Answer to Grant Bingeman question of 21 June 1998 :
Assumptions : wire length = 1.0 meter
field strength = 1 volt / meter
wavelength ( Lambda ) = 1 meter
conjugate load : Rr - jX = Rl + jX
( source or radiation resistance = load impedance )
only real resistances considered
horizontal dipole in free space
Question : will the induced voltage equal the field strength ?
what is the maximum voltage for a resistor in the center
of the dipole ?
Answers : Assumptions will be applied to three different dipoles :
1. Hertz dipole - short compared to wavelength with uniform
current distribution.
2. short dipole - short with triangular current distribution.
3. Lambda - Half dipole - dipole length = 1/2 Lambda = 1 meter
Characteristics of dipoles :
Dipole Rr= Rad.Res. Effect.Receive Area Numerical Gain
Hertz 80*pi^2*(l/L)^2 1.5*L^2/4*pi 1.5
short 20*pi^2*(l/L)^2 1.5*L^2/4*pi 1.5
L/2 73.1 1.64*L^2/4*pi 1.64
" Open Voltage " for E = 1 V/m on 1 m long wire :
V = E * l = 1 volt
Voltage when load resistance = radiation resistance : Voltage will be
dericed from received power, when field strength is E = 1 V/m :
P = S * Ae [ watt ]
where S = power density [ W / m^2 ]
Ae = effective receive area [ m^2 ] of dipole
S = 1/2*E^2/Zo = 1.326E-3 [ W / m^2 ]
where Zo = 120 * pi = 377 ohm ( free space impedance )
Received power from above :
Hertz Dipole: P = 1.583E-4 [ W ]
short Dipole: P = 1.583E-4 [ W ]
L/2 Dipole : P = 1.731E-4 [ W ]
Determine received voltage from received power :
Ve = [ 2*P*(Rr + Rl)^2/Rl ]^1/2
where Ve = effective voltage
Received voltage :
Hertz Dipole : Ve = 1.0 [ V ]
short Dipole : Ve = 0.5 [ V ]
L/2 Dipole : Ve = 0.32 [ V ]
Received Ve with high resistance load, e.g., 100 k ohm :
Hertz Dipole : Ve = 5.67 [ V ]
short Dipole : Ve = 5.64 [ V ]
L/2 Dipole : Ve = 5.89 [ V ]
Definition : Ve = Vpk/2^1/2
Vpk = Ve*2^1/2
Max Schmitt
Received on Tue Jul 21 1998 - 10:24:09 EDT
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