Fundamentals of Measurement Technology Prof Wang Boxiong
Fundamentals of Measurement Technology (9) Prof. Wang Boxiong
4.6 Inductive transducers Inductive transducers are based on the voltage output of an inductor (or coil) whose inductance changes in response to changes in the measurand a classification of inductive transducers 1. Variable self-inductance a. Single coil(simple variable permeance) b. Two coil (or single coil with center tap) connected for inductance ratio 2. Variable mutual inductance a. simple two coi b. Three coil (using series opposition) 3. Variable reluctance a. Moving iron b. Moving coil C. Moving magnet
• Inductive transducers are based on the voltage output of an inductor (or coil) whose inductance changes in response to changes in the measurand. • A classification of inductive transducers : 1. Variable self-inductance a. Single coil (simple variable permeance) b. Two coil (or single coil with center tap) connected for inductance ratio 2. Variable mutual inductance a. Simple two coil b. Three coil (using series opposition) 3. Variable reluctance a. Moving iron b. Moving coil c. Moving magnet 4.6 Inductive transducers
4.6. 1 Self-inductance arrangements 1. Simple permeance-varying A simple permeance -varying transducer is composed of an iron core. a coil and an armature an air ga is arranged between the core and the armature when a current i flows through the coil, a magnetic flux m is generated within it, whose magnitude is proportional to the current z Won=li (4.22) where number fo turns self inductance
1. Simple permeance-varying 4.6.1 Self-inductance arrangements A simple permeance-varying transducer is composed of an iron core, a coil and an armature. An air gap is arranged between the core and the armature. When a current i flows through the coil, a magnetic flux m is generated within it, whose magnitude is proportional to the current i : W Li m = （4.22） where W = number fo turns L = self inductance (H )
4.6.1 Self-inductance arrangements I-coil 2-core armature b Fig. 4.15 Principle of permeance-varying transducer
4.6.1 Self-inductance arrangements Fig. 4.15 Principle of permeance-varying transducer 1－coil 2－core 3－armature
4.6.1 Self-inductance arrangements Also according to ohms law of magnetic circuit Wi (423) R where Wi=magnetic motive force R m reluctance H Substituting eq (4.23)into Eq (4.22) yields W L (424) R
Also according to Ohm’s law of magnetic circuit m m R W i = （4.23） where Wi = magnetic motive force (A ) Rm = reluctance ( −1 H ) Substituting Eq. (4.23) into Eq. (4.22) yields Rm W L 2 = （4.24） 4.6.1 Self-inductance arrangements
4.6.1 Self-inductance arrangements Neglecting the iron loss in the magnetic loop and assuming the air gap is small, then the total reluctance of the magnetic circuit 126 R (425) A where / length of the iron circuit ( m u=permeability of the iron core f /m A =crOSs-sectional area of the iron, A=ab(m) length of the air gaps() Ho=permeabiltiy of free space( vacuum)Ao =4T X10(H/m Ao =cross-sectional area of the air gap(
Neglecting the iron loss in the magnetic loop and assuming the air gap is small, then the total reluctance of the magnetic circuit: 0 0 2 A A l Rm = + （4.25） where l = length of the iron circuit (m ) = permeability of the iron core (H / m ) A = cross-sectional area of the iron, ) 2 A = a b（m = length of the air gaps (m ) 0 = permeabiltiy of free space ( vacuum) 4 10 ( / ) 7 0 H m − = A0 = cross-sectional area of the air gap ( 2 m ) 4.6.1 Self-inductance arrangements
4.6.1 Self-inductance arrangements Since the first term at the right-hand side of eq.(4.25), the reluctance of the iron is much smaller than the second term the reluctance of the air gap then the total reluctancem, with the first term neglected, is approximately 26 (426)
Since the first term at the right-hand side of Eq. (4.25), the reluctance of the iron, is much smaller than the second term, the reluctance of the air gap, then the total reluctance R m , with the first term neglected, is approximately 0 0 2 A Rm （4.26） 4.6.1 Self-inductance arrangements
4.6.1 Self-inductance arrangements Substituting Eq. (4.26)into Eq.(4.24)gives (427) 2 The self-inductance is proportional to the cross-sectional area of the air gap Ao, and is inversely proportional to the length of the air gap
Substituting Eq. (4.26) into Eq. (4.24) gives 2 0 0 2 2 W A L = （4.27） The self-inductance is proportional to the cross-sectional area of the air gap, A0 , and is inversely proportional to the length of the air gap, . 4.6.1 Self-inductance arrangements
4.6.1 Self-inductance arrangements The sensitivity of the transducer dL w S (428) ds 2 Sensitivity s is inversely proportional to 8.As is not a constant, nonlinearity will occur. This kind of transducers operate often over a range of small change in the air gap
The sensitivity of the transducer 2 0 0 2 2 W A d dL S = = − （4.28） Sensitivity S is inversely proportional to 2 . As is not a constant, nonlinearity will occur. This kind of transducers operate often over a range of small change in the air gap. 4.6.1 Self-inductance arrangements
4.6.1 Self-inductance arrangements From Eq (4.28)we obtian WuoA WuoA WuoA △6 S 04-0 0410 262 2(0+△)2N 26 If there is a very small air gap, that is,△δ<<δo, the sensitivity s can be further approximated as W-LoA S (429) 26
From Eq. (4.28) we obtian (1 2 ) 2 2( ) 2 0 2 0 0 0 2 2 0 0 0 2 2 0 0 2 − + = − = − W A W A W A S If there is a very small air gap, that is, 0 , the sensitivity S can be further approximated as 2 0 0 0 2 2 W A S = （4.29） 4.6.1 Self-inductance arrangements