Chapter 27: Electrostatic Discharge

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1 ELECTROMAGNETIC COMPATIBILITY HANDBOOK 1 Chapte 7: Electostatic Dischage 7.1 When chaging by induction, why should the (initially) neutal object to be chaged have a small time constant elative to the peiod (of oscillation) of the extenal electic field and a small time constant elative to the contact time with the gounded object? 7. Discuss the validity of the statement, To chage an object it must come in contact with anothe object. 7.3 In efeence to the low-noise cable discussion in this chapte, epeat the entie analysis, including the discussion, fo the peiod of time immediately afte the ai gap closes and the chage is patially neutalized at the inteface. 7.4 Using the fequency-domain expessions povided in this chapte fo the electic fields fo both layes in a Maxwell s capacito, detemine the coesponding time-domain expessions. 7.5 A voltage souce is applied to a small spheical electode that poduces a constant volume chage density of ρ V (a) at = a. The medium aound the electode has an outwad adial velocity of U. The conductivity and pemittivity of the suounding moving ohmic medium ae σ and ε, espectively. Detemine the steady-state volume chage density and electic field distibutions. [Zahn] 7.6 Nea the tip of a lit cigaette, ions of volume chage density ρ(a) ae geneated at = a. The smoke caies these ions adially outwad fom the tip with a velocity distibution of U, whee is the adial distance fom the cigaette. Detemine the steady-state distibution of chage eveywhee aound the cigaette as a function of I (the constant, steady-state cuent fom the cigaette), b (the mobility of the ions in fee space), ρ(0), and. Hint: the adial cuent I 4π. density is equal to ( ) 7.7 The conductivity of the eath s atmosphee is given by σ ( ) = a b( R) whee a, b, and R ae constants (R is the adius of the eath). If the electic field at the eath s suface is given as E ( R) a ˆ, detemine the steady-state cuent density distibution eveywhee in the eath s atmosphee. What is the total cuent diected outwad fom the eath s suface? Hint: let J = J a ( ) ˆ 7.8 A point chage is located midway between two, intesecting, lage, gounded, conducting planes with an angle of 60 between them. If the gounded planes ae eplaced with image chages, clealy show the position and sign of all five of the image chages. 7.9 Veify that each of the following chage distibutions appea like a point chage fa fom the distibution by using a seies appoximation fo each of the electic field distibutions. Clealy define fa fo each distibution.

2 ELECTROMAGNETIC COMPATIBILITY HANDBOOK a) finite-length line chage b) unifomly chaged cicula ing c) unifomly chaged cicula disk d) linealy vaying chaged cicula disk 7.10 Detemine whethe the electic field is geneally zeo eveywhee (in the stated egion) fo each of the given chage distibutions and mateials. Use Gauss s law, supeposition, and/o counteexamples to explain you easoning. a) inside a solid conducting sphee with a unifom distibution of chage along its suface b) inside a solid conducting sphee with a nonunifom distibution of chage along its suface c) inside the cavity of a thin conducting spheical shell with a unifom d) inside the cavity of a thin conducting spheical shell with a nonunifom e) inside a solid insulating sphee with a unifom distibution of chage along its suface f) inside a solid insulating sphee with a nonunifom distibution of chage along its suface g) inside the cavity of a thin insulating spheical shell with a unifom h) inside the cavity of a thin insulating spheical shell with a nonunifom How can a nonunifom distibution of chage be obtained along a spheical conducting body? How can a nonunifom distibution of chage be obtained along a spheical insulating body? 7.11 The voltage on an ESD bag deceases fom 1 kv to 100 V ove a time of 60 s. Fom this infomation detemine as many chaacteistics of this bag as possible. State all assumptions. 7.1C Fo the situation shown in Figue 1, detemine the electic field expession fo each of the thee egions, a, d, and b. Solve fo all of the constants of integation. Neglect end effects. The dielectic constant of the slab of thickness d is equal to k. Although the fee suface chages ρ S1 and ρ S ae shown with equal magnitude and opposite sign, do not assume this in the analysis. If a is much less b, detemine whethe the electic field in egion b is mainly detemined by ρ S. Is this infomation useful when measuing the electic field in egion b fom ρ S only?

3 ELECTROMAGNETIC COMPATIBILITY HANDBOOK 3 0 a a d fee space Φa k Φd fee space Φb a d b x ρ S1 ρ S Figue E Using the method of images and S ' ( ) ρs ' ds ' Φ ( ) = 4 πε ' deive the integal potential expession fo a unifomly chaged disk of adius R at a distance of d fom the cente of a gounded conducting sphee of adius a: Φ = π R ρs ρ ' dρ ' dφ ' 4 πε o 0 0 ρ 'sin φ ' ρ 'cos φ ' π R ( x d ) ( y ) ( z ) ρ a ρ ' dρ ' dφ ' S 4 πε o 0 0 d ( ρ ') a d a ρ 'sin φ ' x y d ( ρ ') d ( ρ ') o a ρ 'cos φ ' z d ( ρ ') Clealy shown all steps. To detemine some of the angles fo the pojection, it might be helpful to examine the coodinate system tansfomation elationships given in the appendix In a newspape poduction line, pape is olled at high speeds along insulating olles. How should the chage be bled off?

4 4 ELECTROMAGNETIC COMPATIBILITY HANDBOOK 7.15 A woke pous benzene liquid fom a plastic containe though a metal funnel into a lage plastic vessel. What steps should be taken to educe the pobability of an electostatic dischage? 7.16 In one of the last assembly steps in a puzzle factoy, the puzzle pieces tavel down a funnel to the puzzle box. Unfotunately, the company is eceiving complaints about missing pieces (a eal disappointment). The company has detemined that puzzle pieces ae occasionally sticking to the funnel. Recommend a solution if the funnel is plastic. Recommend a solution if the funnel is metallic Most of the electical hazads associated with the filling of potable gas cans occu with metal containes insulated fom gound. It seems that vey little spaking can be obtained between a gounded sphee and a chaged plastic containe. Howeve, if a metal funnel is used in the mouth of the containe, then a spak can be geneated. Explain whethe these statements ae easonable. 7.18E An electic field field mill is used to measue an electic field with a magnitude of E n (nomal to the senso s plate). Assume that the exposed aea of the sensing plate by the otating blade, which has a adian fequency of ω, is a peiodic tiangula wave as shown in Figue. senso aea A π ω Figue π ω t Using the Fouie seies fo the esultant cuent into a paallel RC cicuit, detemine the fist thee nonzeo tems fo the steady-state voltage acoss the RC cicuit in the time domain. Using these thee nonzeo tems, detemine the maximum amplitude of the voltage With an ESD simulato, why should an isolation tansfome be used at the ac outlet fo both the equipment unde test and ESD simulato? 7.0 Would the 1 MΩ o 50 Ω input of a scope be moe likely to sense the shuffling of feet along a ug? Explain 7.1 Fom the standpoint of educing the effects of ESD, should the capacitance between the powe conducto and gound be lage o small (Q = CV)? 7. To help ensue that the input to a micopocesso is not due to an ESD event, the softwae checks the input state twice. Detemine an appopiate time inteval between the initial check and veification check. 7.3 A manufactue claims to have a wieless wist stap. Detemine whethe this can be done.

5 ELECTROMAGNETIC COMPATIBILITY HANDBOOK Seveal simple methods ae available fo educing painful ESD dischages fom the finge. A metal thimble o the tip of a metal key can be used to dischage the body to a gounded object. A specially made ing with a lage metal head can also be used. The head of the ing is isolated fom the est of the ing, which is in diect contact with the finge. If the esistance fom the ing s head to the band in contact with finge is 1.5 MΩ, estimate the capacitance equied to dissipate most of the chage ove about a one second inteval. Detemine the specific insulating mateial that could be used, as well as its (easonable) dimensions. The mateial s dielectic stength should also be consideed. 7.5 Rug ats (babies who cawl ove capets) ae quite susceptible to electostatic shock. This is due to the tibochaging between the child and the synthetic o wool capet. Imagine that one ovely active child eaches a potential of 15 kv immediately befoe touching the family kitty! (This voltage is elative to gound that exists beneath the ug.) Unfotunately, the kitty was chaged to a value of 0.5 µc (the cat had peviously ubbed against the couch). The self capacitances and the coefficient of induction pio to child-kitty contact follow: c = 130 pf, c = 100 pf, c = 70 pf bb kk kb The subscipts b and k epesent the baby and the kitty, espectively. Detemine the total chage on the child, the voltage of the cat, and the total enegy associated with the child and the cat. 7.6 In efeence Poblem 7.5, imagine that the ai between the child and cat beaks down just pio to contact; in othe wods, the child and the kitty get an old-fashioned shock. Detemine the final voltage of and chage on this ambunctious child and the cat afte this shock (when they ae touching). Now, what is the total enegy associated with the child and the cat? 7.7 In efeence to Poblem 7.5, epeat the analysis if the cat is not chaged pio to contact. The initial voltage of the child is still 15 kv. Is this a good assumption? Explain. Is the shock intensity less than, equal to, o geate than the chaged case? Explain. 7.8 In efeence to Poblem 7.5, estimate the self capacitance of the child and the cat afte touching? Discuss the poblems associated with the following paametes: c = 130 pf, c = 40 pf, c = 70 pf bb kk kb 7.9 The coefficient of self capacitance of a little ed wagon was measued using a battey-poweed electomete. All objects suounding the wagon wee gounded, and the wagon had insulating wheels. One input of the electomete was connected to the cable connected to the wagon and the othe input of the electomete was connected to a test voltage V T. The electomete measued the chage esiding on the wagon due to the test voltage V T. (Befoe the application of this test voltage, the wagon was tempoaily gounded to dissipate any chage on the wagon, in the electomete, and in the cable.) Unfotunately, thee is

6 6 ELECTROMAGNETIC COMPATIBILITY HANDBOOK always instumentation loading. Assume the shunt input capacitance of the electomete is C E, and the capacitance of the cable connecting the instument to the wagon is C c. Detemine a elationship fo the coefficient of self capacitance of the wagon in tems of V T, C E, C c, and Q EM, whee Q EM is the chage measued by the electomete In efeence to Poblem 7.9, detemine a elationship fo the actual voltage of the wagon elative to gound as a function of V T, C E, C c, and C W, whee C W is the actual capacitance of the wagon In efeence to Poblem 7.30, when is C W Q = V EM T and an exact value fo C c not equied? The electomete essentially measues the voltage acoss the known capacitance C E. Assume that V T =100 V, C E = 0.01 µf, and C c = 100 pf. In this case, is the instumentation loading negligible? 7.3 In efeence to Poblem 7.9, why was a battey-poweed electomete specified? What should the oute shield of the cable, at the wagon end, be connected to? 7.33 An explosion has occued at a ban-flake food pocessing plant. The plant manage has hied you to detemine whethe this was (potentially) an electostatic-based explosion. Assume that the ban dust concentation was in the explosive ange. The facts povided by the plant manage follow: (1) the flake poduct emeges fom a scew feede at 1.5 kg/s with a density of appoximately 40 kg/m 3, filteed though a sceen, and foced with ai pessue though an 5 inch diamete metallic tube; () the metallic tube extends fom the fouth floo to the fist floo; (3) typically one-half of the tube is filled; (4) one nonmetallic, PVC (k 3.), 1/8 inch thick, 1 inch long, 5 inch inne diamete tube section exists midway along the metallic tube whee metal detectos ae usually located; and (5) on the fist floo, poduct (with plenty of dust) is accumulated into 100 pound, plastic-lined boxes. (The metal detectos ae used to detect hamful metallic objects in the ban.) Duing a typical opeation, the field exteio to the PVC tube, when caying the flake poduct, is geate than 10 kv/cm. This field was detemined using a field mete held 1 inch fom the tube. 1) Estimate the chage pe mete in the tube (in C/m). ) Estimate the coesponding flake chage pe kg (in C/kg). 3) Estimate and sketch the potential distibution and the electic field inside the metal pipe assuming the metal pipe is gounded. 4) Estimate the total chage accumulated in the 100 lb box and electic field at the top of the ban flake heap. Is the field sufficient to beak down the ai and ignite the dust?

7 ELECTROMAGNETIC COMPATIBILITY HANDBOOK Geneally, the capacitance inceases with the aea of the conductos and deceases with spacing between the conductos. Fo the capacitance fomula X (povided by you instucto) given in this chapte s capacitance table, qualitatively vay each of the paametes and detemine whethe the capacitance inceases o deceases. Detemine whethe these qualitative esults ae in ageement with the given geneal capacitance statement. Finally, allow one of the paametes in the capacitance fomula to become vey lage o vey small. Then, compae this new esult with anothe capacitance fomula fo anothe configuation The capacitance of a peson inside a vehicle is given as 330 pf while a peson outside a vehicle is given as 150 pf. Detemine unde what assumptions these numbes ae easonable. [Geneal]

Phys102 Second Major-182 Zero Version Monday, March 25, 2019 Page: 1

Phys102 Second Major-182 Zero Version Monday, March 25, 2019 Page: 1 Monday, Mach 5, 019 Page: 1 Q1. Figue 1 shows thee pais of identical conducting sphees that ae to be touched togethe and then sepaated. The initial chages on them befoe the touch ae indicated. Rank the