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 lownoise receiver environments are far more important
in ensuring long distance radio transmission.
DATA BASED ON QUARTERWAVELENGTH
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} * dl^{2} / wavelength^{2} 
1.5 
1/2wave DIPOLE
(sinusoidal current distribution) 
73.0 
1.64 
1/4wave VERTICAL MONOPOLE OVER PERFECT GROUND
(sinusoidal current distribution) 
36.5 
3.28 
SHORT VERTICAL MONOPOLE OVER PERFECT GROUND
(H < 1/8wave),
TOP CAPACITIVELY LOADED TO RESONANCE
(uniform current distribution) 
160 * (PI)^{2 }* h^{2 }/ wavelength^{2} 
3.0 
SHORT VERTICAL MONOPOLE OVER PERECT GROUND
(H <1/8wave),
BASE INDUCTIVELY LOADED TO RESONANCE
(linear current distribution) 
40 * (PI)^{2} * h^{2} / wavelength^{2} 
3.0 
SMALL LOOP (LARGEST DIMENSION < 0.15wave),
area A, number of turns N
(uniform current distribution) 
320 * (PI)^{4} * A^{2} * N^{2} / wavelength^{4} 
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 = I^{2} *
Rrad , in watts
Calculate power density at a distance D away, S = Prad * Gd /
(4 * (PI) * D^{2}) , in watts/meter^{2}
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 * wavelength^{2} / (4 * (PI)
)
(square meters)

Effective Length
Leff= SQRT( Rrad * Gd * wavelength^{2}
/ (120 * (PI)^{2} ) )
(meters)

current element, length dl 
0.1194 * wavelength^{2} 
dl 
1/2wave DIPOLE
(sinusoidal current distribution) 
0.1305 * wavelength^{2} 
0.31794 * wavelength 
1/4wave VERTICAL MONOPOLE OVER PERFECT GROUND
(sinusoidal current distribution) 
0.2610 * wavelength^{2} 
0.31794 * wavelength 
SHORT VERTICAL MONOPOLE OVER PERFECT GROUND
(H < 1/8wave),
TOP CAPACITIVELY LOADED TO RESONANCE
(uniform current distribution) 
0.2387 * wavelength^{2} 
2 * H 
SHORT VERTICAL MONOPOLE OVER PERECT GROUND
(H <1/8wave),
BASE INDUCTIVELY LOADED TO RESONANCE
(linear current distribution) 
0.2387 * wavelength^{2} 
H 
SMALL LOOP (LARGEST DIMENSION < 0.15wave),
area A, number of turns N
(uniform current distribution)
(untuned loop Q = 1; if tuned, use circuit Q) 
0.1194 * wavelength^{2} * Q^{2} 
2* (PI) * A * N * Q / wavelength 
HOW TO USE THIS TABLE:
Determine the received power density S, in watts/meter^{2}
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!
