Electro-Magnetic Waves

Electric and Magnetic interference which propagates/radiates in space at the speed of light (c = 299792458 m/sec). The fundamental variables are:

E electric field
D electric flux density (D = ε E)
H magnetic field B magnetic displacement (B = µ H)
ρ density of charges J density of currents (div J + ∂ρ/∂t = 0)

Electromagnetic Waves are produced by sources that can be divided into two types: currents and fields. Four Maxwell equations fully define all sources and fields:

  1. curl E = – ∂B / ∂t
  2. curl H = J + ∂D / ∂t
  3. div D = ρ
  4. div B = 0

for harmonic waves:

  1. (1) curl E = -jωµ H
  2. curl H = J + jωε E
  3. div E = ρ/ε
  4. div H = 0

Frequency and Wavelength

cycles in Time

Fig 1: Wavelength vs Time

Electo-Magnetic waves are harmonic functions of time thus they have specific wavelength λ (Greek symbol LAMDA ((distance between planes of equal phase)) and frequency f (cycles per second).

λ f = c For practical purposes: λ (cm) = 30 / f (GHz)

In Figure One we can see that a cycle is where the full phase of a wave crosses the Zero line, where as a Wavelength is measured from the top of the peak of the Wave to the next peak.
Oscilloscopes for Radio Amateurs: Add a Scope to Your Ham Shack Will give you a better understanding of how to use an Oscilloscope in your shack for measuring many things.

Electro-Magnetic Frequency
3khz – 300GHz 0.003 – 4 x 1014Hz 4 – 7.5 x 1014Hz 7.5 x 1014 – 3 x 1016 Hz < 1020 Hz
Radio, Microwaves and Millimeter waves Infrared Visible Light X-Rays Gamma Rays (γ)


Within the Bottom section 3Khz to 300Ghz we have the following:

Radio Frequency
3 – 30 kHz 30 – 300 kHz 0.3 – 3 MHz 3 – 30 MHz 30 – 300 MHz 0.3 – 3 GHz 3 – 30 GHz 30 – 300 GHz


Out of interest, specifically is that HF covers up to 30mhz, which means that 10m is within the VHF band, so for all of you HF only people, if you work ten meters, your actually working VHF!!!

Within the Radio Frequency table the UK bandplans are available here

Planar Waves

Propagation of EM Waves in free space

Propagation of EM Waves in free space

In free space all forms of propagation converge into a “TEM” (Transversal Electric Magnetic) mode in which equal phase surfaces are planes. The free space waves are called “planar waves”. The electric field has only one direction (θ ) The magnetic field has only one direction (φ) and both are perpendicular to propagation vector (r). The “Wave Impedance” is the ratio between the E field and the H field E/H = 120π = 377 Ω This is where a lot of Maxwell’s equations are used.




Power and Energy

The EM waves carry energy along the vector of propagation. The average amount of energy as a function of time is the power (measured in Watts). The EM power ( P) propagates along the vector r (“poynting vector”) P = 0.5 ∫ (E X H) dS.


-30db 0.001
-20db 0.01
-17db 0.02
-10db 0.1
-6db 0.25
-3db 0.5
0db 1
3db 2
6db 4
10db 10
13db 20
20db 100
30db 1000


As you may recall Decibels are also used to represent Power as dBW and DBm

dBw / dBm
-57 dBW 2 x 10^-6 Watts
-20 dBW 0.01 Watt
0 dBW 1 Watt
10 dBW 10 Watts
or in dBm
-66 dBm 0.25 x 10^-6 mW
0 dBm 1 mW
20 dBM 100 mW

And also used to represent the Gain of Antenna’s
The “gain relative to a dipole” is thus often quoted and is denoted using “dBd” instead of “dBi” to avoid confusion. Therefore in terms of the true gain (relative to an isotropic radiator) G, this figure for the gain is given by: GdBd = 10 x Log10 (G / 1.64)

Diffraction Principal

For more information on Fresnel and Frounhofer their research was in the way of Optics!

EM waves are created by antennas in accordance with the diffraction principle (super-position of all point sources). The creation of planar waves depends on the completion of diffraction and interference of the antenna sources. We separate the distance from antenna into three regions:

  1. Reactive Near Field
  2. Radiated Near Field (“Fresnel zone”)
  3. Far Field (“Frounhofer zone”)

Antenna DefractionThe Reactive Near Field:

In the immediate vicinity of the antenna, we have the reactive near field. In this region, the fields are predominately reactive fields, which means the E- and H- fields are out of phase by 90 degrees to each other (recall that for propagating or radiating fields, the fields are orthogonal (perpendicular) but are in phase). R < 0.62√D3

Where the antenna acts as a resonator and its impedance is influenced by the existence of near objects. R reactive < λ/2π to λ/4 In this region one should avoid any obstacle to the antenna including radomes.

The boundary of this region is commonly given as:

The Radiated Near Field (Fresnel): The radiating near field or Fresnel region is the region between the near and far fields. In this region, the reactive fields are not dominate (do not have a commanding influence on; exercise control over.); the radiating fields begin to emerge. However, unlike the Far Field region, here the shape of the radiation pattern may vary appreciably with distance.

Where the antenna radiates but the waves are not planar. R near field > 0.6 √ d³/λ
Note that depending on the values of R and the wavelength, this field may or may not exist.

The Far Field (Frounhofer): This as you may expect is the region where the antennas wave no longer changes shape with distance!  Although the fields still die off as 1/R, the power density dies off as 1/R^2 which is a natural occurrence in physics.

Where the antenna completes the diffraction process and waves are planar. R far field > 2d²/λ d is the typical dimension of the antenna

If the maximum linear dimension of an antenna is D (being a typical antenna), then the following 3 conditions must all be satisfied to be in the far field region:

  1. R > 2D2
  2. R >> D
  3. R >> λ

More to follow

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