antenna gain and its erp

erp of an antenna

as we know antenna gain is a relative term.
the total radiated power by an antenna is always less than or equal to the input power. but its erp is very large

what is the physical meaning of erp ? how is it diff from total rad power?

erp vs eirp

Antenna gain is often quoted as EIRP, that is "Effective Isotropic Radiated Power", or the apparent power transmitted assuming that the antenna radiates equally in all directions, IE. the field is assumed to be spherical from a point source with an equal power transmitted in all directions. EIRP is the product of Power supplied to the antenna and the antennas gain.

Since the antenna emits in a spherical field,

gain = (4.pi.Area)/((wavelength)(Wavelength))

and EIRP = gain.Power transmitted
(assuming 100% efficiency)

In practice the gain is normally that of the main lobe, assumed to be spread over the imaginary sphere.

ERP is power radiated in a given direction, normally the direction of maximum radiation,

ie Antenna gain(ERP) = Antenna Gain.Directivity

If figures are expressed in dBi it is refering to a reference of an isotropic antenna, if dBd the reference is a dipole (0dBd = 2.15dBi) Figures given in dBd are used as the dipole is the most practical smallest/lowest antenna that can be made for callibration. Isotropic antennas do not exist they are used purely in theory, often for system calculations.

Making sure you have the correct figure is very important as the values will cause big big differences in any calculations you make! Especially if it is for legal requirement limits!

reference antenna for erp

Sorry read part of your question again...

ERP is an artificially constructed figure to measure how well a directive antenna concentrates energy in a specific direction.

Consider the difference in brightness between an identical value spotlight and a normal bulb, its the same power in...But one is effectively more bright dur to its directive component.

The Directivity of the antenna is defined as

D=EIRP/(Total Radiated Power)
ie. EIRP = D.TRP
or ERP=D.TRP.Ag

and in physics terms TRP is the time averaged power density of the signal across the entire radiating sphere... PHEW. ( think I've got that right, its been a few years)

Erm... this stuff gets rather confusing when you try to explain it, especially as you then get into the mess of calculations with dBi dBd dBm dBw, formulas which use EIRP, those that use ERP....

I'll have another think & see if I can't write it any clearer...

erp times antenna gain

3rd Time lucky.....

Total Radiated Power is the power radiated per unit solid angle(radiation intensity), integrated over all solid angles.

ie. for a isotropic radiator (sphere) where power is radiated equally over all angles...

rad int = TRP/4.pi

Directive gain adds nothing to the signal, it mearly concentrates it in a given direction. Directive gain is the radiation intensity normalised by isotropic intensity, and an antennas directivity is its maximum value so for a directive antenna.

rad int = TPR.D/4.pi

Now if that power was emitted isotropically then TPR.D would be the effective radiated power or ERP in the given direction, if in the direction of maximum gain Prad(max).D(max) would be the effective Isotropic radiated power or EIRP.

The antennas gain is normalised to the power in at the terminals, not to the total radiated power. and so the efficiency is

e=Prad/Pin and so for an ideal antenna gain & directivity correspond exactly.

G=eD


ERP is like a spotlights brightness,
EIRP is the equivalent lightbulb power required to reach the Spotlights brightness, therefore EIRP is higher than ERP.

ERP is power in * antenna gain
EIRP is power in * antenna gain(max).

Most FCC regulations are specified in ERP meaning that a directive antenna can put you over the TPR limits even if the transmitter is not more powererful. (Since TPR in that direction is greater, and therefore a higher EIRP)

as an example with a antenna gain of 100 and 1W:
(ERP is referenced to a 1/2 wave dipole not isotropic and 2.15dB difference equates to * 1.64)

ERP = 100W
EIRP = 100 * 1.64 = 164W

I hope this helps, I Don't think I can clarify this any more since you really need to consider directions in all the above sums, maybee someone else can though