Electric and magnetic field sensor and integrator equations

Transcription

1 Techncal Note - TN12 Electrc and magnetc feld enor and ntegrator uaton Bertrand Da, montena technology, 1728 oen, Swtzerland Table of content 1. Equaton of the derate electrc feld enor Integraton of the gnal Example of calculaton Equaton of the derate magnetc feld enor Integraton of the gnal Example of calculaton ppendx 1 : graphcal reult Equaton of the derate electrc feld enor The charge nduced on the enor are flowng through the mpedance of the meaurng ytem. The current produced by the enor proportonal to the ualent urface and to the frt tme derate of the charge dplacement. The ualent crcut of the enor the followng: and the uaton : (t) C (t) (t) D(t) the mpedance een by the enor C the capactance of the enor the ualent urface D the electrc dplacement Ung the Laplace tranform, the uaton become: D() C () () j, j, 2 f 1/7 montena technology a e de Montena oen Swtzerland phone fax

2 So the repone of the enor gen by: D() () C 1 1) For the dfferentatng mode (low fruency doman: C << 1): () D() wth j, j, 2 f and E : D 0 (f) 2f 0 E(f) emark: F c 1 2 C or n the tme doman: (t) D(t) 2) For the elf ntegratng mode (hgh fruency doman: C >> 1): () C D() or n the tme doman: (t) C D(t) 2. Integraton of the gnal The tranfer functon of the ntegrator n () 1 () C 1 C the tme contant of the ntegrator. So the repone of the full ytem (enor + ntegrator) : D() () C 1 1 C 1 2/7 montena technology a e de Montena oen Swtzerland phone fax

3 Wth both followng condton: dfferentatng mode of the enor (low fruency doman: C << 1); fruency of the gnal to be ntegrated large enough (C >> 1); the repone of the full ytem become: () C D() or n the tme doman: (t) C D(t) or n relaton wth the electrc feld (V/m): (t) 0 C E(t) wth D 0 E n free pace 3. Example of calculaton The followng calculaton carred for a SGE2G enor connected through an IT1-2U ntegrator to the 1 MΩ nput of an ocllocope. The data are the followng: the mpedance een by the enor (50 Ω) the ualent urface (5.4 x 10-3 m 2 ) C tme contant of the ntegrator (1.2 ) 0 = x V -1 m -1 3 (t) E(t) Th ge a correcton factor of the enor of 2 mv / kv/m. 3/7 montena technology a e de Montena oen Swtzerland phone fax

4 4. Equaton of the derate magnetc feld enor The magnetc nducton generate a oltage nduced proportonal to the ualent urface and to the frt tme derate of the magnetc nducton. The ualent crcut of the enor the followng: and the uaton : (t) L (t) (t) B(t) the mpedance een by the enor L the nductance of the enor the ualent urface B the magnetc nducton Ung the Laplace tranform, the uaton become: B() L () () Then the repone of the enor gen by : () B() L 1 1) For the dfferentatng mode (low fruency doman: L/ << 1): () B() wth j, j, 2 f and H: B 0 (f) 2f 0 H(f) emark: F c 2L or n the tme doman: (t) B(t) 4/7 montena technology a e de Montena oen Swtzerland phone fax

5 2) For the elf ntegratng mode (hgh fruency doman: L/ >> 1): () B() L or n the tme doman: (t) B(t) L 5. Integraton of the gnal The tranfer functon of the ntegrator n () 1 () C 1 C the tme contant of the ntegrator So the repone of the full ytem (enor + ntegrator) : () B() L 1 1 C 1 Wth both followng condton: dfferentatng mode of the enor (low fruency doman: L/ << 1); fruency of the gnal to be ntegrated large enough (C >> 1); the repone of the full ytem become: () C B() or n the tme doman: (t) C B(t) or n relaton wth the magnetc feld (n /m): (t) 0 C H(t) wth H 0 B n free pace 5/7 montena technology a e de Montena oen Swtzerland phone fax

6 6. Example of calculaton The followng calculaton carred for a SGM1-8G enor connected through an IT1-2U ntegrator to the 1 MΩ nput of an ocllocope. The data are the followng: the mpedance een by the enor (50 Ω) the ualent urface (1 x 10-3 m 2 ) C tme contant of the ntegrator (1.2 ) µ0 = x 10-6 V -1 m -1 3 (t) H(t) Th ge a correcton factor of the enor of 1 mv / /m. 6/7 montena technology a e de Montena oen Swtzerland phone fax

7 7. ppendx 1 : graphcal reult The followng graphc how example of calculaton appled on a typcal electrc derate enor. Fgure 1 : epone of the enor alone (relaton put oltage / E feld) Fgure 2 : epone of the ntegrator alone (put oltage / nput oltage) Fgure 3 : epone of the full ytem (relaton put oltage / E feld) The fgure 1 how both fruency doman: 1) the dfferentatng low fruency regon and 2) the hgh fruency elf ntegratng regon (aboe ab 3 GHz n th example). The enor mut be degned to hae a tranton fruency between thee 2 regon hgh enough. The combnaton of the enor wth the ntegrator ge an ntermedate fruency range for whch the repone of the full ytem flat. Therefore the ntegrator mut be pecally degned for the enor. The tme contant ha alo a drect nfluence on the leel of the flat regon, that to ay on the entty of the whole ytem. emark: the reonance fruence of the enor and of the ntegrator are not repreented here. Veron B - V:\Note_applcaton\_doc\TN12_enor_ uaton.doc 7/7 montena technology a e de Montena oen Swtzerland phone fax