EMC Related Formulae

EMC Related Formulae

dB?V to Volts Volts to dB?V dBV to Volts Volts to dBV dBV to dB?V dB?V to dBV

LogLinear Voltage

V = 10((dB?V -120)/ 20) dB?V = 20 log(V ) + 120 V = 10(dBV / 20) dBV = 20log(V )

dB?V = dBV + 120 dBV = dB?V - 120

dBm to Watts Watts to dBm

dBW to Watts Watts to dBW dBW to dBm dBm to dBW

LogLinear Power

W =10((dBm - 30)/10)

dBm = 10 log(W ) + 30

W =10(dBW /10)

dBw = 10 log(W ) dBm = dBW + 30 dBW = dBm - 30

dBuA to uA uA to dBuA dBA to A A to dBA dBuA to dBA dBA to dBuA

LogLinear Current

?A = 10(dB?A/ 20)

dB?A = 20 log(?A)

A = 10(dBA/ 20)

dBA = 20 log( A) dBA = dB?A - 120 dB?A = dBA + 120

LogLinear Impedance

dB(ohms) to ohms Z = 10(dB(ohms) / 20) ohms to dB(ohms) dB(ohms) = 20 log(Z )

Term Conversion

dBm to dBuV dBuV to dBm dBuA to dBm dBm to dBuA dBuA to dBuV dBuV to dBuA

dB?v = 90 + 10 log(Z ) + dBm dBm = dB?V - 90 - 10 log(Z ) dBm = dB?A +10 log(Z ) - 90 dB?A = dBm -10 log(Z ) + 90 dB?V = dB?A + 20 log(Z ) dB?A = dB?V - 20 log(Z )

Volts to Amps & Watts

A= V Z

Amps to Volts & Watts V = A * Z

W =V2 Z

W = A2 * Z

Watts to Volts & Amps V = W * Z

A= W Z

RF related, Field Strength & Power Density

dBuV/m to V/m V/m to dBuV/m

V / m =10(((dB?V / m) -120) / 20)

dB?V / m = 20 log(V / m) + 120

dBuv/m to dBmW/m2

dBm/ m2 = dB?V / m -115.8

dBmW/m2 to dBuV/m dBuV/m to dBuA/m dBuA/m to dBuV/m dBuA/m to dBpT dBpT to dBuA/m

dB?V / m = dBm/ m2 + 115.8 dB?A / m = dB?V / m - 51.5 dB?V / m = dB?A / m + 51.5 dBpT = dB?A / m + 2 dB?A / m = dBpT - 2

W/m2 to V/m

V / m = (W / m 2 ) *377

V/m to W/m2 wound coil Flux Density

W / m2 = (V / m)2 377

?T = 4 (turns)(amps) 20(radius, m)

uT to A/m A/m to uT

A / m = ?T 1.25

?T = 1.25 * ( A / m)

Robert Richards

Page 1

03/30/03

Antenna (Far Field)

Gain, dBi to numeric Gainnumeric = 10(dBi /10)

Gain, numeric to dBi dBi = 10 log(Gainnumeric)

Gain, dBi to Antenna Factor AF = 20 log(MHz) - dBi - 29.79

Antenna Factor to gain in dBi dBi = 20 log(MHz) - AF - 29.79

Field Strength given Watts, Numeric Gain, Distance in meters

V / m = 30 * watts * Gainnumeric Meters

Field Strength given Watts, dBi gain, Distance in meters

V / m = 30 * watts *10(dBi /10) Meters

Transmit Power needed, given desired V/m, Antenna numeric gain, Distance in meters.

watts = (V / m * meters)2 30 * Gainnumeric

Transmit Power needed, given V/m, Antenna dBi gain, Distance in meters

watts = (V / m * meters)2 30 *10(dBi / 10)

Amplitude Modulation

Peak power, given CW power and modulation %.(sine wave AM)

Wpeak = WCW (1 + (Mod % * 0.01))2

Average power, given CW power level and modulation % (sine wave AM)

Wavg

=

Wcw * (2 + (Mod% * 0.01)2 ) 2

Average power, given peak power and modulation %

Wavg

=

Wpeak * (2 + (Mod% * 0.01)2 ) 2 * (1 + (Mod% * 0.01))2

Robert Richards

Page 2

Current Probe

dB(ohm) to Zt (transfer impedance)

Zt = 10(dB(ohm) / 20) Zt to dB(ohm)

dB(ohm) = 20 log(Zt ) Conductance (Gt) in dB(s) to transfer impedance, (Zt) in dB(ohms)

Zt = -Gt Transfer Impedance in Zt (dB(ohms)), to Conductance in Gt (dB(s))

Gt = -Zt Power needed for BCI Probe (50), given voltage level into 50 load (V) and Probe Insertion Loss IL .

watts = 10((IL + 10 log(V 2 / 50)) /10)

Watts needed for 150 Ohm EM Clamp

watts = 10((IL + 10 log(V 2 /150)) /10)

Conducted current level using current measuring probe given probe factor in dB(ohm) and probe terminal voltage in dBuv

dB?A = dB?V - dB(ohm)

Conducted current level, given probe factor in Zt (ohms) and terminal voltage in dBuv

dB?A = dB?V - 20 log(Zt )

dB calculations

Compute db delta (volts)

dB

=

20

log

V1 V2

Compute dB delta (amps)

dB

=

20

log

A1 A2

Compute dB delta (watts)

dB

=

10

log

W1 W2

compute new voltage w/ db delta

(dB + 20 log(Vgiven )

Vnew = 10

20

compute new wattage w/ db delta

(dB + 10 log(Wgiven )

Wnew = 10

10

03/30/03

VSWR/reflection coefficient/return loss VSWR given Fwd/Rev Power

1+ VSWR =

1-

Prev Pfwd

Prev Pfwd

VSWR given reflection coefficient VSWR = 1 + 1-

Reflection coefficient, , given Z1/Z2 ohms = Z1 - Z2 Z1 + Z2

Reflection coefficient, , given fwd/rev power = Prev Pfwd

Return Loss, given fwd/rev power

RL(dB) = 10 log

Pfwd Prev

Return Loss, given VSWR

RL(dB) = -20 log VSWR - 1 VSWR + 1

Return Loss, given reflection coefficient RL(dB) = -20 log( )

Mismatch loss, given fwd/rev power

ML(dB)

= 10 log

Pfwd Pfwd - Prev

Mismatch loss, given reflection coefficient ML(dB) = -10log(1 - 2)

Misc Linear interpolation with log of freq

Value =

Log ( FX Log(FU

/ FL ) / FL )

* (XU

-

XL)+

XL

where

FL = lower frequency FU = Upper frequency XL = Value at lower frequency XU = Value at upper frequency FX = Frequency of desired value

TEM Cell Power Needed

Watts = (V * Height * 0.5)2 Z

where V = field strength in V/m Z = TEM cell impedance in ohms

Robert Richards

Page 3

03/30/03

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