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Frequency to wavelength
 
In free space, one wavelength equals 299,800 meters divided by frequency in kilohertz. Examples:
 
frequency
 free-space
                                     wavelength  
(kHz)                          (meters)  (feet)  
530                               566      1856  
900                               333      1093  
1400                             214       703  
1700                            176       579  

Radio waves travel more slowly in a conductor than in space. One result is that practical antennas can be 3 to 5 percent smaller than the free-space wavelength size. For example, a half wavelength at 1 MHz is about 150 meters, but a half-wave dipole made for that frequency only needs to be 142 to 145 meters long. The exact electrical length of an antenna depends on the ratio of wavelength to conductor diameter, and on the effect of supporting insulators at the ends.

radiation resistance and efficiency
"Radiation resistance" (not to be confused with impedance) refers to the energy absorbed into free space from the antenna circuit. A higher radiation resistance indicates more energy is being radiated into space.
 
The approximate radiation resistance (RR) of a short vertical antenna (not endowed with loading coils or capacitance hat) can be found by this equation:
 
   400 height2  
RR = --------- 
   wavelength2  

Example: An antenna for a frequency of 1700 kHz (wavelength = 176 meters) is 5 meters tall. Radiation resistance is about 0.32 ohms.
 
If the antenna is 1/16 wavelength tall, the radiation resistance will be around 2 ohms. If 1/8 wavelength tall, 7.5 ohms.
The efficiency of a vertical antenna system is given by: 
  
                                    RR  
efficiency = ---------------------------------  
   ( RR + Ground Loss + Loading Coil Loss )  

Example: Radiation resistance is 2 ohms, ground loss is 3 ohms, and loading coil loss is 2 ohms. Efficiency is 0.285 or about 29 percent. If 10 watts were input to this antenna, 2.9 watts would be radiated into space and the rest would be dissipated in the system losses.

 
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