

Log ? Linear

? dBm?30 ?

?

?

10 ?

? dBm?13 ?

?

?

? 20 ?

dBm to Watts

Watts ? 10?

? dB?A?86 ?

?

?

20 ?

?

dB?V to Volts

Volts ? 10?

Volts ? 10

Volts ? 10

? dB?V ?120 ?

?

?

20

?

? dB?A?120 ?

?

?

20

?

?

? dBm?47 ?

?

?

? 20 ?

dB?A to Amps

Amps ? 10

? dB?V ?154 ?

?

?

20

?

?

dB? to ?

? ? 10?

Amps ? 10

Amps ? 10

? dB? ?

?

?

20 ?

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033109

Term Conversion / Ohms law

dBm to dB?A

dB?A ? dBm ? 10 ? Log(?) ? 90

dB?V to dB?A

dB?A ? dB?V ? 20 ? Log(?)

A

W

dB?V ? dB?A ? 20 ? Log(?)

Ohms Watts

?

W

W

V

dB?A to dB?V

V

A

Volts Amps

V?A

2

A

dB?V ? dBm ? 10 ? Log(?) ? 90

?

dBm to dB?V

W

dBm ? dB?A ? 10 ? Log(?) ? 90

dB?A to dBm

A??

V

A

dBm ? dB?V ? 10 ? Log(?) ? 90

dB?V to dBm

V

?

W ??

Log

Volts

?

Watts ,

?

Amps ?

Voltspeak ? 2 ? Voltsrms ?

Volts

?

dB Calculations

dB ? Watts

? Watts1 ?

??

dB ? 10Log??

? Watts2 ?

dB ? Volts

? Volts1 ?

??

dB ? 20Log??

? Volts2 ?

dB ? Amps

? Amps1 ?

??

dB ? 20Log??

? Amps2 ?

New Volts w/dB ?

New Amps w/dB ?

?

Voltage levels for a sine wave

Volts ? Amps ? ? , Volts ? Watts ? ?

New Watts w/dB ?

2

2

Watts ? Amps2 ? ? , Watts ?

Amps ?

V

Sine Wave

Voltsrms ?

Find Amps

2

??

2

Find Volts

A

Find Watts

W

Linear

V

W

Voltsavg ?

Voltspeak

2

2

?

?

?

2

?

2? 2

? Voltspeak ?

? VoltsAvg

? VoltsAvg

2? 2

?

? VoltsAvg

Voltspeak? peak ? 2 ? Voltspeak

? dB? ?10? Log (Wattsstart ) ?

?

?

10

?

?

WattsNew ? 10

? dB? ? 20? Log (Voltsstart ) ?

??

??

20

?

?

VoltsNew ? 10

? dB? ? 20? Log ( Ampsstart ) ?

?

?

20

?

?

AmpsNew ? 10

dB Correction for distance change (antenna far field)

? distance2 ?

??

dB ? 20 ? Log??

? distance1 ?

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033109

w/ Impedance of air = 377 ?

Current Injection

dB?V/m to dBm/m2

dBm / m 2 ? dB?V / m ? 115.8

Power needed for BCI probe (50?) for given

Insertion loss(IL(dB))

dBm/m2 to dB?V/m

dB?V / m ? dBm / m 2 ? 115.8

2

?

?

??

? IL?10? LOG? Volts 50 ? ?

?

??

?

?

?

10

?

?

?

?

dB?A/m to dB?V/m

dB?V / m ? dB?A / m ? 51.5

dB?V/m to dB?A/m

dB?A / m ? dB?V / m ? 51.5

dB?A/m to dBpT

dBpT ? dB?A / m ? 2

dBpT to dB?A/m

dB?A / m ? dBpT ? 2

Watts/m2 to V/m

V / m ? Watts / m ? 377

2

V/m to Watts/m2

Watts / m 2 ?

V

Watts ? 10

?

? IL?10?LOG Amps2 ?50

?

?

10

?

Watts ? 10

? ??

? IL? dB?A?73 ?

?

?

10

?

Watts ? 10?

Power needed for BCI probe or EM Clamp (150?)

for given Insertion loss(IL(dB))

2

?

?

??

? IL?10? LOG? Volts 150 ? ?

?

??

?

?

?

10

?

?

?

?

2

m

Watts ? 10

377

?

? IL?10? LOG Amps2 ?150

?

?

10

?

Radiated Field

Watts ? 10

? dB?V / m?120 ?

?

?

20

?

dB?V/m to V/m

V / m ? 10?

V/m to dB?V/m

dB?V / m ? 20 ? Log(V m) ? 120

?

?

? ??

?

?

Conducted current measurement using a current

probe. Where reading is in dB?V and probe factor

is dB? or ?

New V/m with dB?

dB?A ? dB?V ? dB?

? dB? ? 20? Log (V m start ) ?

?

?

?

?

20

?

?

dB?A ? dB?V ? 20 ? Log(?)

V / mnew ? 10

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)

Power needed for TEM Cell

?

Log??

?

valuenew ?

?

Log??

?

Power needed for GTEM Cell

freqnew ?

?

freqlower ??

? ?valueupper ? valuelower ? ? Valuelower

frequpper ?

?

freqlower ??

Watts ?

Watts ?

?V m ? Height ? 0.5?2

?(50?)

?V m ? SpectrualHeight?2 ?1.08

?(50?)

Wave length (?)

?[meters] ?

300

MHz

1

4

?[meters] ?

75

MHz

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033109

Reflection Coefficient (?)

Period

Time(s) ?

1

Hz

Hz ?

1

Time(s)

VSWR

??

??

VSWR given Fwd/Rev power

VSWR ?

Wattsrev

1?

Wattsfwd

Wattsrev

1?

Wattsfwd

??

WattsRe v

WattsFwd

?load ? ? Amp

?load ? ? Amp

VSWR ? 1

VSWR ? 1

? ? RL( dB) ?

?

?

20

?

?

? ? 10

Return Loss (RL) in dB

VSWR given Return Loss (RL)

VSWR ?

? ? RL( dB ) ?

?

?

20

?

?

1 ? 10

? ? RL( dB ) ?

?

?

20

?

1 ? 10?

VSWR Given Impedance (Z)

ZO>ZL

VSWR ?

?O

?L

ZL>ZO

VSWR ?

?L

?O

VSWR given reflection coefficient (?)

VSWR ?

1? ?

1? ?

? VSWR ? 1 ?

RL(dB) ? ?20 ? Log?

?

? VSWR ? 1 ?

? Wattsfwd ?

??

RL(dB) ? 10 ? Log??

? Wattsrev ?

RL(dB) ? ?20 ? Log???

Transmission Loss (TL) in dB

?

?

Wattsfwd

?

TL(dB) ? 10 ? Log?

? Watts ? Watts ?

fwd

rev ?

?

TL(dB) ? ?10 ? Log?1 ? ?2 ?

? ? ?? ? RL( dB) ?? ?2 ?

?

?

TL(dB) ? ?10 ? Log?1 ? ?10? 20 ? ? ?

?

?

? ?

? ??

?

? ? VSWR ? 1 ?2 ?

?

TL(dB) ? ?10 ? Log?1 ? ?

? ? VSWR ? 1 ?? ?

?

?

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033109

Field Strength

Antenna Equations

Far Field Distance

30 ?Watts ? Gainnumeric

V /m ?

Meters

Dipole & Log-periodic antenna

FarField ?

Horn antenna

FarField ?

?

2 ??

2 ? apeture2

?

Watts ?

Watts ?

Gain over isotropic GainNumeric ? 10

GaindBi ? 10 ? Log(Gainnumeric )

?Meters? V m?2

?V m ? meters?2

30 ? Gainnumeric

?V m ? meters?2

? GaindBi ?

?

?

10 ?

30 ? 10?

? GaindBi ?

?

?

? 10 ?

GaindBi

30 ? Watts ?10

Meters

V /m ?

Far Field Equations

GainNumeric ?

? GaindBi ?

?

?

? 10 ?

Power needed if gain remains constant (in Far

Field) using same antenna and changing field level

or test distance.

30 ?Watts

? ?Meters ? V m ?2 ?

?

? 10 ? Log??

?

? 30 ? Watts ?

GaindBi ? 20 ? Log(MHz) ? AF ? 29.79

For Field Change

WattsNew ? WattsOld

For Distance Change

WattsNew ? WattsOld

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

? Angle3dB ?

Spot meters ? 2 ? Distance meters tan ?

?

2

?

?

Distancemeters ?

Spot meters

Angle3dB ?

2 ? tan??

2 ??

?

?V m New ?2

?V mOld ?2

?MetersNew ?2

?MetersOld ?2

Power for given Amplitude Modulation %

Wattspeak ? WattsCW ? ?1 ? ?% ? 0.01??

2

Wattsavg ?

Wattsavg ?

?

2

?

?

2

?

WattsCW ? 2 ? ?% ? 0.01?

2

Wattspeak ? 2 ? ?% ? 0.01?

2 ? ?1 ? ?% ? 0.01??

2

Power for given Pulse Modulation

Duty Cycle %

Wattspeak ?

Wattsavg

% ? 0.01

? Spot meters ?

Angle3dB ? 2 ? tan ?1 ?

?

? 2 ? Distance ?

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033109

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