rfcalc_watttodBm

Bird Electronic Corporation www.bird-electronic.com (866) 695-4569 2/6/06 JN By: Jim Norton, Applications Engineer

RF Calculators Select a calculator tab at the bottom of this page for assistance with your radio frequency (RF) needs.

Calculators available include Power, VSWR & Return Loss, Frequency & Wavelength, Attenuation, Directivity, Cable Loss, Masking Effect, Field Strength, Free Space Loss and Metric Conversions.

Bird Electronic Corporation

www.bird-electronic.com

(866) 695-4569

Power Calculator Enter power and select units to determine equivalent values.

Enter Power = Power = Power = Power = Power = Power = Power =

2.000 33.010 2,000,000,000,000.000 2,000,000,000.000 2,000,000.000 2,000.000 2.000 0.002

Watts (W)

dBm Picowatts (pW) Nanowatts (nW) Microwatts (uW) Milliwatts (mW) Watts (W) Kilowatts (kW)

1 kW = 1,000 W 1 W = 1,000 mW = 1,000,000 uW 1 W = 1,000,000,000 nW = 1,000,000,000,000 pW Power (dBm) = 10 x Log [ Power (Watts) ] + 30 dB

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VSWR & Return Loss Calculator Enter forward and reflected power or match to determine equivalent values.

Enter Enter Calculates Calculates Calculates Calculates

Forward Power Reflected Power VSWR Return Loss Match Efficiency Rho

100.00 4.00 1.50 -13.98 96.00 0.20

Watts Watts

Enter Calculates

Power Power

50.00 Watts 46.99 dBm

Enter Calculates

Power Power

47.00 dBm 50.12 Watts

dB %

Power (dBm) = 10 x Log [ Power (Watts) ] + 30 dB

Enter 1.500 VSWR 1 = 1.500 VSWR = -13.979 Return Loss (dB) = 96.000 Match Efficiency (%) = 0.200 Rho

VSWR = Voltage Standing Wave Ratio Pf = Forward Power (Watts) Pr = Reflected Power (Watts) VSWR = [1+Sqrt(Pr / Pf)] / [1-Sqrt(Pr / Pf)] Return Loss (dB) = 10 x Log ( Pr / Pf ) Match Efficiency (%) = 100% x (1 - Pr / Pf) Rho = Sqrt ( Pr / Pf )



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Frequency & Wavelength Calculator Enter frequency or wavelength and select units to determine equivalent values.

Enter Frequency = Frequency = Frequency = Wavelength = Wavelength = Wavelength = Wavelength =

900.000 900,000.000 900.000 0.900 0.333 33.333 1.094 13.123

Megahertz (MHz)

Kilohertz (kHz) Megahertz (MHz) Gigahertz (GHz) Meters (m) Centimeters (cm) Feet (ft) Inches (in)

1 MHz = 1,000 kHz 1 GHz = 1,000 MHz Wavelength (Meters) = 300 / Frequency (MHz)

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Attenuation Calculator Enter power or attenuation to determine values.

Enter Enter Calculates Calculates Calculates

Input Power Output Power Input Power Output Power Attenuation

50.00 25.00 46.99 43.98 3.01

Watts Watts dBm dBm dB


Input Power Attenuation Input Power Output Power Output Power

50.00 3.00 46.99 43.99 25.06

Watts dB dBm dBm Watts

Enter Calculates

Power Power

50.00 Watts 46.99 dBm

Enter Calculates

Power Power

47.00 dBm 50.12 Watts


Output Power Attenuation Output Power Input Power Input Power

25.00 3.00 43.98 46.98 49.88

Watts dB dBm dBm Watts

Output Power (dBm) = Input Power (dBm) - Attenuation (dB) Power (dBm) = 10 x Log [ Power (Watts) ] + 30 dB



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Directivity Error Calculator Enter directivity, forward power and reflected power to determine directivity errors. Enter Enter Enter Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates

Directivity of Coupler Forward Power Reflected Power Forward Power Minimum Forward Power Maximum Forward Power Min Error Forward Power Max Error Reflected Power Minimum Reflected Power Maximum Reflected Power Min Error Reflected Power Max Error VSWR Minimum VSWR VSWR Maximum Return Loss Minimum Return Loss Return Loss Maximum

30.000 100.000 4.000 98.739 101.269 -1.261 1.269 2.835 5.365 -29.123 34.123 1.402 1.500 1.608 -15.529 -13.979 -12.649

dB Watts Watts Watts Watts % % Watts Watts % %

Directivity is a measure of the ability of a directional coupler to discern between the forward and reflected traveling wave in a transmission system. Power meters, antenna monitors and analyzers are coupler based test equipment which are used to measure forward and reflected power as well as VSWR and return loss. Directivity errors result in measurements which may vary between maximum and minimum values.

dB dB dB

The following is a step-by-step procedure to calculate the results which are displayed above: Given Given Given Calculates Calculates Calculates Calculates Calculates Calculates Calculates

Directivity of Coupler Forward Power Reflected Power Directivity Power Ratio Directivity Forward Power Directivity Reflected Power Forward Voltage Reflected Voltage Directivity Forward Voltage Directivity Reflected Voltage

30.000 100.000 4.000 1,000 0.004 0.100 70.711 14.142 0.447 2.236

dB Watts Watts Watts Watts Volts Volts Volts Volts

Dir = Directivity of Coupler Pf = Forward Power Pr = Reflected Power Directivity Power Ratio = 10 ^ (Dir / 10) Pfd = Pr / Directivity Power Ratio Prd = Pf / Directivity Power Ratio Vf = Sqrt (Pf x 50 Ohms) Vr = Sqrt (Pr x 50 Ohms) Vfd = Sqrt (Pfd x 50 Ohms) Vrd = Sqrt (Prd x 50 Ohms)

Note, voltage vectors add when in phase or subtract when 180 degrees out of phase with each other Calculates Forward Voltage Minimum 70.263 Volts Vf (Min) = Vf - Vfd Calculates Forward Voltage Maximum 71.158 Volts Vf (Max) = Vf + Vfd Calculates Reflected Voltage Minimum 11.906 Volts Vr (Min) = Vr - Vrd (or 0 if Vrd > Vr) Calculates Reflected Voltage Maximum 16.378 Volts Vr (Max) = Vr + Vrd Calculates Forward Power Minimum 98.739 Watts Pf (Min) = (Vf (Min) ^ 2) / 50 Ohms Calculates Forward Power Min Error -1.261 % Error = 100% x (Pf (Min) - Pf) / Pf Calculates Forward Power Maximum 101.269 Watts Pf (Max) = (Vf (Max) ^ 2) / 50 Ohms Calculates Forward Power Max Error 1.269 % Error = 100% x (Pf (Max) - Pf) / Pf Calculates Reflected Power Minimum 2.835 Watts Pr (Min) = (Vr (Min) ^ 2) / 50 Ohms Calculates Reflected Power Min Error -29.123 % Error = 100% x (Pr (Min) - Pr) / Pr Calculates Reflected Power Maximum 5.365 Watts Pr (Max) = (Vr (Max) ^ 2) / 50 Ohms Calculates Reflected Power Max Error 34.123 % Error = 100% x (Pr (Max) - Pr) / Pr Calculates Rho Minimum 0.167 Rho (Min) = Sqrt (Pr (Min) / Pf (Max)) Calculates Rho 0.200 Rho = Sqrt (Pr / Pf) Calculates Rho Maximum 0.233 Rho (Max) = Sqrt (Pr (Max) / Pf (Min)) Calculates VSWR Minimum 1.402 VSWR (Min) = (1 + Rho (Min)) / (1 - Rho (Min)) Calculates VSWR 1.500 VSWR = (1 + Rho) / (1 - Rho) Calculates VSWR Maximum 1.608 VSWR (Max) = (1 + Rho (Max)) / (1 - Rho (Max)) Calculates Return Loss Minimum -15.529 dB Return Loss (Min) = 10 x Log (Pr (Min) / Pf (Max)) Calculates Return Loss -13.979 dB Return Loss = 10 x Log ( Pr / Pf ) Calculates Return Loss Maximum -12.649 dB Return Loss (Max) = 10 x Log (Pr (Max) / Pf (Min))



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Cable Loss Calculator Enter cable, jumper, connector and other loss parameters to determine transmission cable system insertion loss. Cable loss is the total insertion loss of your transmission cable system. This typically includes insertion loss of the transmission cable, jumper cables, connectors and lightning protection. Loss of other components (e.g. VSWR/power monitor, duplexer, combiner or filter) may also come into play.

Enter Enter Calculates Enter Enter Calculates Enter Enter Calculates Enter Enter Calculates Enter Enter Enter Calculates

Cable Loss/100 m or ft Cable Length (m or ft) Cable Loss Top Jumper Loss/100 m or ft Top Jumper Length (m or ft) Top Jumper Loss Bottom Jumper Loss/100 m or ft Bottom Jumper Length (m or ft) Bottom Jumper Loss Loss per Connector Number of Connectors Connector Loss Lightning Protection Loss VSWR/Power Monitor Loss Other Component Loss Total Cable System Loss

1.13 230.00 2.60 3.23 10.00 0.32 3.23 20.00 0.65 0.05 8 0.40 0.10 0.00 0.00 4.07

dB m or ft dB dB m or ft dB dB m or ft dB dB dB dB dB dB dB

Loss per 100 Meters or Feet at Frequency Length in Meters or Feet Transmission Cable Insertion Loss Loss per 100 Meters or Feet at Frequency Length in Meters or Feet Top/Antenna Jumper Cable Insertion Loss Loss per 100 Meters or Feet at Frequency Length in Meters or Feet Bottom/Tx Jumper Cable Insertion Loss Connector Insertion Loss Two Connectors per Pair Connector Insertion Loss Lightning Protection Insertion Loss VSWR/Power Monitor Insertion Loss Loss of Combiner, Duplexer, Filter, etc. Transmission Cable System Insertion Loss



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Masking Effect Calculator Enter cable loss and match or forward and reflected power to determine the masking effect.

Enter Enter Calculates

Cable Insertion Loss VSWR at Transmitter VSWR of Antenna

3.00 dB 1.50 2.33


Cable Insertion Loss Return Loss at Transmitter Return Loss of Antenna

3.00 dB -14.00 dB -8.00 dB

CL = Cable Insertion Loss RLt = Return Loss at Transmitter RLa = Return Loss of Antenna = RLt - (2 x CL)

Enter Enter Enter Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates Calculates

Cable Insertion Loss Forward Power at Transmitter Reflected Power at Transmitter Rho at Transmitter VSWR at Transmitter Return Loss at Transmitter Forward Power at Transmitter Forward Power at Antenna Reflected Power at Transmitter Reflected Power at Antenna Forward Power at Antenna Reflected Power at Antenna Rho of Antenna VSWR of Antenna Return Loss of Antenna

3.00 100.00 4.00 0.20 1.50 -13.98 50.00 47.00 36.02 39.02 50.12 7.98 0.40 2.33 -7.98

CL = Cable Insertion Loss Pft = Forward Power at Transmitter Prt = Reflected Power at Transmitter Rhot = Sqrt (Prt / Pft) VSWRt = (1 + Rhot) / (1 - Rhot) RLt = 10 x Log (Prt / Pft) Pft (dBm) = 10 x Log (Pft (Watts)) + 30 dB Pfa (dBm) = Pft (dBm) + CL Prt (dBm) = 10 x Log (Prt (Watts)) + 30 dB Pra (dBm) = Prt (dBm) - CL Pfa (Watts) = 10 ^ ((Pfa (dBm) - 30) / 10) Pra (Watts) = 10 ^ ((Pra (dBm) - 30) / 10) Rhoa = Rho of Antenna = Sqrt (Pra / Pfa) VSWRa = (1 + Rhoa) / (1 - Rhoa) RLa = 10 x Log (Pra / Pfa)

dB Watts Watts

dB dBm dBm dBm dBm Watts Watts

dB

Antenna measurements taken at the transmitter end of the cable will be masked by the cable loss.



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Field Strength Calculator Enter signal power level, frequency and antenna gain to determine field strength.

Enter Enter Enter Calculates Calculates Calculates Calculates Calculates Calculates

Signal Power Level Frequency Receive Antenna Gain Antenna Factor Signal Level Signal Level Field Strength Field Strength Field Strength

-30.000 155.000 3.000 11.007 77.000 88.007 0.025 25.138 25,138.057

dBm MHz dB dB dBuV dBuV/m V/m mV/m uV/m

The field strength of the signal emitted by a radio antenna is usually expressed in units of microvolts per meter (uV/m). This may be calculated if the signal power level (dBm), frequency and the gain of the receive antenna are known.

Antenna Factor (dB) = 20 Log (Frequency (MHz)) - Antenna Gain (dB) -29.8 Signal Level (dBuV) = Signal Level (dBm) + 107 dB Signal Level (dBuV/m) = Signal Level (dBuV) + Antenna Factor (dB) Field Strength (uV/m) = 10 ^ (Signal Level (dBuV/m) / 20) 1 V/m = 1,000 mV/m = 1,000,000 uVm



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Free Space Loss Calculator Enter frequency and distance to determine free space loss.



Frequency Distance Free Space Loss

Frequency Distance Free Space Loss

800.000 MHz 1.000 Miles 94.662 dB

800.000 MHz 1.000 Kilometers 90.529 dB

Free Space Loss is the power loss of a radio signal as it travels through free space. Losses due to sources such as earth, trees, buildings, cables and connectors as well as antenna gains are not considered.

Free Space Loss (dB) = 36.6 + 20 x Log (Frequency (MHz) x Distance (Miles)) 1 Mile = 1.6093 Kilometers



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Metric Conversions Enter quantity and select units to determine equivalent values.

Length Enter = = = = = = =

1.000 160,934.400 63,360.034 5,279.936 1,759.979 1,609.344 1.609 1.000

1 in = 2.54 cm

Weight Miles (mi)

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Centimeters (cm) Inches (in) Feet (ft) Yards (yd) Meters (m) Kilometers (km) Miles (mi)

1 m = 3.28 ft

Enter = = = = = = =

1 mi = 1.6 km

1 oz = 28.35 g

Area Enter = = = = = = =

1.000 10,000.000 1,550.005 10.764 1.000 0.000 0.000 0.000

1.000 1,000.000 35.274 2.205 1.000 0.022 0.001 0.001

Kilograms (kg)

4

Grams (g) Ounces (oz) Pounds (lb) Kilograms (kg) Hundredwt (cwt) Tons (ton) Tonnes (t)

1 kg = 2.2 lb

1 t = 1.1 ton

Temperature Square m

4

Square cm Square in Square ft Square m Acres Square km Square mi

1 sq in = 6.45 sq cm 1 sq m = 10.76 sq ft 1 sq mi = 2.6 sq km

Enter = = = =

0.000 32.000 0.000 491.690 273.150

Celsius (C)

Fahrenheit (F) Celsius (C) Rankine (R) Kelvin (K)

C = 5/9 (F - 32) R = F + 459.69 K = C + 273.15

2

Volume Enter = = = = = = =

2.000 2,000.000 67.628 2.113 2.000 0.528 0.071 0.002

Liters (l)

4

Milliliters (ml) Fluid Oz (fl oz) Quarts (qt) Liters (l) Gallons (gal) Cubic Ft (cu ft) Cubic M (cu m)

1 fl oz = 29.6 ml 1 liter = 1.06 qt 1 gal = 3.8 liters 1 cu m = 35.3 cu ft

rfcalc_watttodBm

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