1、IM-08-901 1AbstractDesign details and measurement results of the eddy-current displacement transducer with extended linear range and automatic tuning are presented. The transducer is based on resonant impedance inversion method of transfer curve linearization where the displacement probe circuit is
2、kept in resonance by the resonance control loop. The transducer exhibits extended linear range due to compensation of displacement probe losses by a negative impedance converter (NIC) at the transducer input. Particular attention is paid to the NIC design and its temperature compensation. The new vo
3、ltage controlled NIC circuit is introduced which can be easily realized with a standard commercial integrated circuit (LM 1496). Details of the transducers reference generator and the NIC control voltage generator are presented too. The transducers linear range extends from 0.25 mm to 3.75 mm (appro
4、ximately 44% of the 8 mm probe diameter) while maintaining non-linearity within 2% F.S. This is at least 75% improvement to the best commercially available eddy-current displacement transducers (80 mil 2 mm linear range for 8 mm probe). Further linearization could be achieved by post-linearization o
5、f the detected signal.Index TermsContactless displacement transducer, eddy-currents, resonant impedance inversion, probe losses compensation, negative impedance converter (NIC), linear range extension, automatic resonance tuningI. INTRODUCTIONHE block-diagram of the eddy-current displacement transdu
6、cer with extended linear range and automatic tuning is depicted in Fig.1. The initial design of this transducer was introduced in 1, but without the probe losses compensation, e.g. no extension of the linear range was attempted. The detailed analysis of the transducer performance was not presented i
7、n 1, as well. The transducer consists of a probe and a signal-processing unit connected to the probe via coaxial extension cable. The probe is a simple, usually coreless coil placed in the tip of a suitable probe body. The purpose of signal-processing unit is to excite the probe with a high frequenc
8、y current (1 MHz) and to detect the voltage developed across the parallel tank circuit comprised of the probe impedance (lossy inductance) and the total parallel capacitance consisting of the cable capacitance and the transducer input capacitance. The detected voltage is resolved into the in-phase (
9、I) and quadrature (Q) components. The in-Manuscript receivedDarko Vyroubal is with the Polytechnic of Karlovac, Trg J.J Strossmayera 9, 47000 Karlovac, Croatia. (e-mail: darko.vyroubalvuka.hr)09Preamp.I-Demod.Q-Demod.I-LPFQ-LPFEroAmp.Out Amp.CT RefrnceExcitaionCure Signal-Procesing UitExcitaionCrlPr
10、obe CilTargetdrob-TargetCuplin In-hase DtcoruadrteDtcTunigotrlZ(d)V iProbe-TargtDisplcmn VoNICX0X1Y0YZ0Z1VtFig.1 Block-diagram of the improved eddy-current displacement transducer with extended linear range and automatic tuning. It is based on the block-diagram introduced in 1 phase component is pro
11、portional to the probe-to-target displacement and is used for displacement transducing, while the quadrature component is proportional to the resonance detuning and is used by the automatic resonance control loop to keep the tank in resonance. The physical basis of probe-to-target displacement trans
12、ducing, as well as the probe mathematical model are in more details described in 2. II. THE EQUIVALENT INPUT CIRCUITThe equivalent input circuit is comprised of the probe equivalent impedance, Z(d) in parallel to the total capacitance, C and parallel to the total input resistance, R. The probe equiv
13、alent impedance model is developed in 2 as a series lossy tank circuit above the series (current) resonance, e.g. the reactance is inductive. The probe reactance, as well as, the probe series resistance (probe losses) are sensitive to probe-to-target displacement. The probe resistance is used for di
14、splacement transducing in the signal processing unit. The total parallel capacitance consists of the cable capacitance, CP and the tuning capacitance, CT comprised of the preamplifier input capacitance in parallel to the capacitance of the tuning varicap diode. As the preamplifier input capacitance
15、is very low compared to the varicap capacitance, it can usually be ignored. The total input resistance is comprised of parallel connection of the negative resistance, RN of the negative impedance converter (NIC) and the equivalent input resistance, Ri of the preamplifier in parallel to the excitatio
16、n current generator. The equivalent input circuit diagram is in Fig.2.Eddy-Current Displacement Transducer with Extended Linear Range and Automatic Tuning Darko Vyroubal, Member, IEEETIM-08-901 2CPTRiNjX(d)Z(d)r(d)-jrj0R0r V (d)ProbeCableTransducer iFig.2 The equivalent input circuit diagram.The pro
17、be impedance elements are 2:X0 - probe intrinsic inductive reactance when not influenced by the eddy-currents in the target, e.g. probe far from the target.Xr(d) - probe reflective capacitive reactance, result of eddy-current losses in the target, displacement dependent.X(d) - total probe inductive
18、reactance, displacement dependent.R0 - probe intrinsic series loss resistance when not influenced by the eddy-currents in the target, e.g. probe far from target.Rr(d) - probe reflective series loss resistance, result of eddy-current losses in the target, displacement dependent.r(d) - total probe ser
19、ies loss resistance, displacement dependent.The equivalent input circuit impedance can be expressed as. (1)jeZjZImeThe circuit is in resonance when the impedance phase angle equals zero, what makes the very parameter used by the resonance control loop as the error signal. It is reasonable to assume
20、that the resonance control will exhibit small residual error. e.g. residual . Considering as detuning measure, one can resolve impedance in resonance by inspection of the equivalent circuit. (2)iNres RRdXdZ;)()(22with the parallel capacitive reactance, XC required for the resonance tuning, maintaine
21、d by the resonance control loop050101502012345678910Displacemnt, dReq OhmReq (simulation) (hyprbl)Req (asured)R0Fig.3 Comparison of measured 1 and simulated 2 total probe series loss resistance to the interpolated hyperbola. (3)tan)()()(22RdXrdXCThe real part of the impedance then equals. (4)2tan1)(
22、ReresZdand the in-phase voltage developed across the tank is equal to the voltage drop on ReZ(d) produced by the excitation current.III.RESONANT IMPEDANCE INVERSIONBy inspection of (2) there follows that ReZ(d) is displacement dependent through r(d), as well as through X(d). Dependence of r(d) and X
23、(d) on displacement was experimentally established in 1 and theoretically analyzed in 2. The variation over the displacement range is for X(d) some 10%, while for r(d) it is approximately 10:1. This is the reason why r(d) is used for displacement transducing. Comparison of measured 1 and simulated 2
24、 r(d) (here labeled Req as in 1 and 2) to the interpolated hyperbola is in Fig.3. From Fig.3 follows almost hyperbolic behavior of r(d) C/d over small to medium displacement range, while for large displacements it is almost constant, masked by the probe intrinsic series loss resistance R0. The total
25、 probe series loss resistance, r(d) can be modeled as a series connection of the probe reflective series loss resistance, Rr(d) which is almost hyperbolic 1, 2 and the constant probe intrinsic series loss resistance, R0. Introducing this model into (2) gives . (5)BdAXdrdZrres )()()()( 202As X(d) is
26、only slightly dependent on d and almost ten times IM-08-901 30.E+2.34.0E+6.38.0E+1.4.20E+1.4012345678910Displacemnt, dProbe In-phase imdance, ZOhm Z1(RN=-4k)2 53(-7k)Z4 RN=105(-2k)6 MFig.4 Linearization of the transducer for various amount of negative resistance added by the NIC.bigger than r(d) 1,
27、2 one can assume A and B in (5) almost constant in respect to d. On the other hand R can be made negative by proper adjustment of RN, canceling R0 in B and making B in (5) to vanish. Then becomes almost resdZ)(linear in d. (6)dDCArResZ)()(as Rr(d) is almost hyperbolic in respect to d, and dCRr/)(the
28、 linearization of the transducer is achieved through resonant impedance inversion. The amount of negative resistance RN added by the NIC is limited in order to keep the total resistance of the input circuit positive (otherwise the transducer would turn into oscillator). Simulation results for variou
29、s values of RN and r(d) as in 2, as well as for Ri = 10 k are in Fig.4. The linear range for RN = - 4 k is approximately 1.5-5.5 mm, while for RN = - 20 M (almost no negative conductance applied) it is 0.5-2.5 mm. Application of the negative resistance has sigificantly extended the linear range. The
30、 side effect is introduction of approximately 1 mm of additional linear range offset from the probe tip what can be easily accommodated for by displacing the probe coil for this amount deeper into the probe body.IV.SENSITIVITYThe transducer transfer curve is dependent on applied negative conductance
31、 (Fig.4) and on the performance of the resonance control, e.g. residual impedance phase error (4). Both are prone to variation induced by many factors like operating temperature, element tolerances, aging etc. Sensitivities to RN and are analyzed in order to establish transducer design constraints.A
32、. Sensitivity to RNSensitivity to RN follows after partial differentiation of (2) in -4-3-2-10Sensitvy012345678910-4.E+036-8.10+4-.2E0-1.6+48-2.0EDisplacemnt, d RN Fig.5 Sensitivity of to displacement d and negative resistance RN.rZ)(. (7)NresNresdZRRSresN)()()(respect to RN. From (7) follows that t
33、he sensitivity is dependent on d. It is plausible, as for small to medium d the probe losses are mainly caused by eddy-currents in the target, while for large d it is mainly caused by probe intrinsic losses and RN. The sensitivity dependence on d and RN is in Fig.5. As expected, sensitivity is the h
34、ighest for large d and maximum negative conductance applied. However, it is reasonably limited to approximately 3. Such a sensitivity is not prohibitively high, making the transducer construction feasible by careful design.B. Sensitivity to Sensitivity to follows after partial differentiation of (4)
35、 in respect to . (8)tan2)(Re)(edZSdFrom (8) it is evident that the sensitivity to resonance detuning could be quite large because , as well as, tan rise rapidly with detuning if the tank quality factor, QT is at least reasonably high (QT 10). Further assessment of sensitivity to resonance detuning r
36、equires analysis of the resonance control loop performance.V. RESONANCE CONTROL LOOPThe resonance control loop model is derived from Fig.1 and the clarification of in-phase and quadrature detection process of the voltage across the tank as in Fig.6. Detectors are simple switches followed by IM-08-90
37、1 4In-phase dtector In-phase LPFQuadrturedtector QuadrtureLPFVi(d) TTT/2X1(t)Vi(t)T/2T/4 T/2T/2T/2X0(t)Y1(t)Y0(t) Vi(d)Fig.6 The in-phase and quadrature detection of the voltage at the input of the signal processing unit.low-pass filters extracting DC voltages proportional to displacement and the re
38、sidual phase error. The detected quadrature component Y1 of Vi, is low-pass filtered producing a DC voltage Z1 . (9)sin)(1diwhich is in the error amplifier combined with amplifier offset and amplified to the tuning voltage level. (10)sin)()(dVKdViostwhere K is the amplifier gain and Vos is amplifier
39、 offset voltage. The varicap sensitivity to the tuning voltage is in (11) 3, where CP is the tank parallel capacitance and Qp is the probe quality factor, (not the total tank )(/)(drXdQpquality factor, QT although for low parallel loading, PTQe.g. high R ). (11)11)(nBtVBt VCwhere CVB is the varicap
40、capacitance at the varicap bias voltage VB, is the PN junction contact potential ( 0,7 V in Si) and n is the exponent describing the varicap PN junction type (n = 1/2 for abrupt junction, n = 1/3 for graded junction). CV(Vt) is the change of the varicap capacitance at the varicap bias voltage, VB re
41、lative to the control voltage, Vt - VB.The tank impedance phase sensitivity to the varicap capacitance is evaluated by analysis of the equivalent input circuit in Fig.2. (12)VBPpCdQd1)()(arctn)(With CV = 0 tank is assumed to be in resonance.The control loop equation is derived from Fig.1 by inspecti
42、on. For steady-state phase error the loop equation reads. (13)0VtCwhere 0 is the initial resonance detuning phase error.Combining (9), (10), (11), (12) and (13), the resonance control loop steady-state equation is derived 1sin)(11)(arctn)(0 iosBVPp dVKCdQd (14)The resonance control loop model based
43、on (14) is in Fig.7. Equation (14) is a trigonometric equation that was solved numerically for various combinations of initial tank resonant frequency detuning, error amplifier gain and offset. The initial detuning phase error is proportional to the tank resonant frequency detuning and the probe qua
44、lity factor QP which is displacement dependent.IM-08-901 5Fig.7 The resonance control loop model. (15)resPdQ,)(2arctn0where is the relative resonant frequency detuning that was in solution to (14) assumed to be limited to 10%. The total equivalent amplifier offset voltage was assumed to be within 10
45、 mV (rather conservative for modern operational amplifiers). Solution to (14) was sought for minimum and maximum negative conductance of the NIC applied (RN = - 20 M and RN = - 4 k, respectively) and for low, medium and high error amplifier gain (K = 10, K = 100 and K = 1000, respectively). In Fig.8
46、 there are limits of the residual phase error. As could have been expected, the residual error gets smaller as the control loop gain rises. The loop gain is dependent on the amplifier gain, but as well as on the phase detector sensitivity which is proportional to the voltage across the tank. This vo
47、ltage decreases due to increased damping by eddy-currents as the probe gets closer to the target, resulting in decrease of the loop gain. These effects contribute to the rise of residual phase error for decreasing displacement, but for even smaller displacement the error decreases after peaking. As
48、the displacement gets even smaller, the tank quality factor (QT) becomes very small due to heavy damping by the eddy-currents. This results in smaller phase error for the same frequency detuning () as the steepness of the tank phase characteristic decreases for small QT. From Fig.8 it is apparent that the residual phase error is prohibitively high for low amplifier gain (K= 10) and the minimum n
