# RF formulas

#### Description

EMC Related Formulae Term Conversion

Log↔ ↔ Linear Voltage dBµV to Volts

V = 10((dBµV − 120) / 20)

dBm to dBuV

dBµv = 90 + 10 log( Z ) + dBm

Volts to dBµV

dBµV = 20 log (V ) + 120

dBuV to dBm

dBm = dBµV − 90 − 10 log( Z )

V = 10(dBV / 20)

dBuA to dBm

dBm = dBµA + 10 log( Z ) − 90

dBV to Volts

dBV = 20 log (V )

dBm to dBuA

dBµA = dBm − 10 log( Z ) + 90

Volts to dBV

dBµV = dBV + 120

dBuA to dBuV

dBµV = dBµA + 20 log( Z )

dBV to dBµV

dBV = dBµV − 120

dBuV to dBuA

dBµA = dBµV − 20 log( Z )

dBµV to dBV

Log↔ ↔ Linear Power

Volts to Amps & Watts

A=

V Z

W=

V2 Z

dBm to Watts

W = 10((dBm − 30) / 10)

Amps to Volts & Watts

V = A* Z

W = A2 * Z

Watts to dBm

dBm = 10 log(W ) + 30

Watts to Volts & Amps

V = W *Z

A=

dBW to Watts

W = 10(dBW / 10)

Watts to dBW

dBw = 10 log(W )

dBW to dBm

dBm = dBW + 30

dBm to dBW

dBW = dBm − 30

W Z

RF related, Field Strength & Power Density

Log↔ ↔ Linear Current

dBuV/m to V/m

V / m = 10(((dBµV / m) − 120) / 20)

V/m to dBuV/m

dBµV / m = 20 log (V / m ) + 120

dBuv/m to dBmW/m2

dBm / m2 = dBµV / m − 115.8

dBmW/m2 to dBuV/m

dBµV / m = dBm / m 2 + 115.8

dBuA to uA

µA = 10(dBµA / 20)

dBuV/m to dBuA/m

dBµA / m = dBµV / m − 51.5

uA to dBuA

dBµA = 20 log( µA)

dBuA/m to dBuV/m

dBµV / m = dBµ A / m + 51.5

dBA to A

A = 10(dBA / 20)

dBuA/m to dBpT

dBpT = dBµA / m + 2

A to dBA

dBA = 20 log( A)

dBpT to dBuA/m

dBµA / m = dBpT − 2

dBuA to dBA

dBA = dBµA − 120

W/m2 to V/m

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

dBA to dBuA

dBµA = dBA + 120 V/m to W/m2

W / m2 =

wound coil Flux Density

µT =

uT to A/m

A/m =

A/m to uT

µ T = 1.25 * ( A / m)

Log↔ ↔ Linear Impedance dB(ohms) to ohms

Z = 10(dB(ohms) / 20)

ohms to dB(ohms)

dB(ohms ) = 20 log (Z )

Robert Richards

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(V / m ) 2 377

4π (turns)( amps ) 20( radius, m ) µT 1.25

03/30/03

Current Probe

Antenna (Far Field)

dB(ohm) to Zt (transfer impedance)

Gain, dBi to numeric

Z t = 10( dB (ohm) / 20)

Gainnumeric = 10( dBi / 10)

Zt to dB(ohm)

Gain, numeric to dBi

dB (ohm) = 20 log( Z t )

dBi = 10 log(Gainnumeric )

Conductance (Gt) in dB(s) to transfer impedance, (Zt) in dB(ohms)

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

Z t = −Gt

Antenna Factor to gain in dBi Transfer Impedance in Zt (dB(ohms)), to Conductance in Gt (dB(s))

dBi = 20 log( MHz ) − AF − 29.79

Gt = −Z t

Field Strength given Watts, Numeric Gain, Distance in meters

Power needed for BCI Probe (50Ω), given voltage level into 50Ω load (V) and Probe Insertion Loss I L .

30 * watts * Gainnumeric

V /m =

Meters

watts = 10

Field Strength given Watts, dBi gain, Distance in meters

Watts needed for 150 Ohm EM Clamp

30 * watts * 10(dBi / 10 ) Meters

V /m =

watts = 10

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

(( I L + 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

(V / m * meters ) 2 30 * Gainnumeric

dBµA = dBµV − dB (ohm)

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

(( I L + 10 log(V 2 / 50)) / 10)

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

(V / m * meters ) 2

dBµA = dBµV − 20 log( Zt )

30 *10 ( dBi / 10)

dB calculations Amplitude Modulation Compute db delta (volts)

V  dB = 20 log  1   V2 

Compute dB delta (amps)

 dB = 20 log  

Compute dB delta (watts)

W  dB = 10 log  1   W2 

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

compute new voltage w/ db delta

Average power, given peak power and modulation %

Wavg =

Vnew

W peak * (2 + ( Mod % * 0.01) 2 ) 2 * (1 + ( Mod % * 0.01)) 2

 ( dB∆ + 20 log(V given )     20  = 10

compute new wattage w/ db delta

Wnew

Robert Richards

A1   A2 

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 ( dB∆ + 10 log(W given )     10  = 10

03/30/03

VSWR/reflection coefficient/return loss

Misc

VSWR given Fwd/Rev Power

Linear interpolation with log of freq

1+

Prev Pfwd

Value =

1−

Prev Pfwd

where

VSWR =

VSWR given reflection coefficient VSWR =

1+ ρ 1− ρ

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 =

Reflection coefficient, ρ, given Z1/Z2 ohms ρ=

Log ( FX / FL ) * ( XU − X L ) + X L Log ( FU / FL )

Z1 − Z 2 Z1 + Z 2

where

(V * Height * 0.5) 2 Z V = field strength in V/m Z = TEM cell impedance in ohms

Reflection coefficient, ρ, given fwd/rev power

ρ=

Prev Pfwd

Return Loss, given fwd/rev power  Pfwd RL ( dB ) = 10 log   P  rev

   

Return Loss, given VSWR  VSWR − 1  RL( dB ) = −20 log   VSWR + 1 

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

Mismatch loss, given fwd/rev power  Pfwd ML ( dB ) = 10 log   Pfwd − Prev 

   

Mismatch loss, given reflection coefficient

ML(dB) = −10 log(1 − ρ 2 )

Robert Richards

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03/30/03