ERP,EIRP,dB and dBm definition in RF Planning

ERP,EIRP,dB and dBm definition in RF Planning, half wave dipole, radiated power, expression of power, power gain, ERP,EIRP,dB and dBm calculation.

ERP,EIRP,dB and dBm calculation are Most important thing to take care in RF Planning of any site.

Isotropic RF Source

  • A point source that radiates RF energy uniformly in all directions (I.e.: in the shape of a sphere)
  • Theoretical only: does not physically exist.
  • Has a power gain of unity I.e. 0dBi.

Effective Radiated Power (ERP)

  • Has a power gain of unity i.e. 0dBi
  • The radiated power from a half-wave dipole.
  • A lossless half-wave dipole antenna has a power gain of 0dBd or 2.15dBi.

Effective Isotropic Radiated Power (EIRP)

  • The radiated power from an isotropic source

EIRP = ERP + 2.15 dB

  • Radio signals travel through space at the Speed of Light

C = 3 * 108 meters / second

  • Frequency (F) is the number of waves per second (unit: Hertz)
  • Wavelength (l) (length of one wave) = (distance traveled in one second)/   (waves in one second)

l= C / F

If frequency is 900MHZ then wavelength l =3 * 108 = 900 * 106= 0.333 meters


  • dB is a a relative unit of measurement used to describe power gain or loss.
  • The dB value is calculated by taking the log of the ratio of the measured or calculated power (P2) with respect to a reference power (P1). This result is then multiplied by 10 to obtain the value in dB.

dB = 10 * log10(P1/P2)

  • The powers P1 ad P2 must be in the same units. If the units are not compatible, then they should be transformed.
  • Equal power corresponds to 0dB.
  • A factor of 2 corresponds to 3dB

If P1 = 30W and P2 = 15 W then

10 * log10(P1/P2) = 10 * 10 * log10(30/15)

= 2


  • The most common “defined reference” use of the decibel is the dBm, or decibel relative to one milliwatt.
  • It is different from the dB because it uses the same specific, measurable power level as a reference in all cases, whereas the dB is relative to either whatever reference a particular user chooses or to no reference at all.
  • A dB has no particular defined reference while a dBm is referenced to a specific quantity: the milliwatt (1/1000 of a watt).
  • The IEEE definition of dBm is “a unit for expression of power level in decibels with reference to a power of 1 milliwatt.”
  • The dBm is merely an expression of power present in a circuit relative to a known fixed amount (i.e., 1 milliwatt) and the circuit impedance is irrelevant.}
  • dBm = 10 log (P) (1000 mW/watt)

where  dBm = Power in dB referenced to 1 milliwatt

P = Power in watts

  • If power level is 1 milliwatt:

Power(dBm) = 10 log (0.001 watt) (1000 mW/watt)

= 10 log (1)

= 10 (0)

= 0

  • Thus a power level of 1 milliwatt is 0 dBm.
  • If the power level is 1 watt

1 watt Power in dBm = 10 log (1 watt) (1000 mW/watt)

= 10 (3)

= 30

  • dBm = 10 log (P) (1000 mW/watt)
  • The dBm can also be negative value.
  • If power level is 1 microwatt

Power in dBm = 10 log (1 x 10E-6 watt) (1000 mW/watt)

= -30 dBm

  • Since the dBm has a defined reference it can be converted back to watts if desired.
  • Since it is in logarithmic form it may also be conveniently combined with other dB terms.


  • To convert  field strength in dbmv/m to received power in dBm with a 50W optimum terminal impedance and effective length of a half wave dipole l/p

0dBu = 10 log[(10-6)2(1000)(l/p)2/(4*50)] dBm

At 850MHZ

0dBu = -132 dBm

39dBu = -93 dBm

Related Posts

Article Topics :