Derivative time-domain sensor and fibre optic correction factor calculation
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1 Technical Nte - TN15 Derivative time-dmain enr and fibre ptic crrectin factr calculatin Marc Sallin and Bertrand Daut, mntena technlgy, 1728 Ren, Switzerland Table f cntent 1. Intrductin Meaurement etup Grund-field D-dt enr Grund-field B-dt enr Free field D-dt enr Free field B-dt enr Balun Attenuatr and caxial cable Optical fibre, tranmitter and receiver Ocillcpe Crrectin factr (free field D-dt enr) Crrectin factr (free field B-dt enr) Crrectin factr (grund field D-dt enr) Crrectin factr (grund field B-dt enr) Attenuatr value electin (free field D-dt enr) Attenuatr value electin (free field B-dt enr) Attenuatr value electin (grund field D-dt enr) Attenuatr value electin (grund field B-dt enr) Intrductin The meaurement f puled electric r magnetic field i a delicate tak that require me ignal ptprceing. In rder t ae the meaured field frm the value read n the cillcpe, everal crrectin factr mut be taken accunt in the calculatin. Thi technical nte explain the urce f the crrectin factr and hw t ue them in an apprpriate way. Thi technical nte review the fllwing type f enr: Grund field electric time-dmain enr Grund field magnetic time-dmain enr Free field electric time-dmain enr Grund field electric time-dmain enr Thi technical nte refer t electric and magnetic time-dmain enr which are nt calibrated with repect t a pecific field, i.e. their mechanical dimenin i ufficient fr a cmplete determinatin f their behaviur. The main parameter f thi type f enr i called the equivalent urface and i nly linked t the mechanical dimenin f the receiving element. 1/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
2 Fr explanatin abut enr which are calibrated with repect t a pecific field and that are delivered with a calibratin factr, pleae refer t TN21 Derivative time-dmain enr calibratin prcedure fr further detail. Pleae nte that all the enr can either be ued with their equivalent urface r with their calibratin factr. 2. Meaurement etup The general chematic f the meaurement chain fr a derivative enr i hwn belw. The ame principle can be applied fr a D-dt and a B-dt enr (grund field r free field enr). Pleae nte hwever that the balun i nt needed in the cae f the grund field enr. It cnit in the fllwing device: a D-dt r B-dt (grund field r free field) enr a balun (nly needed in the cae f free field enr) an attenuatr everal caxial cable an ptical tranmitter a fibre ptic an ptical receiver an cillcpe (with egratin functin capabilitie) Each abve mentined device ha a crrectin factr that mut be ued in the calculatin f the field. After a quick review f the fur type f enr and their related equatin, the crrectin factr fr each device i detailed in the fllwing paragraph. The rle f the attenuatr lcated between the enr and the fibre ptic i the prtectin f the tranmitter input, which i limited by manufacturer pecificatin. The chice f the minimum attenuatr value i al derived belw. 2/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
3 3. Grund-field D-dt enr The grund field D-dt enr tranfrm an electric field a vltage, whe hape i the derivative f the electric field wavefrm. Thi type f enr mut be lcated ver a grund plane and cnit in nly ne ingle channel. It equatin i the fllwing: D v1 = R eq, with D E = ε R i the impedance een by a ingle channel f the enr in Ω. A i the equivalent area f a ingle channel f the enr in m 2. D i the electric diplacement. ε0 i the electric permittivity f free pace. Mre detail abut the derivatin f that frmula can be fund in TN12 Electric and magnetic field enr and egratr equatin. 4. Grund-field B-dt enr The grund field B-dt enr tranfrm a magnetic field a vltage, whe hape i the derivative f the magnetic field wavefrm. Thi type f enr mut be lcated ver a grund plane and cnit in nly ne ingle channel. It equatin i the fllwing: B v 1 = A eq, with B H = µ A i the equivalent area f a ingle channel f the enr in m 2. B i the magnetic flux denity. µ0 i the magnetic permeability f free pace. Mre detail abut the derivatin f that frmula can be fund in TN12 Electric and magnetic field enr and egratr equatin 3/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
4 5. Free field D-dt enr The free field D-dt enr tranfrm an electric field a vltage, whe hape i the derivative f the electric field wavefrm. A free field enr i cmped f tw identical channel, which are enitive t the ame field, but meaure in ppite directin. S the equatin fr bth channel are the fllwing: v = R 1 eq, D D v 2 = R eq, with D E = ε R i the impedance een by a ingle channel f the enr in Ω. A i the equivalent area f a ingle channel f the enr in m 2. D i the electric diplacement. ε0 i the electric permittivity f free pace. Therefre the utput vltage acr bth channel i the fllwing: v - v 1 2 = 2 R ε E Remark: Free field enr are either pecified with the equivalent area f a ingle enr A r with the ttal equivalent area f the enr Aeq,tt. It i imprtant t verify which value mut be taken accunt fr the calculatin. The relatin between the equivalent area f a ingle channel and the ttal equivalent area i the fllwing: A eq, tt = 2 A eq, A i the equivalent area f a ingle channel f the enr in m 2. Aeq,tt i the ttal equivalent area f the enr in m 2, al called "differential equivalent area". In cae the enr i pecified with the ttal equivalent area, the enr equatin turn t: v - v = R 1 2 eq,tt ε E 4/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
5 6. Free field B-dt enr The free field B-dt enr tranfrm a magnetic field a vltage, whe hape i the derivative f the magnetic field wavefrm. A free field enr i cmped f tw identical channel, which are enitive t the ame field, but meaure in ppite directin. S the equatin fr bth channel are the fllwing: v = A 1 eq, B v 2 B = A eq, with B H = µ A i the equivalent area f a ingle channel f the enr in m 2. B i the magnetic flux denity. µ0 i the magnetic permeability f free pace. Therefre the utput vltage acr bth channel i the fllwing: v - v = µ H Remark: Free field enr are either pecified with the equivalent area f a ingle enr A r with the ttal equivalent area f the enr Aeq,tt. It i imprtant t verify which value mut be taken accunt fr the calculatin. The relatin between the equivalent area f a ingle channel and the ttal equivalent area i the fllwing: A eq, tt = 2 A eq, A i the equivalent area f a ingle channel f the enr in m 2. Aeq,tt i the ttal equivalent area f the enr in m 2, al called "differential equivalent area". In cae the enr i pecified with the ttal equivalent area, the enr equatin turn t: v - v = A 1 2 eq, tt µ H 5/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
6 7. Balun The balun i needed t tranfrm tw balanced ignal v1 and v2 a ingle unbalanced ignal. It i nly needed when free field enr are ued. A the grund field enr have nly ne ingle channel v1, they can directly be cnnected t ret f the meaurement circuit. Becaue f the ernal tplgy and the input filtering f thi circuit, thi tranfrmatin reduce the ignal level. Thi device can therefre be ummarized with the fllwing equatin: v1 - v v = 3 K Bal 2 KBal i the attenuatin f the balun in db. 8. Attenuatr and caxial cable The value f the attenuatr mut be chen that the vltage v4 i alway belw the maximum input vltage f the tranmitter. (ee paragraph 15 fr mre detail). If nt, the vltage ignal might be ditrted and therefre give wrng reult. v = 4 v 3 K Att KAtt i the attenuatin f the attenuatr in db. The le f the attenuatr and the caxial cable frming the meaurement chain can be cnidered a a ingle attenuatin. At high frequencie, caxial cable can n mre be een a perfect element, a they hw me attenuatin which i dependant n the frequency (lw-pa effect). Therefre all cable mut be taken accunt fr the calculatin f the crrectin factr. KAtt mut be meaured with a netwrk analyer, in rder t check the deviatin f the attenuatin frm the nminal value. 6/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
7 9. Optical fibre, tranmitter and receiver The fibre ptic i ued becaue the metallic caxial cable diturb the electrmagnetic wave t be meaured r if the ditance between the enr and the cillcpe i t large. It cnit f a tranmitter, a fibre ptic and an ptical receiver. The equatin i the fllwing: v 4 v = 5 K Opt KOpt i the attenuatin f the whle ptical link in db. KOpt mut be meaured with a netwrk analyer. Special care mut be taken when meauring the fibre ptic link: Allw at leat minute warm-up after the tranmitter and receiver are witched n. The utput ignal f the netwrk analyer mut be belw the maximum input vltage allwed by the tranmitter. Due t their ernal electrnic circuit, me fibre ptic link can even hw me gain fr certain frequencie. Fr me fibre ptic link, KOpt i extremely enitive t any variatin f the ptical cnnectr. The pecified variatin f attenuatin fr different cnnectin i ±1 db. If precie meaurement are needed, it i recmmended nt t dicnnect the ptical cnnectr, nce the attenuatin meaurement i perfrmed. Sme advanced fibre ptic link can perfrm a elf-calibratin. In that cae, the variatin due t the cnnectr i included in the calibratin and the prblem diappear. Sme fibre ptic link have an autmatic gain cntrl feature that cmpenate fr the cnnectin le. Thi i the cae fr the mntena fibre ptic link like the MOL3000 and MOL Al in that cae, the prblem diappear. T illutrate thi lat p, a erie f meaurement wa perfrmed with a fibre ptic link that de nt have a elf-calibratin nr autmatic gain cntrl feature. The fllwing graph hw the S21 v frequency fr the fibre ptic link fr 8 different ptical cnnectin. Between each meaurement, the ptical cnnectr are nly dicnnected and recnnected. In thi cae, the deviatin i abut le than 1 db. 7/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
8 A lutin t imprve the repeatability i t alway cnnect the fibre ptic in the ame directin, i.e. ne end f the cable alway t the tranmitter and the ther end alway t the receiver. A viible frm the abve graph, the repne f the fibre ptic link i nt flat ver the pecified frequency range. The attenuatin can be apprximated by an average f the attenuatin ver the frequency range f the meaurement ignal.. Ocillcpe The cillcpe diplay the vltage v5, which i in fact an image f the derivative f the meaured electric field. In rder t g back t the electric field pule hape, the ignal mut be egrated with a pecial functin f the cillcpe. Thi reult in Y, whe unit i [V] (Vlt x ecnd). Y 5 = v dt + k The channel cupling mut be et t 50 Ω. An adequate egratin cntant k mut be given t the egratin functin f the cillcpe. 8/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
9 11. Crrectin factr (free field D-dt enr) Accrding t all the abve mentined cntributin, the electric field wavefrm can be recvered frm the egrated cillcpe meaurement with the fllwing frmula: E = KBal + K Att + K Opt 2 R ε Y i the egrated vltage at the cillcpe diplay in V. R i the impedance een by a ingle channel f the enr in Ω. A i the equivalent area f a ingle channel f the enr in m 2. KBal i the attenuatin f the balun in db. KAtt i the attenuatin f the cmbinatin f the attenuatr and the caxial cable in db. KOpt i the attenuatin f the fibre ptic link in db. ε0 i the permittivity f free pace (8.85 x -12 F/m) Example Impedance een by a ingle channel f the enr: 50 Ω Equivalent area f a ingle channel f the enr: -3 m 2 Balun attenuatin: 8 db Attenuatr: 40 db Optical link attenuatin: 1 db E 8dB+ 40dB+ 1dB = E = The crrectin factr i m. 9/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
10 12. Crrectin factr (free field B-dt enr) Accrding t all the abve mentined cntributin, the magnetic field wavefrm can be recvered frm the egrated cillcpe meaurement with the fllwing frmula: H = A KBal + K Att + KOpt eq,tt µ Y i the egrated vltage at the cillcpe diplay in V. Aeq,tt i the ttal equivalent area f the enr in m 2. KBal i the attenuatin f the balun in db. KAtt i the attenuatin f the cmbinatin f the attenuatr and the caxial cable in db. KOpt i the attenuatin f the fibre ptic link in db. µ0 i the permeability f free pace (1.256 x -6 H/m) Example Ttal equivalent area f the enr: 9 x -6 m 2 Balun attenuatin: 8 db Attenuatr: 40 db Optical link attenuatin: 1 db H 8dB+ 40dB+ 1dB = H = The crrectin factr i Ω m. /14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
11 13. Crrectin factr (grund field D-dt enr) Uing the ame a in Paragraph 11, but etting the balun attenuatin t zer and taking accunt nly ne ingle channel lead t the fllwing equatin: E = R K Att + K Opt ε Y i the egrated vltage at the cillcpe diplay in V. R i the impedance een by a ingle channel f the enr in Ω. A i the equivalent area f a ingle channel f the enr in m 2. KAtt i the attenuatin f the cmbinatin f the attenuatr and the caxial cable in db. KOpt i the attenuatin f the fibre ptic link in db. ε0 i the permittivity f free pace (8.85 x -12 F/m) 14. Crrectin factr (grund field B-dt enr) Uing the ame a in Paragraph 12, but etting the balun attenuatin t zer and taking accunt nly ne ingle channel lead t the fllwing equatin: H = A K Att + KOpt µ Y i the egrated vltage at the cillcpe diplay in V. A i the equivalent area f a ingle channel f the enr in m 2. KAtt i the attenuatin f the cmbinatin f the attenuatr and the caxial cable in db. KOpt i the attenuatin f the fibre ptic link in db. µ0 i the permeability f free pace (1.256 x -6 H/m) 11/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
12 15. Attenuatr value electin (free field D-dt enr) The attenuatr mut be chen that the input vltage f the fibre ptic tranmitter v4 i alway belw the maximum vltage Vmax,tranmitter: v 4 < V max, tranmitter Expanding the equatin fr v4: 2 R ε KBal + K Att E < V max, tranmitter The time-derivative f the electric field can be apprximated by the fllwing exprein: E E E t t peak rie Epeak i the peak electric field value f the meaured pule in V/m. trie i the rie-time % - 90 % f the meaured pule in. Finally the requeted attenuatin KAtt in db can be derived a: K Att 2 R > lg V ε max, tranmitter E t peak rie K R i the impedance een by a ingle channel f the enr in Ω. A i the equivalent area f a ingle channel f the enr in m 2. KBal i the attenuatin f the balun in db. Vmax,tranmitter i the maximum allwed vltage at the input f the tranmitter in V. ε0 i the permittivity f free pace (8.85 x -12 F/m) Example: Pule peak electric field: 50 kv/m Pule rie-time %-90%: 2 n Impedance een by a ingle channel f the enr: 50 Ω Equivalent area f a ingle channel f the enr: -3 m 2 Balun attenuatin: 8 db Tranmitter input peak vltage: 250 mv Bal k K Att lg > 8dB = 250m 2n 30.9 db 12/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
13 16. Attenuatr value electin (free field B-dt enr) The attenuatr mut be chen that the input vltage f the fibre ptic tranmitter v4 i alway belw the maximum vltage Vmax,tranmitter: v 4 < V max, tranmitter Expanding the equatin fr v4: A eq,tt µ KBal + K Att H < V max, tranmitter The time-derivative f the magnetic field can be apprximated by the fllwing exprein: H H H t t peak rie Hpeak i the peak magnetic field value f the meaured pule in A/m. trie i the rie-time % - 90 % f the meaured pule in. Finally the requeted attenuatin KAtt in db can be derived a: A K Att > lg V eq,tt µ H max, tranmitter peak t rie K Aeq,tt i the ttal equivalent area f the enr in m 2. KBal i the attenuatin f the balun in db. KOpt i the attenuatin f the fibre ptic link in db. Bal Vmax,tranmitter i the maximum allwed vltage at the input f the tranmitter in V. µ0 i the permeability f free pace (1.256 x -6 H/m). Example: Pule peak magnetic field: 0 A/m Pule rie-time %-90%: 0 p Ttal equivalent area f the enr: 9 x -6 m 2 Balun attenuatin: 8 db Tranmitter input peak vltage: 250 mv K lg Att > 8dB = 25.1 db 250m 0p 13/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
14 17. Attenuatr value electin (grund field D-dt enr) Uing the derivatin f Paragraph 15 in the pecial cae f the grund field D-dt enr enable t cmpute the requeted minimum attenuatin value a: K Att R > lg Vmax, ε tranmitter E t peak rie Epeak i the peak electric field value f the meaured pule in V/m. trie i the rie-time %-90% f the meaured pule in. R i the impedance een by a ingle channel f the enr in Ω. A i the equivalent area f a ingle channel f the enr in m 2. Vmax,tranmitter i the maximum allwed vltage at the input f the tranmitter in V. ε0 i the permittivity f free pace (8.85 x -12 F/m) 18. Attenuatr value electin (grund field B-dt enr) Uing the derivatin f Paragraph 16 in the pecial cae f the grund field B-dt enr enable t cmpute the requeted minimum attenuatin value a: K Att A > lg V µ H max, tranmitter peak t rie Hpeak i the peak magnetic field value f the meaured pule in A/m. trie i the rie-time %-90% f the meaured pule in. A i the ttal equivalent area f the enr in m 2. Vmax,tranmitter i the maximum allwed vltage at the input f the tranmitter in V. µ0 i the permeability f free pace (1.256 x -6 H/m). Verin D - V:\Nte_applicatin\_dc\TN15E_Senr_crrectin_factr.DOC 14/14 mntena technlgy a Rute de Mntena Ren Switzerland phne fax
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