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Voltage and Current Output from a “Stubby” Dipole Immersed in a

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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

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.

1000 Volts/meter E Field

Copper Rod

Length = 20 cm

Radius = 5 cm

Conductivity = 5.99e7

Vout Plus

Iout

Hi Resistance Rod

Length = 10 cm

Radius = 5 cm

Conductivity = 6.36e-7

Vout

Copper Rod

Length = 20 cm

Radius = 5 cm

Conductivity = 5.99e7

Vout Minus

1000 Volts/meter E Field

3-D Sensor Physical Layout

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

Contour Plot of Potential (referenced to the load resistance vertical axis center)

Contour Plot of Potential (referenced to the load resistance vertical axis center)

Contour Plot of log base 10 of Electric Field Strength

(three = 1000 volts/meter)

Plot of Electrical Field Strength Magnitude along the Solution Domain Centerline (volts/meter)

Plot of log base 10 of Electrical Field Strength Magnitude along the Solution Domain Centerline

(zero = 1 volt/meter)

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

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