4.6.1 Self-inductance arrangements M R d 2 Metal plate Coil system Metal conductor Fig. 4.18 Principle of eddy- Fig. 4.19 Equivalent circuit of the eddy-current current transducer transducer and the measured object
4.6.1 Self-inductance arrangements Fig. 4.18 Principle of eddycurrent transducer Fig. 4.19 Equivalent circuit of the eddy-current transducer and the measured object
4.6.1 Self-inductance arrangements The metal conductor is represented by a short-circuit coil coupled linearly with the transducer coil. A mutual inductance is defined as the degree of coupling between the elements and M decreases when the gape Increases R1 and are the resistance and inductance of the coil. an&2 and2 are the resistance and inductance of the conductor respectively
4.6.1 Self-inductance arrangements The metal conductor is represented by a short-circuit coil coupled linearly with the transducer coil. A mutual inductance M is defined as the degree of coupling between the elements, and M decreases when the gap increases. R1 and L1 are the resistance and inductance of the coil, and R2 and L2 are the resistance and inductance of the conductor respectively
4.6.1 Self-inductance arrangements By kirchhoff s law of current and voltage we have r,1+JoL,l -,=E (4.30) JOMI+R212+ jOL 0 Solving the above group of equations yields E (432) M M R,+ R+ill R2+(L2) RA+(OL )2 OL MI Mo L2l+ jOMR2I 2=J0 (433) R2+JOL? R2+2L
By Kirchhoff’s law of current and voltage, we have − + + = + − = 0 . 2 2 . 2 2 . 1 . . 2 . 1 1 . 1 1 j M I R I j L I R I j L I j M I E （4.30） Solving the above group of equations yields + + − + + = 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 . . 1 ( ) ( ) L R L M R j L R L M R E I （4.32） 2 2 2 2 2 . 2 1 . 2 1 2 2 2 . 1 . 2 R L M L I j MR I R j L M I I j + + = + = （4.33） 4.6.1 Self-inductance arrangements
4.6.1 Self-inductance arrangements Further we can obtain the equivalent resistance of the con,,after being affected by metal conductor in the following relation M M Z=R+R2 p+OL +jOL, -oi (434) R2+2L The equivalent inductance of the coil is then M L=L-L 4.35) R4+
Further we can obtain the equivalent resistance of the coil, Z , after being affected by metal conductor in the following relation: + + − + = + 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 R L M j L L R L M Z R R （4.34） The equivalent inductance of the coil is then 2 2 2 2 2 2 2 1 2 R L M L L L + = − （4.35） 4.6.1 Self-inductance arrangements
4.6.1 Self-inductance arrangements L is related with the static magnetic effect The second term of Eq (4.35)is dependent of the eddy-current effect. The eddy-current generates a magnetic field, which opposes the original magnetic field and thus reduces the inductance of the coil
• • The second term of Eq. (4.35) is dependent of the eddy-current effect. The eddy-current generates a magnetic field, which opposes the original magnetic field and thus reduces the inductance of the coil. 4.6.1 Self-inductance arrangements L1 is related with the static magnetic effect