仪表与量测PPT课件-Chapter 2 Measurement of Current and Voltage.ppt

chapter 2 measurement of current and voltage i. zoltan,basic considerations measureing networks signal converters types of meter measuring instruments,basic considerations,direct voltage direct current mean value mean absolute value root-mean-square (rms) vaule pean value instantaneous value vector components frequency spectrum,basics - ranges of current measurements,basics - ranges of voltage measurements,1nv,1v,1mv,1v,1kv,1mv,dc nanovoltmeters,dc dmm,ac,electromechanical voltmeters,extenders,basics - voltage/current measurement model,dut - device under test esc - external signal converters ml - measuring leads sc - internal signal converters v/a - meters,measuring networks - source,source,measuring leads,measuring instrument,u,i,voltage source,current source,in,out,in,out,ideal,nonideal,measuring networks - measuring leads,source,measuring leads,measuring instrument,measuring networks - meters,source,measuring leads,measuring instrument,v,voltmeter,h,l,a,h,l,ammeter,measuring networks - loading error - v meter,u,v,measuring networks - loading error - i meter,i,a,measuring networks - asymmetric network,u,v,in,ground voltage differences cause extra error,ground (earth) is a conducting connection by which an electrical circuit or electrical equipment is connected to the earth or to some conducting body of relatively large extent that serves in place of earth.,measuring networks - symmetric - multiple grounded,u,v,h,l,distrubing current caused by different grounding potential,measuring networks - symmetric - single grounded,u,v,h,l,measuring networks - common mode voltage,u,a),b),i,a common mode voltage (voltage/current source are always floating on top of it),measuring networks - effect of common mode voltage,u,v,in,h,l,common mode voltage has no effect only when zg is zero.,measuring network - common mode voltage prevention,u,v,h,l,g,guard shield,guard shield,measuring network - common mode voltage prevention,double guard shield,v,h,l,g,guard shield,in,ground shield,measuring network - interference sources,signal source,measuring lead,c,g,measuring instrument,h,l,u,interference source,i,load,m,g: stray capacitance c: stray resistance m: mutual inductance,measuring network - interference elimination,elimination: satic and magnetic shielding of measuring networks,b,c,g,u,in,out,twisted pair: reduce effective cross section (m),guard shield,ground shield: copper (electrical fields, c, r),magnetic shield: mumetall plates (m),measuring network - interference elimination,elimination: satic and magnetic shielding of the source,a) using coxial cable,source,load,i,b) using coaxial cable combined with full shielding,source,load,i,measuring network - interference elimination,elimination: magnetic shield of transformer leakage magnetic field can be further reduced using a toroidal core.,transformer,magnetic shield,measuring network - interference elimination,thermoelectric voltage common source of error in low voltage measurement voltages are produced by junctions of different materials having different temperatures eg. thermoelectric potential of pb/sn solder with respect to copper is 1.3 uv/degree (c). eleminated by using the same material and/or good thermal coupling of all junctions (heat sink) fundamental limit to current and voltage measurement is johnson noise in the resistance,signal converters - errors,h,signal converter model,ideal linear signal converter model,in phase transfer ratio error quadature transfer ratio error,signal converters - errors,offset,calibration error,linearity error,offset: constant component of the error that is independent of the inputs. calibration error: difference between the actual transfer ratio and the ideal ration. linearity error: the deviation of the output quantity from a specified linear reference.,signal converters - errors,resolution error,hysteresis error,phase error,resolution error: the error due to the inability of a converter to respond to change of a variable smaller than a given increment. hysterisis error: the difference between the increasing input value and decreasing input value that produce the same output value. phae error: the phase between input and output. for sinusoidal waveform, the phase is dependent on he frequency.,signal converters - errors,temperature dependent error: due to the change in ambient temperature or temperature variation due to self-heating. (temperature stability, temperature coefficient). load error: loading error is due to the effect of a load impedance upon the converter or signal source driving it.,temperature dependent error,load error,no load,signal converters - rlc elements (zinke and seither 1982).,signal converters - rlc elements (zinke and seither 1982).,range: 0.1w to 20mw tolerance: 0.05 to 0.005 percentage temperature coefficient: 25 to 5 ppm/degree (110 ppm) long term stability: 0.005 percent / year inductance tolerance: 1.5mh (80nh) capacitance tolerance: 1.5pf (0.5pf),wire-wound resistors,signal converters - rlc elements (zinke and seither 1982).,inductor (air core),rs: series copper resistance ge: conductance due to eddy-current loss in the winding c: the winding capacitance g: dielectric loss of capacitance c l: frequency dependent change of the inductanct,signal converters - rlc elements (zinke and seither 1982).,inductor (air core),d: dissipation factor three components: ohmic loss eddy-current loss dielectic loss high inductance - special alloy of high permeability toroidal inductor is perferred for small stray magnetic field. air-core inductor has the highest stability and a neglibible variation with current. iron-core inductor is less stable because permeability changes age and current.,signal converters - rlc elements (zinke and seither 1982).,capacitors,l,r,r: metallic resistance in the leads and plats l: the series inductance of the leads and plates gp: dc leakage conductance c: frequency dependent capacitance co: dc capacitance d: dissipation factor (loss tangent),signal converters - rlc elements (zinke and seither 1982).,capacitors,skin effect,dielectric absorption,signal converters - resistance voltage dividers,voltage divider are used for range extension at high input voltage, the stray capacitance between the resistor r2 and the bround becomes predominant.,signal converters - resistance voltage dividers,r2 is broken into three sections each enclosed in its own shield. each shield is held at the mid-potenial of the section the voltage is provided by the auxiliary voltage divider. the capacitive current from the resistor to the shield is reduced.,signal converters - variable resistance voltage dividers,signal converters - series resistance voltage dividers,9r,90.1r,90.01r,9,0,9r,90.1r,90.01r,9,0,in,out,0,10,signal converters - ladder network resistance dividers,signal converters - inductance voltage dividers,signal converters - cascade inductance voltage dividers,signal converters - capacitance voltage dividers,in,out,signal converters - high voltage capacitance dividers,three terminal capacitor,signal converters - pwm dc potentiometer,in,s(t),s,out,s(t)uin,pwm - pulse width modulation the period is t1+t2. the uout is proportional to the width of the pulse with t1. the low pass filter is periodically connected to the input by the switch for a time t1.,t1 t1+t2,signal converters - voltage transformers principle,voltage transformer,voltage transformers are intended fro range extension and isolation. the transfer factor is the turn ration between secondary and primary winding.,signal converters - voltage transformer model,z1 and z2 are the leakage impedances which consist of copper resistances (r1, r2) and leakage inductances (l1, l2). zo includes magnetizing inductance lo and core-loss resistance ro. the relative error of h is,signal converters - vt error compensation,nd: a detection winding uo is the reproduced input. u1-uo is the loss uc is the compensation.,signal converters - vt practical soluations,practical soluation: use a multi-ratio voltage transformer. the accuracy class of voltage transformer of industrial purposes is 0.1-5% at line frequency. the rated secondary voltages are 100, 110, 115, 120, 200, and 230v. standard vt are applicable up to 400kv 40-300hz.,signal converters - vt ratio transformer,ratio transformer is used to produce accurate voltage ratios. voltage ratio is determined by the turn ratio. the ratio tranformer is a very accurate device, used in impedance measurements.,signal converters - current transformer (ct),current transformers (ct) are used for range extension and isolation. i1 is the primary current to be measured, zl is the load impedance. he tranfer factor of the ideal ct is determined by the turn ratio.,signal converters - current transformer model,z1 and z2 are leakage impedance. zo, the magnetizing impedance, is the main source of error. the relative error of h is,signal converters - current transformer - two stage,the second stage is composed of a inner core and compensation winding nc. the compensation current ic approximately equal to the magnetizing current if nc=n2.,outer core,inner core,inner core,outer core,signal converters - current transformer - active,active cv is composed of a cv and a power amplifier (a). the core can be much smaller. the power amplifier produce a current i1 such that nd detectct no signal (negnative feedback),signal converters - cv - active model,the power amplifier is modeled by a controlled voltage source. it has a very low input impedance because the residual flux in the core is near to zero. the input impedance is approximately equal to the primary leakage impedance z1. it is also called a zero-flux current transformer. the error is,signal converters - cv - hybrid,hybrid cv is for very accurate application. hybrid cv combine a two-stage cv with an active cv. the energy-carrying outer core acts as a magnetic shield for the inner core, reducing the sensitivity to external magnetic field.,signal converters - cv - practical solution,use multi-ratio current transformer the accuracy class of ct is 0.1-5%. the rated secondary currents for industry are 1, 2, and 5a. the rated secondary current for instrument is 1-100ma. standard cv is up to 100ka, 40-300hz. the ratio accuracy is 1ppm.,signal converters - cv - multiple input,multi-input cv can be used for weighted summation and subtraction of current.,+,1,-,n,signal converters - dc current transformer,the lower the frequency, the larger the core of an ac ct. dc cts are designed for operation from 0hz. hg - hall generator (by hall efect),signal converters - dc current transformer,a dc ct is composed of two-winding transformer, a hall generator (hg) in the air gap of the core, a power amplifier. the magnetic induction b is detected by the hall generator. the voltage uh is generated in the hall plate due to the hall efect. the amplifier generates the secondary current i2. in the balanced state, the magnetic induction in the air gate is the hall voltage is the secondary current is given by the true secondary current is given by,signal converters - measuring amplifier,measuring amplifiers are used for the measurement of low-level signal. consider the amplifier as the first order with offset.,signal converters - ma - amplifier - error compensation,input voltage of amplifier a is proportional to the phase error of the inverting amplifier. the compensating current ic reduces the phase error.,signal converters - ma - noninverting amplifier,cmrr is the common mode rejection ratio,+,-,in,out,signal converters - ma - differential amplifier,ucm: commond input uo: input offset e is the relative tolerance of the resistance ri,signal converters - ma - instrumentation amplifier,+,-,+,-,+,-,cm,out,sense,ref,signal converters - ma - instrumentation amplifier,ias are closed loop, differential input gain blocks, high input impedance and high cmrr. used for exracting and accurately amplifying low level differential signals floating on high common-mode voltage. four terminal load - sense, ref, out, cm.,signal converters - ma- instrumentation amplifier,cm, the degradation of cmrr due to the distributed capacitace on the input lines can be reduced as shown.,signal converters - ma - isolation amplifier,provides ohmic isolation between the input signal and the output of the amplifier. ia followed by an isolation stage. uiso - across isolation buffer. provide isolation protection, measure low level on high cm voltage for breaking ground loop.,-,+,out,isolation barrier,signal converters - ma - chopper amplifier,chopper amplifiers are used for microvolt-range measurement. dc is converted to ac, amplifiered by an ac amplifier, then converted to dc again. s1 and s2 are controlled by the same frequency for modulation and demodulation. lpf provides dc output proportional to the input. avoid the drift problem of direct coupled amplifier. there are chopper-stabilized op that have a high dc-ac performance.,a,in,out,signal converters - voltage to current converter,votlage measurement can be carried out by an ammerter using a voltage to current converter. the followings are the resistance voltage to current coverter,a,passive,a,passive, multiple input,a,+,-,active,a,+,-,active, mult-input,signal converters - voltage to current converter,capacitance voltage to current converter can be used for ac measurement only.,a,a,a,+,-,a,+,-,passive,passive, multiple input,active,active, multiple input,signal converters - current to voltage converters,current measurement can be carried out by a voltmeter using a current-to-voltage converter. the followings are resistance current-to-voltage converters.,v,v,v,+,-,v,+,-,passive,passive, multiple input,active,active, multiple input,signal converters - current to voltage converters,capacitance current-to-voltage converters can be used for ac and low current measurements only.,v,v,+,-,v,v,+,-,passive,passive, multiple input,active,active, multiple input,signal converters - rectifiers - passive half-wave,rectifiers are used in ac-dc convertion. types: half-wave, full-wave, phase-sensitive, and peak rectifiers. the largest error is the forward bias ud of the diode.,r,out,in,d,cricuit,transfer function,signal converters - rectifiers - passive full wave,the breakpoints are at +/- 2ud.,cricuit,transfer function,signal converters - rectifiers - active half wave,the forward bias of the diode is compensated by the amplifier. the breadpoint is -ud/a ( a, the gain of the op). r3 prevents the overdriving of the op for positive inputs.,cricuit,transfer function,signal converters - rectifiers - phase sensitive,detect the phase difference between input signal ux and the reference signal ur. (phase detector).,cricuit,transfer function,x,out,signal converters - rectifiers - switching phase sensitive,multiplicatin is carried out by a controlled switch.,-1,+1,-1,s,signal converters - rectifiers - switching phase sensitive,signal converters - rectifiers - peak rectifier,peak rectifiers measure the peak value. the peak is obtained by periodic charging of te capacitor c through the diode d. active one can reduce the diode forward bias voltage. discharging of capacitor c through resistor r causes an error in the peak value, but it makes it possible to follow the changes of the peak value.,passive peak rectifier,active peak rectifier,signal converters - rms converter,rms converters are used for measuring rms value of a signal. differential thermal converter consists of a resistor and a thermocouple. thermocouples t1 and t2 measure the temperature of r1 and r2. input signal heats r1 while a keeps r2 the same temperature as r1. use bipolar transistors as temperature sensors has high sensitivity. the uncertainty of thermal rms converters is 0.05% up to 100khz. thermal voltage converters can be used as ac-dc voltage transfer standard. 0.002-0.001%, 10hz to 100khz.,signal converters - rms converter - rms to dc,rms to dc can be carrired out by a multiplier and an integrator. the ac components of u(t) is filtered by the integrater. actually, it perform an autocorrelation at t=0.,signal converters - rms converter - rms to dc,signal converters - electromechanical converter,the operation of electromechanical ammerters and voltmeters is based on electromechanical conversion (golding 1963) the deflecting torque produced by the current or voltage is balanced by the controlling torque of the spring. permanent-magnet type moving coil can be used for dc measurement. dynamometer type moving coil are for dc or ac rms and can be used for standards