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H U M A N BODY CAPACITANCESTATIC OR DYNAM IC CONC EPT ?

Niels JonassenDepartment of Physics, Bldg;. 307Technical University of Denmark2800 Lyngby, Denmarlkphone: +45 45 25 31 27, fax: +45 45 93 27 66, e-mail: mr.static@scientis,t.com

AbstractA standing, human body insulated from ground by footwear and/or floor covering is in principle an in-sulated conductor and has, as such, a capacitance, i.e. the ability to sto re a charge and possibly dischargethe stored energy in a spark discliarge.In tlie human bo model the himan b o 4 cupacitance (HBC) is traditionally chosen as 100 pF.However, a simple geom etric mo del seems to suggest considera'bly higher values.A series of experiments, where the capacitance of standing persons were determined for various combi-nations of footwear and floor coverings, gave values in the orcler of 100-150 pF, when the capacitancewas determined by an AC-bridge measurement, but 200-400 pF, when the traditional static charge-sharingmethod was used.Further experiments indicate that th e two me thods give the sam e result, whe n the ellectric flux is well lo-cated in a dielectric othet- than air, but that the static method leads to higher value:; when a substantialpart of the flux extends itself through badly defined stray fields.Since the conce pt o f liuman body capacitance is normally used in a static (electric) context, it is suggestedthat the H B C be determined by a static method.No theoretical explanation o f the observed differences is presently at hand.INTRODUCTIONA person, insulated frorn ground by footwearand/or floor covering, is electrically character-ized by her body and grounding resistance andher capacitance. IVliile the c once pt o f body- andgrounding resistance is easy to visualize as pri-marily the resistance along the surface of thebody and the resistance through tlie shoes inseries with the floor, the capacitance is a some-what more elusive concept.The capacitance (with respect to ground) C of aninsulated conductor is defined by the equation:where V is the voltage of the conductor withrespect to ground when the conductor carries acharge q.The voltage V of the conductor is defined by

q = C V (1)

groundV= k v d a (2)

conductor

where E is the field strength along any path fromthe conductor to grounded surroundings.The relationship between charge q and fieldstrengt:l-i E is fundamentally determined by theE - h x 21sgiven by Gauss' theorem (or sentence):

E E * c l S = D * d S = q pS Jwhere S is a surface enclosing the charged bodyand is tlie permittivity of the medium at tliesite of $ and D is the dielectric displacement (orelectric flus density).The distribution of the flux and consequently themagniiude of the capacitance is thus a questionof geome try (and permittivity).I t is probably not possible to accurately modelthe distribution of flux around a charged personin a given environment and thus also not possi-ble to accurately predict the capacitance.

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Several approaches have been suggested, oftenapproximating th e capacitance of a standing per-sonwith that of a free sphere in parallel with a par-allel plate capacitor made up of the feet in agiven distance from a conductive layer in or un-der t he floor [1,2].To this author the sphere-approximation doesnot seem obvious (and also somewhat unflatter-ing for mo st people).Instead we choose to approximate (only as far asthe capacitance is concerned) a person in aroom, Fig. 1,with a cylinder capacitor in parallelwith a parallel plate capacitor.

The cylinder capacitor is made up of tlie verti-cal surface of the person and the walls of theroo m with th e capacitance:5)In r

where h is the height of the cylinder (person) =1.7 m R the average distance to the walls = 2 m,r the radius of the person, = 0.2 m and E = E= 8.85.10- Fsm- the permittivity of vacuum(and air).Introd ucin g these figures in eq . (5) we find:

Fig. 1The parallel plate capacitor is made up of thefeet and the nearest conductive layer in the floorwith the capacitance:

where E, is the relative permittivity of the shoesoles and floo r material = 4-5, A the area of tlieshoe soles = 200-300 cm 2 and t the thickness ofthe insulating layer in the soles and tlie floor = 5-10 m m .Introducing these figures in eq. (6) we findCplate 70-260 pF.If these figures represent the real world weshould thus expect tlie total capacitance to havethe valueCpersoti = 100 - 300 pF.It should be noted that although similar rangeshave been reported in the literature [1,3] a valueas low as 100 p F has been chosen as a standardin Hnn7an Bo Model-testing of semiconductorcom pone nts and devices.The purpose of this paper is to compare theresults of measurements of the human bodycapacitance by different methods and evaluatewhat method p e s the resul t most relevant in astatic electric context.

Ccylinder 40 p F

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METHODS O F MEASUREMENTTh e capacitance with respe'ct to ground of a hu-man body can be measured in two ways.Charge sharingmethodA capacitor with tlie known capacitance C , hasone terminal connected to ,ground and the otherto a static voltm eter, Fig. 2.

a.................................................................................a

The capacitor is charged to a voltage V . If' thevoltage drop s to V when the uncharged persontouches the capacitor, the capacitance of theperson , C p is given by:

(7)AC measurement of body capacitanceMost people working with circuits will consider acapacitor as an AC-component exhibiting a re-actance:

1X C = swhere is the frequency of the current throughthe capacitor.The common AC-method of determining a ca-pacitance is by balancing in a so-called bridge th eunknown capacitance relative to a known ca-pacitance by a corresponding (easily measurable)ratio between resistors.Body and grounding resistanceAs me ntio ned a person's electrical characteristicsalso include the body- and the grounding resis-tance, Fig. 3.

Fig. 3The body resistance, Tlp is the resistance fromthe primary location of a charge on the personto tlie point of discharge. Fo r a standing personthis will normally be from the underside of herfeet to a fingertip.Although this resistance may vary somewhatfrom pe:rson to person a representative valueseems to be about 1kR.The grounding resistance, R .e. the resistancethrough the series of shoes and floor, on theother lialnd, may vary from a few ohm to 10''o h m or higher.Neith er 'of the two resistances have any influenceon the value of C,, determined by a correctlyperform'ed AC-m easurement.If the capacitance is determined by the staticcharge-s:haring me thod , the voltage V, dependson how long the person is in contact with thevoltmeter.. If th e contact time is short comparedto RC,, the d ro p in voltage caused by decayduring c onta ct is negligible.Assuming a contact time of < 0.1 s and C, 200pF the m ethod is good for R :> 5.10'' aFor lower values of R the method is still good ifthe person is placed on a thin sheet of well-insulating; plastic, which will n o t change her ca-pacitance to a me asurable degree.

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Comparison between the charge sharing andthe AC bridge method.T h e tw methods of determining capacitanceswere compared experimentally by measuring aseries of capacitors in the range from 10 pF to10 nF. T he capacitors were various commerciallyavailable, comm only used circuit com pon ents .T he charge-sharing m etho d was performed usinga Keithley 620 electrometer and in most casesusing a starting voltage of about one hundredvolt. The measurements yielded values with astandard deviation on a single determination of afew per cent and well within the guaranteedrange for the com pone nt tested.

VIvolt 98 75 58 45 35 98 75 59.5 47 37vvolt 75 58 45 35 28 75 59.5 47 37 28.5

234 293 289 285 250 234 260 266 270 298CPpF

Th e AC-method was don e with a conventionalAC-bridge at a frequency of 1000 Hz . T he valueswere again within the guaranteed range, howeverthe uncertainty of reading th e values were greaterthan th e accuracy of the measurem ent.In Table 1 is shown an example of a set ofmeasurements of the Human Body Capacitancefor a combination of polymeric soles and a lino-leum floor covering.The grounding resistance of the person wasmeasured by a Keitliley 620 electrometer.It appears that there is a difference of 98 pF (orabout 58 Oo of the AC-value) between th e twodeterminations of the HBC.

linoleum TR PF PF-5 170 268

Cp,ave 268 pF, s(C,)/C, = 8.7 'o

poly I1 linoleum -4no shoes linoleum -2

Poly 1 asp ha1 -1poly I1 asphalt -1

n o shoes asp ha1 -0.3

TableConparison o HBC eternlined 03 tbeAC- awd cbaige sharing nzeasitrenzents

160 235250 614110 216110 212185 385

II shoes I floor resistance HBC, AC HBC, ch-sh

leatherleatherno shoes

asp ha1 -0.2 115 254plastic on metal -0.05 900 2680plastic on metal -0.3 2850 5580

Table2HBC or vurioi4s conibinatioiis of shoes und joor cletet wined by the A C - and the cbat-ge shariq methods

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In order to see if this difference between the re-sults of the two methods is consistent, a series ofmeasurement of tlie HBC with oth er combinztonsof shoes and floor coverings were performed withthe results shown in Table 2.The shoes marked poly I and poly I1 were shoeswith different types of polymeric soles. \Yhh themeasurements marked leather/plastic on metal and nosboes/phsfic on nzetal the person was standing (withleather soled shoes or with no shoes) on agrounded metal plate covered by a thin sheet ofplastic.It appears that the charge sharing method yieldsresults, which are from about 50 Yo to 200 YOhigher than do the AC-method.Since initial measurements indicated good agree-ment between the determinations of the capaci-tance of circuit capacitors with well-defined ca-pacitances determined by the two method:;, it wasdecided to investipte how the geometrical prop-erties of a capacitive item influence the value ofthe capacitance as determined by the AC- and thecharge-sharing method.

In Table .3 are show n th e results of calculations andmeasurements of the capacita:nces of a series ofcapacitive: system s as sho w n in Figs. 4and 5. T h eresults in Table 3 seem to indicate, like the initialmeasurements of the capacitance of commerciallyavailable capacitors, that the AC-bridge methodand the charge-sharing method yield the same re-sult wh en dealing with capacitive systems whe rethe electrk: flux is largely co nfine d t o a well-defineddielectric region.In column 1 of Table 3we h.ave a parallel platecapacitor with air as the dielectric. In this case weshould expec t a substantial strxy field at th e edgesof the plxtes leading to a higher capacitance thanwhat can be calculated from leq (6). As appearsfrom the table, this is what we find with bothmethods of measuring the capacitance, with thecharge-sharing me tho d yielding the h ighest value.

6

/ floor /Fig.4

T o this end, the capacitive systems show n in Figs.4and 5 were used.Fig. 4shows a capa citor consisting of a metal platewith the area A separated from a grounded metalfloor plane by a distance of t. This interspace maybe air or filled by a dielecl-ric with tlie relative p er-mittivity E . In the set-up shown in Fig. 5, a metalliccylinder with the o uter radius r and height isplaced on tlie metal plate. The capacitances of thetwo types of systems may then be estimated fromeqs. 4), (5) and (6).

/ rFig. 5

In column 2 and 3 we are dealing with a parallelplate capacitor where the major part of the fielddetermining the capacitance is extending itselfthrough :i dielectric, and in these cases the twomethods give identical results, and agree with thetheoretical value as calculated fro m eq. (6).In column 4 and 5 we are considering a capacitorcorresponding to the human body model suggestedin Fig. 1 (;md Fig. 5).T h e general result is again that tlie capacitancemeasured by the AC-method is lower than whenmeasured by the static charge-sl iaring m etho d.

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Table 3Conparison o f theoretical capacitances o f dferezt capacitive sy-tenrsand cqbacitances of fhe same ysfenls measured by the AC- a?zd chal;5le-shan'rgmethods

Discussion of resultsWhen an insulated conductor receives a charge itmay cause two types of electrostatic effects: it maycreate a field possibly causing a breakdown, and/orit may dissipate a certain energy in its surroundings.Both of these effects are determined by the chargeand the capacitance of the conductor. Althoughthe capacitance is a geometric/permittive quantity,independent of whether o r not the conductor ischarged, the definition of the capacitance is theratio between a charge and the resulting voltage ofthe conductor.It therefore seems natural to determine the ca-pacitance, which together with the charge is re-sponsible for the electrostatic effects, by compar-ing the voltage of the charged conductor with thevoltage when the conductor shares the samecharge with a con duct or with a known capacitance.And this is, as explained above, the charge-sharingmethod.If an insulated conductor enters as a part of anAC-circuit, i t may partly determine the impedanceof the circuit contributing with a reactance:

where v is the frequency of th e AC-current.A capacitance determined by the static charge-sharing method has the dimension of charge overvoltage while a capacitance determined by an AC-measurement has the (identical) dimension of timeover resistance.Hence it could be speculated that the results ofcharge-sharing measurements depemd on thestaring voltage and that the AC-capacitance of anobject with a badly defined stray field may be fre-quency d ependent.In order to check these speculations, a series ofHBC charge-sharing determinations were done atvoltages up to 5 k (using a capacitive voltage di-vider).Similarly, a make-shift capacitance bridge was puttogether and the HBC was determined for fre-quencies from 100 Hz to 10 kHz.No dependence of the capacitances measured onstarting voltage or frequency could be detected.

1xc=27cvc

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ConclusionThis paper has, for a rather limited range of ob-jects, demonstrated that when we are dealing withsystems with w ell-defined capacitances (i.e. the flusis well located) the static charge-sharing and theAC-methods of measuring capacitances yield com-parable results.When, however, the flus is m ore strayin distrib-uted, as is the case with an insulated human body,the measurements reported here indicate that thecharge-sharing method always yield a higher value.No solid theoretical explanation for the differencecan presently be offered.References1. McAteer, O.J., (1990) Ehctrostafic Dischuge Cofl-2. Seaver, A.E. (1997), ESA nnzd A f r e f i y U3. Dangelmayer, G.T., 1990, E S D Program Manage-

tl-01,McGraw-Hill, N . 169-173

GeoGia~meizt Van Nostrand Reinhold, NY, p. 37

Based on the results reported, it is suggested thatwhen diealing with predicting; electrostatic effectsone should prefer an electrostatic method.One could argue that the AC-bridge method is easyand simple to employ.This is correct.Almost ls simple and easy as the cliarge-sharingmethod.

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