仪表与量测PPT课件-Measurement of Impedances.ppt

measurement of impedances p. osvath,principles of impedance measurement qualitative properties of measurement circuits basic types of measuring circuits measurement of basic impedances impedance analyzers,introduction,impedance measurement is more complex than current and voltage measurement. it is the ratio of these two quantities. it requires modeling of physical objects. basic approach - bridge circuit. modern approach - due to the high-permeability ferromagnetic material inductive dividers ratio transformers current comparators accuracy is increased by 1-2 orders.,introduction - this chapter,impedance measurement circuits effects of measurement leads error due to different stray impedances methods to eliminate these effects,principle of impedance measurement,simple assumption sinusoidal input and sinusoidal outputs the ratio of voltage and current gives the absolute value of impedance at the given frequency phase is measurable three basic types of impedances: r, c, l phases are 0, -90, and +90 degree respectively. the clean impedance:,principle - realistic,physical object model must be involved ideal model cannot describe the voltage-current relationship at different frequency real objects have rather complex physical phenomena. for example - a r (section 2.3.2) is modeled as a r,l,c network. impedance measuring instruments usually measure elements of a two-component (parallel or serial) model of an impedance at a selected frequency.,principle - realistic,important considerations measurement can be understood only within the frame of the modeling procedure. neglecting significant phenomena will result in erroneous measurement. nonlinearities can cause very different measured parameters values at different excitation level. polarisation causes an increase of capacitance in certain frequency bands. measurement design issues validation of the model validity checks measure the parameters of a model not the real “capacitor“.,principle - measure methods,straightforward measure the voltage measure the current divide the voltage by the current high accuracy measurement voltage and current measurements are accomplished by comparisons. the reference for comparison is the voltage on a known impedance or the current flowing through it.,principle - measure by voltage comparison,v,v,unknown impedance standard impedance current source current source,principle - measure by voltage comparison,v,v,principle - measure by current comparison,principle - measure by current comparison,a,a,qualitative properties of measuring circuits,measured value true value absolute error absolute value phase error relative error,definitions of errors,qualitative properties - error types,error estimation: deterministic error: point error probability error: interval estimator,relative error: represented as per cent, per thousand, or parts per million (ppm),constant absolute error: caused by finite sensitivity or constant noise. relative error changes along with the measured value.,qualitative properties - error types example,milli-ohm-meter range 1 w constant error: dr = 0.1mw relative error: 1% error limit: e = +/-(0.1mw + 1%) 1w is measured e = +/- 10.1mw er = +/- 1% 1mw is measured e = +/- 0.11mw er = +/- 10%,qualitative properties - frequency dependence,the main parameters of the impedances (rlc) are expected to be frequency independent. the main sources of frequency dependent error are the standard impedances, stray capacitance/inductance and second order effects. other sources of frequency dependence are lcoated in the structure of the measuring circuit, the connection leads.,qualitative properties - frequency dependence (leads),v,a,measuring instrument,coaxial cable,two-wire measurement,qualitative properties - frequency dependence (leads),r: resistance in w/m g: conductance in s/m l: inductance in h/m c: capacitance in f/m l: cable length,qualitative properties - frequency dependence (leads),two terms in taylor expansion,rg58 c/u c=100pf/m l=0.476mh/m r=36.2mw/m 1m long cp=55pf/m ls=0.238mh/m rs=18.1mw/m 50w wave impedance denominator =1 at 32.5mhz used up to 1mhz,qualitative properties - frequency dependence (leads),f,hz,qualitative properties - frequency dependence (leads),qualitative properties - freq depend - three-wire,v,a,measuring instrument,coaxial cables,shield,qualitative properties - freq depend - three-wire,qualitative properties - freq depend - three-wire,f, hz,qualitative properties - freq depend - three-wire,qualitative properties - freq depend - five-wire,v,a,measuring instrument,coaxial cable,shield,qualitative properties - freq depend - five-wire,qualitative properties - lead - five wires,qualitative properties - lead - five wires,minimal detectable and maximal measurable values micro-ohm-meter resolution of 0.1mw maximal value 10w missleading without giving the error smallest and largest values measurable with the given error. error is 0.1% of the range minimum value 0.1mw maximal value 10w industrial specs resistances: 10-7w to 1013 w capacitances: 10-15 f to 0.1f inductances: 10-8 h to 108 h,qualitative properties - measure range,four arm (wheatstone) bridge bridge with ratio transformer and inductive divider bridge with inductive current comparator electronic impedance measuring circuits t and double t circuits resonance methods,basic types of impedance measuring circuits,types - four arm (wheatstone) bridges,1843 wheatstone invented the circuit 1892 siemens proposed practical solution,nd,arms are built of resistors, capacitors, or inductors. a bridge is a simple form of the voltage comparators.,types - four arm (wheatstone) bridges,nd,relative errors of bridging devices absolute value: phase:,types - four arm bridges - sensitivity,limited sensitivity of the null detectors the deviation of rx causing no deflecting of the null detector. called domain of insensitivity or dead zone. sources: noises of the amplifiers, the friction of the display instrument. in dc null detectors, the noise source are the drift and the so-called flicker or 1/f noise. ac null detectors are frequency selective, direct filtered amplifiers have typical 100nv in 10hz-100khz. the source is mainly from johnson noise of the resistor and distribution noises of semiconductors. frequency transposition (mixer) have higher noise, 1mv.,types - four arm bridges - sensitivity,sensitivity sb is ratio of dud to dzx.,bridge factor.,bridge ratio.,real,imaginary,|h|max=1/2 or f=j,|h|max=1/4 or f=1,types - four arm bridges - sensitivity - example,nd,nd,optimal value when w = 1/rc,optimal value when resonance,types - four arm bridge - frequency dependence,resonance bridge,types - bridge - frequency dependence,types - bridge - earth impedances,nd,a,c,d,b,earth impedance: the impedance to the earth ground, ra rd. if d is connected to earth, the ra effect disppear. similarly for b and c. impossible to have b and d both connected to ground.,nd1,nd2,a,c,b,d,types - bridge - earth impedance removable,a half bridge is connected to the cource, z2 and z4. adjust z2 and z4 such that c has same potential as earth. if nd1 detects no current, b is also earthed. hence, the earth impedance is removed.,wagner earth device,nd1,nd2,a,c,b,d,types - bridge - earth impedance removable,b and c are brougth to earth potential by a complex voltage source connected between d and earth. this is a more mordern solution for higher flexibility and better convergence.,types - bridge - earth impedance removable,the potential difference between node c and earth is detected by an amplifer. the output of the amplifier is connected to node d. if the gain of the amplifier is infinite, the output force the potential difference between c and earth to zero. the main concern is to guarantee the stability of the amplifier-bridge structure. the large unknown zx makes the feedback loop variable and difficult to stabilize with a fixed compensation.,brueckel automatic solution,types - bridge - earth impedance removable,the bridge is connected to earth because high-voltage source is also connected to earth. the low voltage-part is shielded. the shied potential is adjusted to the potential of bridge arm b,c. the zero potential difference between b,c and shield do not allow an error current to flow from b, c to earth. note, the earth current is flow from the amplifier or the shield because the output impedance of the amplifier is much lower than the earth impedance.,high voltage schering bridges,types - bridge - speed of measurement,the bridge circuit is balanced by successive approximation. if an absolute value indicating a null detector is used, the operator has to reach the balanced state by successively search of minimal deflection. a solid curve represents a curve with a fixed r3. a dotted line represents a curve with a fixed c4.,0.2,0,0.2,0.4,0.6,0.8,1.0,0.6,0.4,0.2,0,0.2,0.4,0.6,types - bridge - ratio transformer,the inductive ratio transformer is a voltage transformer with two or more windings. they are wound on a toroidal core made of a high-permeability material. it produces two voltages with a ratio proportional to the ration of the two turns. the resistive divider is temperature dependent with inductive divider is not. proposed by walsh (1930), into practice by watton and pemberton and clark and vanderlyn (1949), high accuracy solution by hill and miller (1962) and deacon (1968),nd,a,b,c,types - bridge - ratio transformer,nc and ng are made of serial connected decade windings. gn and cn are are adjustable. the advantage is the low cost.,nd,types - bridge - ratio transformer,nd,high-accuracy ratio transformer bridge,types - bridge - ratio transformer,combined ratio transformer bridge,nd,types - bridge - ratio transformer - error,error sources inhomogeneity of the core permeability the imperfect coupling between the windings and the interwindiding capacitances. analyzed by binnie and foord (1967) for an unloaded ratio transformer, at f=1khz, a well constructed one has an error in the range of 10-7 to 10-8. for a loaded one, the situation is different.,types - bridge - error - simple ratio transformer,z1 z2 : stray serial capacitances of the windings. zs1 zs2 : stray serial resistances and inductances of the coils.,b,nd,a,load sensitive,types - bridge - error - simple ratio transformer,nd,b,a,c,not load sensitive,types - bridge - ratio transformer - inductive divider,a special but very useful variant of the inductive divider. the ratio error has its maximum at y=0.5. with zl=10w, the error is 10ppm.,types - bridge - ratio transformer - conclusion,inductive ratio transformer is a high accuracy ratio device with no temperature and aging error. it give higher accuracy and higher flexibility than the resistive divider. it can be made insensitive to the load. the disadvanges are its high cost and the reduced accuracy over 100khz. the high-frequency problem can be partially solved using high frequency ferrite cores and a reduced number of turns. despite these improvements, at over 100mhz, a large inductive core is not comparable to a small low-capacitance bulk metal resistor.,types - bridge - ratio transformer - 4-wires,nd,nd,1:1,1:1,types - bridge - current comparator,the inductive current comparator consists of three or more windings on a ferromagnetic core. the current i1 and i2 produces opposite magnetic field in the core. if the two ampere-turns are equal, the resulted induction will be zero: if i1n1=i2n2; b=0.,nd,core,types - bridge - current comparator,types - bridge - current comparator + ratio transformer,nd,core,core,inductive ratio transformer,inductive ratio transformer,types - bridge - current comparator - errors,the source of errors in an inductive current comparator are the magnetic inhomogeneity of the core-winding structure and the stray capacitances. magnetic errors: nonideal magnetic inductor (ideal one has infinitely long linear core and the curve integral of the field is zero) the spatial distribution of the null detector winding is not uniform. capacitive errors: from the stray earth capacitance.,types - bridge - current comparator - errors,types - bridge - current comparator - errors,types - bridge - current comparator - errors - example,a high-voltage capacitance measuring circuit cx=1nf uo=1kv, 50hz. measure situation u1l=1v cs=100pf the relative error:,nd,core,uo,zx,zn,types - bridge - current comparator - sensitivity,(l: magnetic succesptibility),high input impedance null detector,low impedance current detector,h increase with w and nd.,high input impedance null detector,low impedance current detector,h increase with w and nd. output voltage depends on the iron permeability if current is far away from the balancing point, the saturation of the core can reduce the sensitivity.,types - bridge - current comparator - sensitivity,the linearity of the bridge is better. the sensitivity is low.,types - bridge - current comparator - frequency,current-comparator bridges are important in industrial frequencies (50-60hz). the magnetic properties have theoretically higher influence on the errors than the capacitive effects. the error is usually of 1 - 10 ppm. at higher frequency (over 10khz) the capacitive error dominates. at 100khz, the magnetic quality degrades, the capacitive effect is high, an error over 100ppm can be expected. the optimal frequency of an inductive current comparator is 1khz. the error is around 10ppm.,types - bridge - current comparator - 5-terminal,nd,cx has much higher value than cn cn is connected on the potential terminals of cx. in this way, the effects of lead can be eliminated. the error is the leackage from nn to earth when the current is large.,1,2,3,4,5,high-permeability core of the curent comparator produces noise due to mechanical deformation, eg. vibration, of the core. the core is also very sensitive to external magnetic field (high permeability magnets). shield is very important.,types - electronic impedance measuring circuits,electronic voltage ratio generation,electronic current comparator,types - electronic - ac ratio detectors,sectional average integrator,dual-slope voltmeter,sectional average integrator - integrate a whole number of periods. phae sensitive detector - passes +ua when uref0, -ua when uref0.,phase sensitive detecter,types - electronic - ac ratio detectors,s1 s2,measure real,measure imaginary,t1 t2,t3 t4,s1 s2,types - electronic - ac ratio detectors - simplified,dual-slope voltmeter,un is in phase with the signal source of ux (by pll). measure the i/q components of ux and un respectively to determine the amplitude and phase of ux.,types - electronic - ratio generator and current comparator,nd,ix is compared to in. adjust cn and gn such that in is equal to ix.,types - electronic - ratio generator and current comparator,require measure both i and q of x and y.,types - electronic - error,basic errors and sensitivity an electronic solution cannot override the limites of uncertainties of standard impedances. the amplifiers are not ideal (gain, i/o impedances) despite this, electronic circuits provide the highest accuracy because only one standard resistor is used. the phase detection system must be suficiently accurate. dual-slope voltage detection can guarantee the required accuracy.,types - electronic - error,frequency dependence and connections the frequency dependent transfer function of the amplifier yields a systematic error.,a second problem is the stability. the measured impedance is included in the feedback loop. in practice, it is impossible to find a feedback compensation working correctly in all the cases.,types - electronic - 5-terminal measurement,nd,1,2,3,4,5,virtual earth,types - electronic - ratio detector,+,-,+,-,-,+,ratio detector,x,y,re x/y,im x/y,a1 and a2 are connected in noniverting mode so that the impedance are not in the feed