COMPARISON OF TRANSMITTER POWER

Signal strength drops TWO times for every doubling in distance away from the transmitter.
Signal strength at a given distance doubles for every FOUR times increase in transmitter power.
Transmitter power is therefore not that important.  Large, high antennas, and good low-noise receiver environments are far more important in ensuring long distance radio transmission.

DATA BASED ON QUARTER-WAVELENGTH VERTICAL TOWER RADIATOR OVER PERFECT GROUND
POWER
(WATTS)
SIGNAL STRENGTH
AT 1 km (mV / m)
SIGNAL STRENGTH
AT 10 km (mV / m)
SIGNAL STRENGTH
AT 100 km (mV / m)
RECEIVED VOLTAGE AT 
100 km (mV)
1 meter vertical whip
50,000 2214 221.4 22.1 22.1
10000 990 99.0 9.90 9.90
5000 700 70.0 7.00 7.00
1000 313 31.3 3.13 3.13
500 221.4 22.1 2.21 2.21
100 99.0 9.90 0.99 0.99
50 70.0 7.00 0.70 0.70
10 31.3 3.13 0.31 0.31
5 22.1 2.21 0.22 0.22
1 9.90 0.99 0.10 0.10
0.5 7.00 0.70 0.07 0.07



 
 

COMPARISON OF TRANSMITTING ANTENNAS

Antenna
Radiation Resistance
Rrad (ohms)
Directive Gain
Gd
current element, length dl
(uniform current distribution)
80 * (PI)2 * dl2 / wavelength2 1.5
1/2-wave DIPOLE
(sinusoidal current distribution)
73.0 1.64
1/4-wave VERTICAL MONOPOLE OVER PERFECT GROUND
(sinusoidal current distribution)
36.5 3.28
SHORT VERTICAL MONOPOLE OVER PERFECT GROUND
(H < 1/8-wave),
TOP CAPACITIVELY LOADED TO RESONANCE
(uniform current distribution)
160 * (PI)2 * h2 / wavelength2 3.0
SHORT VERTICAL MONOPOLE OVER PERECT GROUND
(H <1/8-wave), 
BASE INDUCTIVELY LOADED TO RESONANCE
(linear current distribution)
40 * (PI)2 * h2 / wavelength2 3.0
SMALL LOOP (LARGEST DIMENSION < 0.15-wave),
area A, number of turns N
(uniform current distribution)
320 * (PI)4 * A2 * N2 / wavelength4 1.5

HOW TO USE THIS TABLE:
 

Determine the desired antenna feed current I, in amperes
Calculate Rrad for the specific antenna to be used for transmitting the signal, in ohms

Calculate transmitter radiated power, Prad = I2 * Rrad ,  in watts

Calculate power density at a distance D away, S = Prad * Gd / (4 * (PI) * D2) , in watts/meter2

Finally, calculate the signal electric field strength, E = SQRT( 120 * (PI) * S ) , in volts/meter

Yes, it really is this simple to determine accurately the theoretical electric field strength in volts/meter from any single conductor antenna used as a transmitting antenna!

Broadcasters prefer vertical grounded antennas because (i) they radiate uniformly regardless of direction, (ii) the angle of radiation is low, along the horizon where it is most useful, (iii) they provide a 2x gain factor over a dipole, because of reflection from the ground, resulting in 1.41x the field strength everywhere, (iv) they provide vertical polarization of the waves and therefore some immunity against power line electrical noise sources which are usually horizontally polarized.  Using a loop antenna for a broadcast receiver also provides some immunity from electric fields due to it being a magnetic loop.  The ground becomes more and more perfect as the frequency is lowered.  550 kilocycles is more than 3x better than 1100 kilocycles.  Lower frequencies are more valuable for ground wave propagation.



 
 

COMPARISON OF RECEIVING ANTENNAS

Antenna
Effective Area
 Aeff = Gd * wavelength2 / (4 * (PI) )
(square meters)
Effective Length
 Leff= SQRT( Rrad * Gd * wavelength2 / (120 * (PI)2 ) )
(meters)
current element, length dl 0.1194 * wavelength2 dl
1/2-wave DIPOLE
(sinusoidal current distribution)
0.1305 * wavelength2 0.31794 * wavelength
1/4-wave VERTICAL MONOPOLE OVER PERFECT GROUND
(sinusoidal current distribution)
0.2610 * wavelength2 0.31794 * wavelength
SHORT VERTICAL MONOPOLE OVER PERFECT GROUND
(H < 1/8-wave),
TOP CAPACITIVELY LOADED TO RESONANCE
(uniform current distribution)
0.2387 * wavelength2 2 * H
SHORT VERTICAL MONOPOLE OVER PERECT GROUND
(H <1/8-wave), 
BASE INDUCTIVELY LOADED TO RESONANCE
(linear current distribution)
0.2387 * wavelength2 H
SMALL LOOP (LARGEST DIMENSION < 0.15-wave),
area A, number of turns N
(uniform current distribution)
(untuned loop Q = 1; if tuned, use circuit Q)
0.1194 * wavelength2 * Q2 2* (PI) * A * N * Q / wavelength

HOW TO USE THIS TABLE:
 

Determine the received power density S, in watts/meter2
Calculate Aeff for the specific antenna to be used for receiving the signal, in square meters

Finally, open circuit antenna voltage, V = 2 * SQRT ( S * Aeff * Rrad ) , in volts

 - OR -

Determine the received electric field strength E, in volts/meter

Calculate Leff , in meters

Calculate open circuit antenna voltage, V = E * Leff , in volts

Either method gives identical results.  Remember when antenna is terminated into a matched load = Rrad, 
actual voltage = 1/2 * V.  Loop antennas for receiving are normally operated open circuit.

Yes, it really is this simple to determine accurately the theoretical open circuit antenna voltage in volts from any single conductor antenna used as a receiving antenna!