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 ?
2 of 6
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 ?? ?
?
?
4 of 6
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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