Ozone Cell

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Ozone Cell

• Alan Millner 01-18-2005

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Review of the Field of a Pair of Oppositely
Charged Plates in Vacuum

• By symmetry, no field outside
• If plates have charge Q, area A, then by Gauss
  Law D ?0E Q/A between plates
• If separation is d, then
• V dE dQ/ ?0A or Q (?0A/d)
• If the capacitance C ?0A/d then
• Q C V
• Energy W ½ QV ½ ?0E2 (dA)
• Or, W ½ C V2

Q
-Q
A
d
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Polarization and Dielectric Constant

• Suppose we have a polarization between the plates
  P proportional to E
• Gauss Law says D P ?0E Q/A
• Define dielectric constant in a material ? by
• P (? -?0) so D ? E Q/A
• So V dE dQ/ ?A , or Q CV
• where capacitance C ?A/d
• (substitute ? for ?0)
• Note W ½ C V2 ½ ? E2 (dA)
• Energy density times volume

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Design Constraints

• Need 4E7 volts/meter across O2 to make O3
• Broad optimum around 30kHz
• Need insulating layer to avoid arc damage
• Alumina from Kyocera is good
• Need 11000 round shape factor for support
• Over 4kV becomes difficult to insulate
• Fewer larger cells are less expensive
• NOW YOU DESIGN AN OZONE CELL

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Ozone Cell Construction
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Equivalent Circuit
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Ozone Cell Analysis
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Energy
W ? vI dt W ? v (dQ/dt) dt ? vdQ For linear
C, Q CV dQ C dv W ? Cvdv from v0 to
vV W ½ C V2 Or W ½ VQ (area under curve of
V vs Q)
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Energy in a field

• V Ed Efield/gap
• QDA Dfieldarea
• W (dA) (? EdD)
• Volume V dA
• W volume energy per unit volume V U
• If linear, D ?E and U ? EdD ½ ? E2

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Displacement current

• I dQ/dt
• Q AD A ?E
• So I d(A ?E )/dt, I/A d(?E )/dt
• We may identify d(?E )/dt as displacement current
  density
• Like jI/A current density
• Note later
• ? Hdr ?? j d(?E )/dt dA
• so a loop around either current J or displacement
  current d(?E )/dt
• produces the same H field

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Fringe fields

• If C Co Cfringe
• W Wo Wfringe
•  
• Cfringe/Co Wfringe/ Wo
• If Efringe lt Eo then
• Cfringe/Co lt Vfringe/ Vo
• Vo dA
• Vfringe d2 P where P perimeter

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Fringe fieldsexample

• Our example of a circular capacitor, radius R
• Vo d? R2
• Vfringe d2 2?R
• Vfringe/Vo 2d/R
• In our example, better than 1.

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Field Patterns
Consider 2 dimes, arranged on an axis, 10 meters
apart, oppositely charged to 1 coulomb What
does the field pattern look like 1. within 1 mm
of the positive dime's surface? 2. one meter from
the positive dime? 3. 5meters from the axis
center? What is the field strength at each
location above?