Voltage and Current Output from a “Stubby” Dipole Immersed in a
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Voltage and Current Output from a “Stubby” Dipole
Immersed in a
Vertically Oriented 1000 Volt/meter E Field
--- a Simple E Field Sensor ---
A Finite Element Model Solved Using FlexPDE
Craig E. Nelson
Consultant Engineer
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Background:
A “stubby” dipole antenna may be used as an electrostatic field sensor. For a long time I have been interested in knowing the extent to which such an antenna sensor will distort the electric field within which it is immersed.
The following numerical experiment provides results for one simple physical situation. No attempt at sensor optimization has been made. Many further extensions of this experiment are easily possible.
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Problem Geometry and Physical Layout
of the
Solution Domain
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Copper RodLength = 20 cmRadius = 5 cm
Conductivity = 5.99e7
Copper RodLength = 20 cmRadius = 5 cm
Conductivity = 5.99e7
Hi Resistance RodLength = 10 cmRadius = 5 cm
Conductivity = 6.36e-7
1000 Volts/meter E Field
Vout Plus
Vout Minus
Iout
1000 Volts/meter E Field
3-D Sensor Physical Layout
Vout
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Solution Domain (cylindrical Geometry)
Centerline
“Stubby” Dipole
1000 Volt/meter E Field
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Equations and Boundary Conditions
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
The Partial Differential Equation to be Solved is: div ( J ) = 0
in cylindrical (r,z) coordinates: div ( J ) = (1/r)*dr( r*Jr)+ dz( Jz) = 0
where: Jr=cond*Er Jz=cond*Ez J=vector( Jr,Jz ) Jm=magnitude(J)
Jr and Jz are the current densities in the r and z directions (amps/meter^2)
and: Er= -dr(U) Ez=-dz(U) E=-grad(U) Em=magnitude(E)
Er and Ez are the electric field strength in the r and z directions (volts/meter)
and: cond = conductivity in the different solution sub domains (siemens/meter)
The Boundary Conditions are:
Natural (U) = 0 on the centerline and domain outer wall (Neuman)Value (U) = FieldStrength*Hdomain/2 on the top surface (Dirichlet)Value (U) = - FieldStrength*Hdomain/2 on the bottom surface (Dirichlet)
where: U is the potential (volts)
and: Fieldstrength and Hdomain are given parameters
note: dr(J) = d(J) / d(r) dz(U) = d(U) / d(z) and so on
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Numerical Experiment Results
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Contour Plot of Potential (referenced to the load resistance vertical axis center)
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Contour Plot of Potential (referenced to the load resistance vertical axis center)
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Contour Plot of Electric Field Strength (volts/meter)
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Contour Plot of Electric Field Strength (volts/meter)
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Contour Plot of log base 10 of Electric Field Strength(three = 1000 volts/meter)
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Contour Plot of log base 10 of Electric Field Strength
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Plot of Potential along the Solution Domain Centerline (volts)
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Plot of Electrical Field Strength Magnitude along the Solution Domain Centerline (volts/meter)
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Plot of log base 10 of Electrical Field Strength Magnitude along the Solution Domain Centerline(zero = 1 volt/meter)
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Model Parameters and Calculated Results
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Summary and Conclusions:
A numerical experiment analysis of a “stubby” dipole antenna electric field sensor has been accomplished.
The analysis shows that the despite a moderately high electric field strength of 1000 volts/meter, the sensor output voltage and current are rather small. Apparently only a few tens of micro volts appear across the resistive load (upper to lower terminal resistance given as 10 megohm) with a load current flow of several pico-amps.
This is because the highly conducting copper dipole arms “short” the electrical field to near zero in regions close to the conductors. It would seem that this particular configuration is far from optimal.
Many other configurations are possible and could be analyzed by the method presented here