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
1 of 6 033109
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
2 of 6 033109
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
3 of 6 033109
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
4 of 6 033109
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
5 of 6 033109
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
6 of 6 033109
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