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
- 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
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