Hello all,
here some equations I found in my book regarding
radiation resistance of dipoles and monopoles:
the original equation based on current profile on dipole/monopole,
all other published equations are derivates therof.
l=physical half length of dipole [m]
d=physical diameter of dipole [m]
w=wavelength in [m]
f=radian angle
k=2*PI*l/w
Rs=120 Ohms / (sin^2(k)*INTEGRAL(f=0 to
0.5*PI){[cos(k*sin(f))-cos(k)]^2/cos(f) df}
restriction: l/w =< 0.38
simple Approximation
Rs=80 Ohms * [1-1.32*(l/w)^2] * tan^2(PI*l/w)
restriction: l/w =< 0.25
more simpler Approximation
Rs=790 Ohms * (l/w)^2
restriction: l/w =< 0.14
Rs for Monopole above groundplane is half the
dipole value in each of above equation, when
l=the physical height of the monopole in [m]
Additionally the equations to calculate the
antenna reactance:
l=physical half length of dipole [m]
d=physical diameter of dipole [m]
w=wavelength in [m]
f=radian angle
Zw=120 Ohms * [ln(4*l/d) -1]
k=2*PI*l/w
Xd=X1d-(Zw/(tan(k)))
Xm=X1m-(Zw/(tan(k)))
restriction: l/w =< 0.25
X1d=552 Ohms * (l/w)^1.85 if 0.14 <= l/w <=0.25
X1d=156 Ohms * (l/w)^1.22 if l/w < 0.14
X1m=276 Ohms * (l/w)^1.85 if 0.14 <= l/w <=0.25
X1m=78 Ohms * (l/w)^1.22 if l/w < 0.14
Best 73
Gamal Soegiono (SWL)
50N01 / 08E27 / JO 40 fa
[email protected]
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