David's Useful Information: Antennas and Propagation


DIPOLE

gain 1.64x

    E*L*SQRT(R)
V = -----------    (approx)
       53.7

i.e. when matched


    (E*L)^2
P = -------
     2888

  where V = voltage across load
        P = power into load
        L = wavelength
        E = field strength (V/m)
        R = dipole impedance


DIPOLE EQUIVALENT CIRCUIT

RA = 412.88*(log(S)^2)+7407.54*(S^-0.02389)-7274.08 ohms

          [       0.89075         ]
CA = 2*H*([ --------------------- ]-0.02541) pF
          [ (log(S)^0.8006)-0.861 ]

LA = 2*H*(148.13*(log(S)^1.012)-61.88) nH

       12.0674*H
CB = ------------- pF
     log(S)-0.7245

  where S = 4*H/D,  H = dipole half length,  D = dipole diameter

ref. Program Synthesizes Antenna Matching Networks for Maximum Bandwidth
Robert J. Dehoney, RF Design May 1995


YAGI-UDA ANTENNA

3 element, dimensions in wavelengths

|    |    |          r = 1/2  e = 1/2  d = 0.9*1/2  a = 1/2  b = 0.8*1/2
|r   |e   |d
|    |    |          gain = 7dB
  a     b

ref. Reference Data for Radio Engineers, 5th edition, p. 25-14


PARABOLIC DISH GAIN

G = n*(PI*d/L)^2

  where d = diameter
        n = efficiency (typ 55%)


SHORT MONOPOLE

R = 40*(PI*h/L)^2

      [   1-ln(h/a)   ]
X = j.[ ------------- ]*L/h
      [ (2*PI)^2*e0*C ]

  where L  = wavelength
        h  = height  (h << wavelength)
        a  = radius
        e0 = permittivity of free space (8.8542E-12)
        C  = speed of light


IMPEDANCE OF FREE SPACE

120*PI ohms


CORNER REFLECTOR

distance from apex of (90deg) corner and dipole between 0.25 and 0.7 wavelength
length at least wavelength
height at least 5/8 wavelength


RECEIVED POWER FROM AN ANTENNA

         [  L^2 ]
P = Sr*G*[ ---- ]
         [ 4*PI ]

      [  (E*L)^2 ]
  = G*[ -------- ]
      [ 480*PI^2 ]

  where Sr = power density (watts/m)
        E  = field strength (V/m)
        G  = antenna gain

ref. Reference Data for Radio Engineers, 5th edition, p. 25-8


HF CHANNEL FADING

Typical fading rates for HF channels 6-16 per minute.

CCIR Classifications

  1)  Good Conditions

        Multipath spread : 0.5 mSec

        Frequency spread : 0.1 Hz

  2)  Moderate Conditions

        Multipath spread : 1 mSec

        Frequency spread : 0.5 Hz

  3)  Poor Conditions

        Multipath spread : 2 mSec

        Frequency spread : 1 Hz

  4)  Flutter Fading (if required)

        Multipath spread : 0.5 mSec

        Frequency spread : 10 Hz


Fading Rate (Hz) = 0.7375 * frequency spread


POLARISATION LOSS
                                                             [      cos(2*a)     ]
relative power = K*(1+-r1*r2)^2+(r1+-r2)^2+(1-r1^2)*(1-r2^2)*[ ----------------- ]
                                                             [ (1+r1^2)*(1+r2^2) ]

  where K  = constant
        r1 = axial ratio of wave
        r2 = axial ratio of antenna
        a  = angle from maximum amplitude

  axial ratio = ratio of minor to major axis of polarisation ellipse

i.e. for linear polarisation, relative power = (1+cos(2*a))/2

ref. Reference Data for Radio Engineers, 5th edition, p. 25-3


FREE SPACE ATTENUATION BETWEEN ISOTROPIC ANTENNAS

          [  Ar*At  ]
a = 10*log[ ------- ]
          [ (d*L)^2 ]

  where a = attenuation in dB
        At, Ar are effective areas
        L = wavelength
        d = distance in metres

  (valid for d >> 2*l^2/L, where l is the largest linear dimension of either antenna)

or;

a = 20*log(f) + 20*log(d) - 27.54

  where f = frequency in MHz

adapted from Reference Data for Radio Engineers, 5th edition, p. 26-19


LIMITS FOR FREE-SPACE TRANSMISSION APPROXIMATION

First Freznel zone should clear all obstacles in the path

Radius of first Freznel zone

    [ L*(d1*d2) ]^0.5
R = [ --------- ]
    [  (d1+d2)  ]

  where L  = wavelength
        d1 = distance from source
        d2 = distance from receiver

ref. Reference Data for Radio Engineers, 5th edition, p. 26-15


EFFECTIVE EARTH RADIUS

Due to decrease of refractive index with height.
Ratio of effective earth radius to true earth radius is usually taken to be 4/3, but can vary
between 0.6 & 5.0 in temperate climates.

ref. Reference Data for Radio Engineers, 5th edition, p. 26-12


DISTANCE TO RADIO HORIZON

d = ((3*K*h)/2)^0.5

  where d = distance in miles
        K = ratio of effective earth radius to true earth radius
        h = height in feet

ref. Reference Data for Radio Engineers, 5th edition, p. 26-12


TRANSMISSION PATH LOSS

a = 20*log(f) + 40*log(d) - 20*log(ht*hr) - 32 

  where a = attenuation in dB
        d = distance in metres
        ht, hr are receiver and transmitter antenna heights in metres

adapted from Egli


FAR FIELD RADIATION PATTERN OF A SHORT DIPOLE

E = (30*I*B/r) * exp(j*(w*t-B*r)) * sin(th)

  where E  = electric field in V/m,  I = current in Amps,  w = frequency (rad/sec),
        B  = 2*PI/wavelength,  r = distance in metres,
        th = spherical co-ordinate azimuth angle in radians.

ref. Estimating Radiated Emissions from Electronic Products
Peter Vizmuller, RF Design August 1996