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Pulsed Power Toolbox




This is the start of a collection of Pulsed Power related formulas and calculators that I found usefull. However, whenever I could find resources on the internet already, I tried to refer to them rather than to re-invent the wheel. Consequently you might also find some of the links provided helpful.
 



Parameters for Nanosecond Pulsed Electric Field Exposures



This calculator allows derivations for 'standard' experiments in electroporation cuvettes as they are common at the Center for Bioelectrics.
The calculator can not be used for more complex geometries and conditions such as used in in vitro experiments!

Standard
Electropoaration Cuvette
gap distance:
d = 1, 2, or 4 mm

   
Calculation of Required Pulse Voltage:
electric field wanted: E =    kV/cm
electrode separation: d =    mm
voltage needed: kV

Energy Delivered Per Pulse:
The calculation uses the input for electric field and gap distance above!
pulse duration: τ =    ns
conductivity of buffer/suspension: σ =    mS/cm
energy: J
energy density: J/cm3

Charge Transfered Per Pulse:
The calculation uses the input for electric field, gap distance, and conductivity above!
charge: µAs

Temperature Increase of Suspension Per Pulse (Adiabatic):
The calculation uses the input for electric field, gap distance, and conductivity above!
temperature-change: K
  
Notes:

  1. The pulse generators at the Frank Reidy Research Centers are usually hooked up to an oscilloscope with Tektronix voltage probe P6015A. Since we usually have not set a calibration value on the oscilloscope the 'real' voltage applied to the cuvette measured in kilovolts (kV) is observed on the oscilloscope in volts (V). This means, if you have/need for example a voltage of 10 kV applied to the cuvette, the pulse amplitud observed on the oscilloscope is 10 V.
  2. The calculations here are only valid for the simple geometry of a cuvette filled with a liquid. More complex geometries, samples and experiments, such as used for example in in vitro experiments can not be analyzed straight forward with the calculators here.
  3. The calculation of the temperature increase assumes a specific heat capacity of 4.2 kJ·kg-1·K-1, it is assumed that it is basically water that is heated. The heated volume is calculated automatically from the gap-distance and the known electrode area, which is the same for any electroporation cuvette independent from the manufacturer.
  4. The transfered charge per pulse (used as scaling parameter for the charging of cell membranes "E·τ") is given in units of "µAs," i.e. "micro-amps-seconds," or equivalent "micro-coulombs."
  5. Conversion from resistivities to conductivities:
    resistivity of suspension: ρ =    Ω·cm
    conductivity: mS/cm
    For all practical purposes, can the conductivity of a cell-suspension substituted by the conductivity of the buffer.
  6. If any of the computations for energy, energy density, charge, or temperature change results in zero, then the calculated value is so small that it is negligible. (Smaller than two digits after the decimal point for the given unit.)
 		  
 



Formulas for the Calculation of Common Inductances*)

(unless otherwise noted use SI-units in all presented formulas)

*) Planar geometries which are not very common in pulsed power systems are not covered in this table. Readers are refered to references 1, 6 and especially 8. More information on rectangular loops can be found here:
http://www.qsl.net/in3otd/rlsim.html

Of course no guarantee is given for the accuracy of the listed formulaes or the calculators although I tried my best to select the formulas carefully from the literature. Please let me know when you find any mistakes.


 

inductance

formula

example

long, thin wire
(as segment of closed circuit)





(reference 1)
  r = mm
  l = cm
nH

conductor from parallel wires
(current runs in same direction)
r << d





(reference 8)
  l = cm
  w = mm
  r = mm
nH

return circuit of parallel wires
(current runs in opposite directions)
r << d





(reference 1)
l = 100 cm
w = 2 cm
r = 0.5 mm
L = 1.478 mH

strip line
(as segment of closed circuit)





(reference 1)
l = 100 cm
w = 50 cm
d = 1.0 mm
L = 1.185 mH

return circuit of parallel plates
(current runs in opposite directions)





(reference 2)
  l = cm
  w = mm
  d = mm
nH

coaxial cable





(reference 2)
  l = cm
  R = mm
  r = mm
nH

loop





(reference 1)
  R = mm
  r = mm
nH

single layer solenoid


 
N: number of turns




"F-factor" is computed automatically



(reference 7)
  R = mm
  l = cm
  N =
mH

"Where great accuracy is required, a correction factor may be applied to the equation to take account of the fact that the coil is wound of spaced round wires rather than with a uniform current sheet. This correction rarely exceeds 0.5%, is greatly for widely spaced turns, and increases with the number of turns." (see reference 7 for details)


single layer short solenoid
(l < 0.8 R)


 
N: number of turns




Nagaoka-factor K is computed automatically



(reference 1)
  R = mm
  l = cm
  N =
mH

single layer long solenoid
(l > 0.8 R)


 
N: number of turns





(reference 1)
  R = mm
  l = cm
  N =
mH

single layer very long (ideal) solenoid
(l >> 2R )


 
N: number of turns





(reference 3)
  R = mm
  l = cm
  N =
mH

multi layer solenoid


  
N: number of turns


"F-factor" and correction factor B are computed automatically

correction factor dL for insulation thickness:


            D : distance between wire centers
            d : diameter of bare wire


(reference 9)
  R = mm
  l = cm
  w = mm
  N =
mH
  R = mm
  N =
  D = mm
  d = mm
mH

multi layer thin wall solenoid


 
N: number of turns







(reference 4)
N = 1000
d = 10 mm
l = 5 cm
mr = 1
L = 1.645 mH

toroid


 
N: number of turns







(reference 4)
  N =
  R = mm
  D = cm
  mr =
mH

spiral (flat coil)


 
N: number of turns




(Wheeler formula)

(reference 1)
N = 20
R = 5 cm
w = 2 cm
L = 63.501 mH
windings cover entire area




(Schieber formula)

(reference 1)
N = 20
R = 5 cm
L = 1.380 nH

Both formulas can also be used for printed flat coils. For the Wheeler formulas errors up to 20% have been reported. A more accurate calculation takes the ratio between coil radius, R, and winding-thickness, w, into account (Grover method). See reference 1 for details.


conical coils


 
The inductance of conical coils is calculated from the geometric sum of the helical and the planar contribution. See reference 5 for details.



LH : inductance of equivalent helical coil
LP : inductance of equivalent planar coil


(reference 5)

   references

    1) Marc T. Thompson, "Inductance Calculation Techniques - Part II: Approximations and Handbook Methods," www.pcim.com, 1999.
    2) home.san.rr.com/nessengr/techdata/inductance/induc.html
    3) H. Stöcker,Taschenbuch der Physik, Verlag Harri Deutsch, Frankfurt/Main, 1994, p. 334 (f = 1).
    4) Formelsammlung Passive Bauelemente, www.iwe.uni-karlsruhe.de/download/WWW_PB_WET_FS.pdf
    5) Herb's Tesla Page (Design Page), http://home.wtal.de/herbs_teslapage/design.html#des-2pri
    6) University of Missouri-Rolla, Electromagnetic Compatibility Laboratory, www.emclab.umr.edu/new-induct, 2001.
    7) F.E. Terman, Radio Engineers' Handbook, McGraw-Hill, New York, 1943, p.53.
    8) F.W. Grover, Inductance Calculations, Dover Publications, Mineola, 2004, p.37.
    9) F.E. Terman, Radio Engineers' Handbook, McGraw-Hill, New York, 1943, p.60.