EMI K-NOTES

Contents Manual for K-Notes ................................................................................. 2 Error Analysis .......................................................................................... 3 Electro-Mechanical Instruments ............................................................. 6 Potentiometer / Null Detector .............................................................. 15 Instrument Transformer ....................................................................... 16 AC Bridges ............................................................................................. 18 Measurement of Resistance ................................................................. 21 Cathode Ray Oscilloscope (CRO) ........................................................... 25 Digital Meters ....................................................................................... 28 Q–meter / Voltage Magnifier ................................................................ 30 © 2014 Kreatryx. All Rights Reserved. 1 Manual for K-Notes Why K-Notes? Towards the end of preparation, a student has lost the time to revise all the chapters from his / her class notes / standard text books. This is the reason why K-Notes is specifically intended for Quick Revision and should not be considered as comprehensive study material. What are K-Notes? A 40 page or less notebook for each subject which contains all concepts covered in GATE Curriculum in a concise manner to aid a student in final stages of his/her preparation. It is highly useful for both the students as well as working professionals who are preparing for GATE as it comes handy while traveling long distances. When do I start using K-Notes? It is highly recommended to use K-Notes in the last 2 months before GATE Exam (November end onwards). How do I use K-Notes? Once you finish the entire K-Notes for a particular subject, you should practice the respective Subject Test / Mixed Question Bag containing questions from all the Chapters to make best use of it. © 2014 Kreatryx. All Rights Reserved. 2 S qo qi 4) Resolution Smallest change in input which can be measured by an instrument 5) Threshold Minimum input required to get measurable output by an instrument 6) Zero Drift Entire calibration shifts gradually due to permanent set 3 .  Limiting error (in terms of measured value) LE  GAE * Full scale deflection Measured value 2) Precision Degree of closeness with which reading in produced again & again for same value of input quantity. When accuracy is measured in terms of error :  Guaranteed accuracy error (GAE) is measured with respect to full scale deflation.Error Analysis Static characteristics of measuring system 1) Accuracy Degree of closeness in which a measured value approaches a true value of a quantity under measurement. 3) Sensitivity Change the output quantity per unit change in input quantity. e. 8) Dead zone & Dead time The range of input for which there is no output this portion is called Dead zone. Absolute Errors : A  Am  Ar Am  Measured value Ar  True value Relative Errors : r = AbsoluteErrors  A  Truevalue AT Am  A  A  A 1  1 r  T T m r 4 .7) Span Drift If there is proportional change in indication all along upward scale is called span drift. To respond the pointer takes a minimum time is called dead time. c) Random errors : Error due to unidentified causes & may be positive or negative. reading the value etc. TYPES OF ERROR a) Gross Error : Error due to human negligency. b) Systematic error : Errors are common for all observers like instrumental errors. i. environmental errors and observational errors. due to loose connection. fractional or relative errors are added. for multiplication & division. If X  X1m Xm2 Xp3  X X  X X   m 1  n 2  p 3  X X2 X3   X1 Precision Index Indicates the precision for a distribution h 1 2 5 .Composite Error : i) Sum of quantities X  X1  X2 x    x1  x2  ii) Difference of quantities X  X1  X2 x    x1  x2  So for sum & difference absolute errors are added. iii) Multiplication of quantities X  X1  X2  X3  X X  X X   1  2  3  X X2 X3   X1 iv) Division of quantities X X 1 X2  X X  X   1  2  X X2   X1 So. .. the pointer vibrates around zero position..    rxn  X1   X 2   Xn  Electro-Mechanical Instruments 1) Permanent magnet moving Coil (PMMC) Deflecting Torque Td = nIAB Where n = no.. of turns I = current flowing in coil A = Area of coil B = magnetic flux density Deflection   G I k G = NBA & K = Spring constant  Eddy current damping & spring control torque in used. 6 .Probable Error r = 0......  It is used to measured DC or average quantity.  For pure AC signal.6745  r 0.  It can directly read only up to 50mV or 100mA.    xn  X1   X2   Xn  Probable Error 2 2 2  X  2  X  2  X  2 rx    rx1    rx2  .4769 h Standard deviation of combination of quantities 2 2 2  X  2  X  2  X  2 x    x1    x2  .. ‘m’ is ratio of final range (as an ammeter) to initial range of instrument.Enhancement of PMMC i) Ammeter For using PMMC as an ammeter with wide range. R m = meter resistance Voltmeter A series multiples resistance of high magnitude is connected in series with the meter. we connect a small shunt resistance in parallel to meter. R sh  ii) Rm m  1  . M = multiplication factor m V Vm R s  Rm m  1  Sensitivity of voltmeter Sv  1 Ifsd  Rs  Rm   / V V Application of PMMC 1) Half wave rectifier meter I I  Iavg  m  7 . I Im  m  multiplication factor Basically. 9 Iavg Sensitivity AC RMS  VDC )  0. For Ac input R s  R m  R f  For DC input VDC  Iavg   I  avg AC Rs  Rm  Rf     0.  Iavg   2VRMS Rs  Rm  Rf   0.45 Iavg (Assuming VDC  VRMS ) DC (Sensitivity)AC  0.9 Sensitivity DC 2) Moving iron meter Deflecting torque.45VRMS .45(Sensitivity)DC 2) Full wave rectifier meter  Iavg  AC  2 2VRMS Rs  Rm  2R f     Iavg DC   Iavg  AC 0. Td  1 2 dL I 2 d I = current flowing throw the meter L = Inductance  = deflection Under steady state 8 .9VRMS Rs  Rm  2R f  VDC Rs  Rm  2Rf   DC (Assuring V  0. i1  i2  I Td  I2 dM d   I2 For AC. 3) Elector dynamometer Deflecting Torque...  2  Air friction Damping is used  Condition for linearity  dL  cons tant d  MI meter cannot be used beyond 125Hz.. It measures RMS value.K  1 2 dL I 2 d   I2  MI meter measures both ac & dc quantities... i1  Im1 sin t i2  Im2 sin  t   Tdavg  I1I2 cos  Where I1  dM d Im1 I2 & I2  2 2 9 . Td  i1 i2 dM d For DC.. In case of AC..... IRMS 1 T     i2  t  dt  T 0  1 2  If i  t   I0  I1 sin wt  I2 sin2wt  . as then eddy current error is constant. IRMS  I20  1 2 2  I1  I2  ... Td  Tc K  V 2 dM R s2 d    V2 It reads both AC & DC & for AC it reads RMS. I1  I2  I 0 Td  I2 (Angel between I1 & I2 ) dM d At balance.Applications of dynamometer 1) Ammeter Fixed coils are connected in series. 2) Voltmeter Rs  Series multiplier resistance I2  I1  V . 10 . Rs 0 cos   1 Td  V 2 dM R 2s d At balance. Tc  Td K  I2 dM d   I2 It reads both AC & DC & for AC it reads RMS. k  Td   Pavg Symbol : Two wattmeter method W1  VRY IR cos  VRY & IR   VL IL cos 30    W2  VBY IB cos  VBY & IB   VL IL cos 30    Where VL is line to line voltage 11 . Td  I1 I2 cos  I dM d V dM Pavg dM cos   Rs d R s d At balance. Moving coil is connected across voltage and thus current  voltage.3) Wattmeter Fixed coils carry same current as load & as called as current coils. a high non-inductive load is connected in series with MC to limit the current. then pf < 0.5 Errors in wattmeter a) Due to potential coil connection % r  IL2rc PT * 100 IL = load current rC = CC Resistance PT = True Power % r  V2 * 100 R sPT V = voltage across PC 12 . P3  W1  W2  3VL IL cos  Q3  3  W2  W1   3VL IL sin   tan   Q3 P3  3  W2  W1   W1  W2   3  W2  W1     tan1     W1  W2   for lag load  3  W2  W1      tan1     W1  W2   for lead load = Remember. = If one of the wattmeter indicates negative sign.IL is line current These expression remain same for  -connected load. In our case W1 is wattmeter connected to R-phase and W2 is wattmeter connected to B-phase. ofrevolutions K 13 .Rs = Series multiplier resistance PT = True Power b) Due to self inductance of PC If PC has finite inductance   Zp  Rp  R s  jwLp Rp  R s Zp  R s  jwLp % r  tan  tan *100  = load pf angle   Lp    Rs      tan1  4) Energy meter Energy = Power * Time WT  VIcos  t * kwhr 1000 3600 WT = True energy  It is based on principle of induction.t Totalno.  Wm  VIsin     * t 3600 kwhr Where Wm = measured Energy  = angle between potential coil voltage & flux produced by it.of Re voluations N  kwhr P.  = load pf angle  Error = Wm  WT  Energy constant =  Measured Energy = Wm  No.  It is an integrating type instrument. Electrostatic voltmeter Deflecting torque. then disc starts rotating slow with only PC excited without connecting any load is creeping. they measure RMS value.  To remove creeping holes are kept on either side of disc diametrically opposite & the torque experienced by both holes is opposite & they stop creeping.  VI cos  t * kw.of Re w / kwhr due to creeping * 100 TotalNo. Td  Tc 1 2 dc V  k 2 d   V2 Condition for linearity 14 .  Otherwise if over voltage is applied on pressure coil then also creeping may happen due to stray magnetic fields. % creeping error = TotalNo.  These are used for high frequency measurements.  In case of AC.  They can measure both AC & DC. Td  1 2  dc  V   2  d  At Balance.hr 1000 3600 W  WT Error = % r  m * 100 WT True Energy = WT  Creeping Error in energy meter  If friction is over compensated by placing shading loop nearer to PC.of Re w / kwhr due to load Thermal Instruments  These instruments work on the principle of heating and are called as Thermal Instruments. r Switch at (A) If Ig  0 Vs  I w l1r Iw  Vs l1r _____________(2) Switch at (B) Vx  I w l2r Iw  Vx l2r ________(3) Vs Vx  l1r l2r Vx  Vs l2 l1 15 . m V Vm Potentiometer / Null Detector Iw = working current Iw  VB _____________(1) Rh  l. dc  cons tant d For increasing the range. we connect another capacitor in series To increase the range from Vm to V Cs  Cm m  1  . r = resistance of slide wire (Ω/ m) l = Total length of slide wire (m) l1 = length at which standard cell ( Vs ) is balanced l2 = length at which test voltage ( Vx ) is balanced Measuring a low resistance R VR S Vs Instrument Transformer  Current transformer Equivalent circuit Turns Ratio = Nominal Ratio  n  N2 N1  X  Xs    tan1  l   Rl  R s  R = Actual Ratio  n  I cos   I sin  Is 16 . it deviates from that value.Errors in current transformer 1) Ratio Error : Current ratio Ip Is is not equal to turns ratio due to no-load component of current. VS  n   IS    XP cos   RP sin    I XP  IRP  Phases angle error    n  nVs       17 X R  Where   tan1     . K R * 100 R K = n = Nominal Ratio % r  R = Actual Ratio 2) Phase Angel Ratio : Ideally. Phase difference between Ip & Is should be 1800 but due to no-load component of current. Phase angle error =   I cos   I sin  180 degrees * nIs  Phase angle between primary & secondary currents = 180    degrees  Potential Transformer Equivalent circuit Turns Ratio = n = N2 N1 Actual Transformation Ratio = R = R  n VP VS  1  IS  RP cos   XP sin    I RP  I XP  . AC Bridges  AC Bridges Balance condition : ID  0 Z1 Z 4  Z2 Z3  Z1 Z 4  Z 2 Z3   1  4     2  3  Z1  Z 2 Z3 Z4   2  3  4  Quality Factor & dissipation factor Quality Factor (Q) 1 2 3 Q wL R Q R wL Q 4 1 wCR Q = wcR Measurement of Inductance (i) Maxwell’s Inductance Bridge Here. we try to measure R1 & L1 18 Dissipation Factor (D) D R wL D wL R D =wcR D 1 wCR . R1  L1  R2R3 R4  r1 CR3 R  R 4  r  R2R3   R4  2 19 .R1  L1  R2R3 R4 L2L3 R4 (ii) Maxwell’s Inductance Capacitance Bridge R1  R2R3 R4 L1  R2R3C4 This bridge is only suitable for coils where 1 < Q < 10 Q = Quality Factor (iii) Hay’s Bridge Used for coils having high Q value R1  L1  R 2R 3R 4 2 C24 1 1  Q R 2R3C 4 1 1  Q 1 Q R 4 C 4 2 2 (iv) Anderson’s Bridge This Bridge is used for low Q coils. (v) Owen’s Bridge R1  R3C 4 C2 L1  R 2R3C4 Measurement Of Capacitance  De-Sauty’s Bridge r1  R2  r2  C1  R4 R3 R3 R4  R1 C2 D = dissipation factor = C1r1 r1 = internal resistance of C1  Schering Bridge R1  R3C 4 C1  C2 R 4 C2 R3 dissipation factor = D = C4R 4 Measurement of frequency  Wien Bridge Oscillator Balancing Condition R3 R4  R1 R2  C2 C1 Frequency of Osculation f 1 2 R1R2C1C2 20 . Measurement of Resistance Classification of Resistance 1) Low Resistance : R ≤ 1Ω . Motor and Generator 2) Medium Resistance : 1Ω < R < 100kΩ . Electronic equipment 3) High Resistance : R > 100 kΩ. winding insulation of electrical motor DC Bridges Medium Resistance Measurement 1. Wheatstone Bridge Finding Theremin Equivalent Ig  Vth R th  R g R   P VTh  V    P  Q R  S  PQ RS R Th   PQ R S For Balance Condition Ig  0  VTh  0  PS = RQ 21 . S v SB. SB  SB  SB   mm  R /R  VThS v  R / R  V. At balance R  1r P  Q S  L  1  r ………….S v  R S  SR  2 For Maximum Sensitivity R S = 1 S R V. Si   mm/mA Ig  = deflection of Galvan meter in mm  2) Voltage sensitivity.(1) For case (2) R & S is reversed S  2r P  Q R  L  2  r ……….(2) From (1) & (2) R S  L  1r 1 r  S R  L  2r 2 r 22 . for case (1)..Sensitivities 1) Current sensitivity . max  4 2. Carey –foster slide wire Bridge r = slide wire resistance in  m . S   mm/V VTh 3) Bridge Sensitivity . ammeter is connected near the load 4. voltmeter is connected near the load R X  RaR v .3. Voltmeter Ammeter Method a) Ammeter near the load Rm  Vv  RX  RA IA Vv = voltage across voltmeter I A = Ammeter current R A = Animator resistance R X = Test resistance. Ohmmeter a) Series Type when R X  0 Im  IFSD = Full scale deflection when R X   Im  0 = zero deflection 23 . % error = Rm  R T RT  100  RA Rx  100% b) Voltmeter near the load Rm  1 Rm  % error = VX Vv  IA IX  Iv IX I v  VX VX Rm  R X RX  R XR v RX  Rv  100% If R X  R aR v . Q = outer ratio arms p. q = inner ratio arms S = standard resistance r = lead resistance R = Test resistance High Resistance Measurement  Loss of charge Method VC  t   Ve R t Rc 0.Rm  R X  Rh  R se   sh  R  Rm   sh  b) Shunt Type RS = current limiting resistor If R X  0 Im  0 = zero deflection If R x   Im  IFSD = Full scale deflection For Half scale Deflection R x  Rh  RmRS Rm  R S Measurement of Low Resistance  Kelvin’s Double Bridge Method Unknown resistance R qr  P p  P S    Q pqr Q q P.4343t  V  C log10    VC  24 .for Half scale deflection  R .  t = time in (seconds) V = source voltage VC = Capacitor voltage Cathode Ray Oscilloscope (CRO)  The velocity of e is changed by changing the pre-accelerating & accelerating anode potential KE =PE 1 mv 2  qVa 2   2qVa m Deflection sensitivity D = deflection height on screen d = distance between plates d = length of vertical deflecting plates L = distance between centre of plate & screen Va = anode potential Vy = Vertical plate Potential D L d Vy 2dVa V mm deflection sensitivity S L d D V  Vy 2dVa mm 25 . No 1  Lissayous Pattern   0 or 360 2 0    90 Or 270    360 3   90 or 270 4 90    270 Or 180    270 5   180 26 . the wave form pattern appearing on screen is called Lissajous Pattern.Lissajous Pattern If both horizontal & vertical deflection plates of CRT is applied with the sinusoidal signal. Case – 1: Both signals have same frequency Vx  Vm sin  w x t   Vy  Vm sin w y t    Vx  Vy  Vm wx  w y  w  = variable S. phase difference =  for anti-clockwise orientation = 360    Case – 2 wx  w y Vx  Vm sinwx t Vy  Vm sinwy t wy wx  fy fx  Number of horizental tangencies Number of vertical tangencies fy fx  4 2 2 27 . phase difference =  2) Lissajous Pattern in IInd & IVth Quadrant X    180  sin1  1   X2  Y   180  sin1  1   Y2  for clockwise orientation. ) for clockwise orientation.Finding  1) Lissajous Pattern in Ist & IIIrd Quadrant X   sin1  1 X  2  1  Y1   sin    Y2    for anti-clockwise orientation phase difference = (360 . 25 0  10V < 12V 1 1 0 0  15V > 12 V 1 0 1 0  12. MSB is set to get voltage corresponding to the digital o/p  If V0 < Va .5 > 12 V 1 0 0 1  11.25 < 12 V D3 T1 T2 T3 T4  In first clock cycle.Digital Meters  Type of converter 1) Dual slope ADC Maximum Conversion Time 2) Successive Approximation Register (ADC) 3) Counter ADC 4) Flash ADC n Clocks 2n Clocks 1 Clock 2n1 Clocks Dual slope A/D Converter Va = analog input VR = Reference input Va  VR T1  T2  T1  T1  2n TCLK Maximum conversion time = 2n1 TCLK  Successive Approximation Register Suppose = VREF  1a V and Va = 12V D2 D1 D0 10 1 5 0 2. then in next cycle next bit is set else. MSB is reset & next bit is set  We continue the same process till we reach LSB. 28 .  If V0 > Va .5 0 1. we can measure from 0 – 999 1  0. R  if 3 1  0. 1 digit can be 0 & 1.Specifications of Digital Voltmeter 1) Resolution The smallest value of input that can be measured by digital meter is called resolution. R  we can measure from 0 – 1999 Resolution.005 2000 4 digit is there than MSB can be 0 – 3.….. 9) 2) Sensitivity S = Resolution x Range 3) Over – Ranging The extra 1 2 digit is called over-ranging If n = 3. 1. 2 2 Resolution . R 1 10n n = No.001 103 if n  3 1 digit. of counts)  29 Full Scale Range of meter . 4) Total Error Error = (% error in reading) x reading + (NO. of full Digits (0.. Qm  wL  R  Rsh  QT wL  R   R   R  1  sh   1  sh  R   R   R   Q T  Qm  1  sh  R   30 . At series resonance XL  XC V R VC  IX C I V XC R V XL R VC = V. Q VC  Q  Practical Q-meter Also includes series resistance of source (oscillator) True Q T  wL R Measured Q.Q–meter / Voltage Magnifier  If works on the principal of series resonance. resonance is achieved at fr2 f2  Cd  1 2  L  C2  Cd  = n f1. Measurement of unknown capacitance Test capacitance is connected at T3 & T4 . Circuit is resonated at C = C1 fr = 1 ………(1) 2 2  C1  CT  C T = Test Capacitance  C T is removed & circuit is resonated at C = C2 fr = 1 2 LC2 ………(2) from (1) & (2) CT  C2  C1  Measurement of self-capacitance  Resonance is achieved at C = C1 f1  1 2 L  C1  Cd  At C = C2 . C1  n2C2 n2  1 31 .