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 * 10^{8} 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 * 10^{8 = }900 * 10^{6= }0.333 meters

**dB**

- 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 * log_{10}(P_{1}/P_{2})

- The powers P
_{1}ad P_{2}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 * log_{10}(P_{1}/P_{2}) = 10 * 10 * log_{10}(30/15)

= 2

**dBm**

- 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.

**dBmv/m**

- 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