Measurement & Instrumentation
Measurement & Instrumentation PHY 6753
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Date Created: 09/23/15
SIGNALS amp MEASUREMENTS signal measurement system temperature 0 Mg 0 mechanical o magnetic eld vacuum pressure 0 articles 0 biochemical 0 special measurement techniques SIGNAL MEASUREMENT SYSTEM Electrical Physical 1gna1 1 Signal lligi iiiigliil llgl Cont rol Signal Human or Computer TEMPERATURE SENSORS Thermocouples Iron reference junction in ill Ivult merer constantan 55 Cu 45 Ni SenSIng junCKlOU constantan o junction voltage of two unlike metals SOyVOC 7270 C 2500 C with various alloys 0 reference junction voltage subtracts from sensing junction voltage reference at 0 C bath or use compensation circui 0 iron constantan chromel alumel copper platinum etc Thermocouple Compensation Circuit Signal amp Measurement o AD580 250V voltage reference 0 AD590 IC temperature sensor 10uAOC 0 type J tempco 515uV0C Ex w referencejunction 200C 0 reference junction voltage 0 C 141 mV 0 reference junction voltage 20 C 151 mV 0 current from AD580 is 293g A 0 Set R2 R3 9161 so that the current there is 273uA which leaves 20uA through R1 0 The voltage above R1 is 250V10mV o If reference temperature changes by say 20 C R1 voltage changes by another 10mV which really doesn t affect the 273uA current through R2R3 o The extra voltage 10mV in this case at reference junction due to its nonzero celcius temperature is thus subtracted as the voltage across R1 thermal contact iron consta nta n A0580 sensing junction constantan type Jquot junction amp Thermistors o semiconductor w negative tempco 4 C o 50 300 C 2R A I0ul 2IOIQT Io fsel B I0ul VCC m Io fsel 1 0 Hr offset A offset IC Temperature Sensors Signal amp Measurement EbersMoll Eq IO IS exp l 3 V 50 N 120 C very simple circuitry lC packages vquot 57 7 2mV25quotC e Emp WK 1m Platinum resistance 0 positive tempco N 04 C 0 very stable Quartz thermometer o resonant frequency of quartz crystal Pyrometer o infrared emission Cryogenic thermometers carbon composition resistors paramagnetic salt semiconductor etc Signal amp Measurement LIGHT SENSORS Photodiodes o photons create eh pairs in the pn junction 0 high speed up to GHz by reverse biasing a a a a 0 Si photodiodes 0 PIN diodes o GaAs 0 moderate sensitivity 1pApW I V 39 39l w M FET imam E A Phototransistors base current provided by photocurrent in BCjunction higher current 1mA 1mWcm2 lower speed 10ps photoDarlingtons 100ps Photomultiplier Tubes PMT 7 photocathode amp dynodes alkali metal approx x10 multiplication at each stage Photocurrent mode wilwgquotquot photon counting mode lt 1pW 106 countss quotquot high sensitivity mAnW Qquot m never expose to bright light ww dark current reduced by cooling to 725 C 7 i hgih speed 2ns 39 PMT Ty pas a SineOn Type dvnades phomcamnde Signal quot M POSITION amp IMAGE SENSORS Po onSens e Photodiodes 1D Photodiode Arrays Hamamatau errers a wrde yarrety or PMTS that can be used m rrnagrng or H r rnrorrnauon rt rs possrbre to create posmon sensmye PMT arrays m a srngre vacuum enyerope There are three basrc types or PMT arrays They are mean my and posmon sensmye Linear 32 LmeavAnude Anay quot726 n quot3353 Mndule 2DITWO Dimensional 2x2 Mumanude rrays Mannm LXA Mumanude Ana Nessa msnnms we LmeavAnude Array Manama H3352 Mndule m Array H Signal amp Measurement CCD ChargeCoupled Device Readout Register Microchannelplate Image Intensifier lutenslfler FigurzZJ 7 CCD Structure flbe roptlc photoelect bundle accelera photocathode mlcrochannel plate ons flberoptlc c d bundle hosphor screen Signal amp Measurement MECHANICAL SENSORS LVDT Linear Variable Differential Transformer 0 transformer w variable core 0 displacement strain pressure etc displacemenl J33 Q 79quot l 393 I core secundary 2 pr imarv saucndarv gt l Capacitance Transducers resonance circuit w sensing capacitor 0 capacitance microphone Interferometry Fiber Optic Sensors Other Transducers 0 metal lm resistance in bridge con guration 0 semiconductor strain gauge 0 optical encoder o RVDT rotational VDT quartz oscillator MAGNETIC FIELD SENSORS Hall Effect Probe 0 generation of transverse voltage in semiconductor current in magnetic eld OkG 01 Signal amp Measurement SQUID Superconducting Quantum Interference Device 0 single quantum of magnetic flux 02uGcm NMR Magnetometer o proton spin precession frequency in magnetic field 0 accuracy 1106 VACUUM PRESSURE BayardAlpert Ionization Guage 10393 1039Mtorr o 1 torr1 mmHg iunmllnclor glass mm ccmienuun m 74 quads vacuum system 7 lilumem Thermocouple 0 TC bonded to heating element 0 higher pressure residual gas cools TC faster 0 110393torr PARTICLE DETECTORS ionization chamber solid state particle detectors surface barrier detectors Cerenkov detectors shower chambers drift chambers Signal amp BIOCHEMICAL SENSORS Microelectrodes o 10100nm in diameter 0 source impedance 1OOMQ o interference stray capacitance Microelectrode amplifier es r z active compensation 1 I m 7 7 via positive feedback for finish freq encv performance e39 m I gt r L Wu input buffers next to probes i4 ma reference next to probe mm H V1 nmvvnulm mtrna iu lwlr mammary mm W 4 quot1 IonSpecific Electrodes murder mum Voltage Clamp o measuring a small current with fixed voltage WI 0 nerve amp cell physiology Wm armada virtuai ground output voltage SPECIAL MEASUREMENT TECHNIQUES ACTIVE FILTERS last edit 72804 passive RC lters filter characteristics active lter types active lter components active lters digital ltering PASSIVE RC Fl LTE RS 1pole 9 33 R V 20dBdec Vin O AMArovout 3 I 6dBoctave CT 7 mo lRC m 1 gv a lRC 1wZRZCZ 2pole 9 513 R V 0 40dBdec Vin O MAAIVVWIOVout 3 ZlZdBoctave CT CT 2 1 27 J5 1 g a Z on 7 V 1wRC RC Npole gvmm AHZUdBldec 3 Nl d jloctave R R R N mo gv 1mRCZfZ attenuation slope 20 N Die dBdec loading of each section s output by following section s input impedance need buffer between each pair of sections 0 RC lter always has smooth knee Active Filters RLC Filters 0 LC filters can have sharp response ZR i aL QC 0 but inductor is poorly characterized circuit element gtgt avoid them if possible 0 opamp substitute for inductor gtgt active filters FILTER CHARACTERISTICS Insertion Loss insertion Loss i3 dB F Low Puss Elond Pass 50 118 Frequency A fc Frequency C insertion Loss dB i3 dB High Pass 60 dB lgt fa Low fc High 5 Frequency D Frequency o a low pass filter 0 b high pass filter 0 c band pass filter 0 d band stop filter Filter Characteristics Frequency Domain passband ripples transition region cutoff frequency stopband phase shift Filter Characteristics Time Domain rise 39 settling time overshoot ringing Active Filters passbarad name iband sk39n vansilien region In gain upland mg Ireqnencv 4 chase smk frequencv IIinean timz deaiy reuuzncy Imear gt I 5 uvnrslmol some a 5 ACTIVE FILTER TYPES o flatness of passband o sharpness of kneeskirt 0 minimal distortion due to phase shift Butterworth Chebyshev Bessel i 0 E5 E D I g Kuuerwmth g 0 Bl Chebvsimv TE 0 5a rippIeI I I nrirmaligetl Irauuenny flat passband soft knee hard knee some ripple 0 r Chainshew amamme response VA V w 05m rumiv summoth uniform time delay minimum distortion of pulse I 2 normuiimd frequencv 3 i am uvershaol a spurs Chzbyshev UidB ripple 39 rnoie Bullerwmm P w 6 pore Bessel ampimma response 0 65770 15 20 mm s Figure 515 Stcpresponsc comparison for 6 poie lowpass llers normalized for 3dB atten ualion a I z ACTIVE FILTER COMPONENTS NIC Negative Impedance Converter AA VVV an AA Active Filters Gyrator Zin 9 Z RZllR77 Z Zm7RZ iocl ij o gyrated capacitor use the gyrated capacitor in place ofinductor in LC filter circuit 1 ZC Zgymw ijRZ oca ZL ij Sallen amp Key Filter 0 cascaded RC s w bootstrap m Zozyb yzmfzoze lam b y14gt14mf1 WA 6 4 gt1 I OEDImfI W O Hmf F ZQZg ymf1 39J39 S 1 Jam ssed M01 Z Dar 2 I I f a 01 gt1 H H 009 A 14bmfZOZAzyquot I1 I K I I I Z ybmf 9 ZH y bmf r 1 WA4 A A I A A I aanos a equ paouuoga e10s3A 58311 H EAIJDV SJeuH eAuov Active Filters High pass filter C1 v m Vent 0 gtgt HampH 507 recipe for npole lter design 0 many advantages but not amenable to tunable lter StateVariable Active Filter 0 tunable lter w highpass lowpass bandpass available on same circuit 0 Biquad Active Filter Imim m A lm W New mu Mum m m lt2 liywr m mime mm mm Active Filters TwinT Notch Filter 0 passive twinT 1 infinite attenuation 0 a gv 5 RC eg removal of 60Hz line noise soft knee of passive filter AAA AAA v aquot L E Vin Vout SwitchedCapacitor Integrator Vin I I Vout E f 0 use MOSFET switches 81 82 each clock cycle changes the voltage on C2 by AV VmC1 C2 C1 Vm f0 32 l der easy to make matched pairs on silicon tuning the integrator gain by changing clock frequency f0 gtgt lgml use these in place of RC integrators in statevariable or biquad filters Active Filters DIGITAL FI LTE RI NG Problems of analog lters 0 large number of expensive high precision parts 0 inductors capacitors crystals controls 0 temperature variation and aging Advantages of DSP filters 0 numerical components 0 unaffected by temperature aging etc o implementation of lters that are impossible or impractical in analog system 0 lters of almost theoretical precision FIR FiniteImpulse Response NonRecursive Filter Ill y k IllXka o hk weighting factor time response 0 HF h frequencyresponse R InfiniteImpulse Response Recursive Filter quot1 y Ay 17 x l x1x2w0 gt yAI17A This corresponds to yexp7tj Aexp7t t 1 rRC 4 4 j 0 software implementation 0 hardware implementation commutating filter Commutating Filter 1 51 E2 NOISE ongrnsornorse rneasuresornorse tranststorn drgrtarnors rnterrerenc srgnargroun 5 stgnar rsotatron orse e generators e External Fluctuations vrbratron ternperature vanauon arnbrent radratron hgm radto cosrmc etc arr current gt try to rnrnrrnrze Source Noise tasernuctuatron rnput power uctuauon random nature or ergnat rnotron or We specrrnen fhckermg ame gt sornewnat unavordabte carerut desrgn or experrmem Detector ampAmplifier Noise Johnson Home Sho Home I W notse turbu ent ow of Current Interference power hne 0H2 capacmve ptckup cnarge bqu up mductwe ptckup rnagnetrc current roop oupnng cabres as antenna rt re ecuon Noise NOISE N DETECTORS ampAMPLIFERS Jonhson Noise Thermal motion of electrons rms amplitude of Johnson noise J4kTRB AAA vvvv 13yV 300K IOkQ 10kHz Distribution of instantaneous amplitude is gaussian a 1 V2 V V dV 7 P gt J27 n exp 2V Frequency spectrum is more or less at white noise b p const Pfnl a b Any resistive part of circuit generates Johnson noise Can be reduced by lowering temperature Shot N oise Statistical uctuation of current due to nite quantum of electric charge e gt 1 rms amplitude of shot noise In 2eIB 57 nA 1A10kHz In16x10 8 57 pA 1 A10kHz In16x10 5 Distribution of instantaneous amplitude is gaussian 1 I2 I 1 d1 7 P J51 exp 21 Frequency spectrum is more or less at white noise P W Noise in pn junction current where current is by diffusion Current in resistive conduction has much less shot noise because of long range correlation Noise Negative feedback reduces shot noise 1f Noise Flicker Noise Fluctuation due to turbulent ow of current Plfn n V 0c typically uV depends on material construction geometry etc 1ffrequency spectrum gt ink noisequot Base current in transistor resistor current Reduce by shifting amp narrowing measurement bandwidth away from dc Interference o 60 Hz ine pickup radio TV etc 0 computer microwave digital equipment 0 electric motor transformer power equipment 0 vibration stray light magnetic eld EMI MEASURES OF NOISE Noise Amplitude o instantaneous noise voltage Vt o rms noise voltage K quotV2 0 distribution of instantaneous noise voltage pVV dV 0 noise frequency spectrum Noise Density 0 noise power oc V oc B 0 mean squared noise density v V B V2 Hz 0 rms noise voltage density vW V J3 VJHz Addition of Uncorrelated Noise 0 V V 2 sz SignaltoNoise Ratio V V SNR10lo 5 2010 5 dB g V M 0 specify bandwidth and center frequency Noise Noise Figure Vl th a resistor R5 connected across input terminal of an amplifier the ratio of output ofthe real amplifierto output of noiseless amplifier ofthe same gain 2 NF1010g1 V dB 4mg 0 v noise voltage of amplifier with noiseless source resistor VZ SNR1010g 5 NF 4kTR good amplifier NF ltlt 3dB Noise Temperature VF10 V2 T THT10 1 quot NF1010g quot1 4k T good amplifier Tn ltlt 290K noiseless ml noisy v our ampli er R 394 am 1 m N 1 m chmn u give sumo v out as in A a TRANSISTOR NOISE Noise Model of Transistor total voltage noise oftransistor ea quot8i z39HRS2 typically an NnVJHZ in N pAJHZ Noise in BJT voltage noise Johnson noise in base collector current shot noise and flicker noise generating voltage noise across emitter intrinsic resistance Noise current noise 0 shot noise and icker noise in base current Noise in FET voltage noise 0 Johnson noise of JFET channel 0 icker noise in MOSFET current noise 0 extremely small 0 use BJT for low source impedance FET for high source impedance Amplifier Distortion smna 1 spectrum low pa5b lter L flicked Spec Lg tugged signal high pass lett HP ichrcd spam m tinged signal DIGITAL NOISE GENERATION 0 noise of known spectrum 0 adjustable bandwidth 0 repeatable PRBS Pseudorandom Bit Sequence 0 feedback shift register clock fa mm muss out 3 a maximal length K 2N 71 is obtained for certain choices of m eg 33bit 10MHz shift register produces K 86 x109 states in 24hrs 100bit 10M Hz takes 4x1015 yrs applications in encryption radar ranging codes sound effect chips Noise Autocorrelation 7 Z Z xxxxik 5kKa Irm Power Spectrum Pf27LZsincZ Af Cl ldB to 72 f am 2 Si 7 quotmt envelope um um at 44 I Clock noise power per hertz him 1 spikes separated by 239 1 clan 2km frequency Noise Voltage for B ltlt f5 vm a l VJHZ f Vm vmxE Analog Noise Generation by LowPass Filtering t o analogRC ler 0 digital ltering INTERFERENCE Sources of Interference o 60Hz line pick up radio TV etc 0 computer microwave digital equipment 0 electric motor transformer power equipment Coupling o capacitive proximity o magnetic wire loop o if antenna effect of cable 0 shielding ltering ground RF Reflection Noise cable m re lecti n o impedance matching load impedance characteristic impedance of cable SIGNAL GROUNDS Grounds within an instrument Figun 757 Ground palhs lcu39 lowlevel signalsv A myquot a Variation in local grounds between instruments lVIUOmV Figure 7 69 Small signal and long wires 0 differential amplifier 0 protection against ground swing Noise Shielded twisted pair a Figum 770 Ground cunnccnons for lawicvcl Signals through shielded cables ISOLATION AMPLIFIER coupling of analog signals between circuits with large difference in ground reference 0 mandatory in medical electronics mlrxi w m cowJoni quotmm v m inns m MMquot Figure 7 75 lsoinunn mupimci ccnccpr o transformercoupled isoamp o opto coupled isoamp capacitorcoupled isoamp iV DMK amnm W n 5 4 numm 7mm mm mm nu mm W 5 mm on w mm aim mm m H mm mm WW 7m quot mm my mom WW5 mm win Am Figure 776 A0295 Lmnxformerrcoupiud isuialian amph cl Comm oman Drum Noise lscl my mum I Isv vch 1 Iw lIL Lrwtll v H r v mm mm gun w I I I I I I I l I I I Figure 777 pmcoupled analog Isolation ampli er Isv quotmm liV imam lIEuuc39icv to voltage Convener Enlwserlockrd luayl Isnomu signal ml Figure 778 Capacitivcly coupled isolation ampli er SIGNAL GUARDING for highimpedance probe eg microelectrode bootstrap shield to the signal voltage eleminate leakage current prevent capacitive coupling drive long cable Figure 780 Using a guard to raise input impedance PHASELOCKED LOOP phase locked loop phase detector low pass lter VCO basic PLL structure applications PLL PHASELOCKED LOOP fsi i Af phase detector input may be sine square etc plus may have noise locks on to signal frequency regenerates clean out ut signal output may be functiongenerated as sine square etc AMFM demodulation frequency synthesis pulse synchronization etc PHASE DETECTOR Phase detector output is a function of phase difference between the signal and reference Detect phase error signal amp integrate average for gtgt 1 f g lf sig amp ref are same frequency then PD output is DC lf sig amp ref are different frequency then PD output has the difference frequency w W qur 1 mm swam PnJmc lowm r u mamas Type Digital 519 VPD ref VPD VPD Iv D 0 2r 0 227 50 duty cycle of both sig amp ref otherwise PLL Type Linear fourquadrant multiplier balanced mixer Vsig VPD Vref D 0 2n V3g VU s1n wt 2V 5 VPD 4 cos p VWf stgns1nwt p 7 Type II Digital edge detection of relative timing of signal and reference reference signal VCD llJl7 laq VPD lead gil ll phase detecinr iJL riiJL 7777 771777 r output a 0 Zn a A046 clids LOW PASS FILTER limit the response bandwidth educe capture range and increases capture time act as ywheel smooth out noise or fluctuation in input signal prevent oscillation VCO VOLTAGECONTROLLED OSCILLATOR OpAmp VCOs VFC VoltagetoFrequency Converters digital output VCO RF VCOs LC oscillator with varactor varactor reversebiased pn junction used as voltage variable capacitor klystron microwave Livcam Q T anrSL d Eiuncd slim dimcllan Duch Cemeee Fig 1437 Modern VCOs use the voltagevariable characteristic or diode PN junctions in tuning BASIC PLL STRUCTURE Voltage Controlled Oscillator vco four Phase Detector Frequency FSD Reference Digital Control Lou E sof NgtltE M out M Fig 1436 A basic phaseIockedloop PLL synthesizer acts to keep the divided down signal from its voltagecontrolled oscillator VCO phaselocked to the divideddown signal from its reference oscillator Fine tuning steps are therefore oossible without the complication of direct svnthesis o eg fref 1024MHz M 1024 so that frequency resolution is fre M 20MHz PLL APPLICATIONS tone decoding AMFM demodulation frequency multiplication frequency synthesis pulse synchronization regeneration of clean signals generation of sine wave locked to pulse freuqncy Frequency Multiplier f Fxgurc 977 PLL FM discriminator AM Detection AM detection by signal recti cation amp low pass lter homodyne detection M Jan l amp All lm ml invinliilulw Shin Figure 979 AM dclccliun Pulse Synchronization CleanSignal Regeneration JULI39L VCD vco 4 so Hz 4046 out Mom 75 messsecond DVM 02 0x a 4040 c L 11mg cou nmr Figure 974 Using a PLL multiplier to generate a clock locked to the 60112 ac line SIGNAL PROCESSING last edit 110205 signal averaging lockin detection phase sensitive detection spectrum analysis SIGNAL AVERAGING Flip coin N times N X qu 11 Repeat Nflip experiment many times Nltgt9 W X m X2 2XltXgtltXY W X2 x1 x2 My 11 2 2 2 2 2 2 x1x2xN x1x2 x1x3 xNilxN Jq00r1 AX rm 000 1 010 1 m7 ltx1x2gt 2 111 X2gtNN2 NN2 N AXWHJV XocN AXmocxJV SNRAlt gt 0cm Multichannel Scaler Boxcar Integrator Transient Averager Signal Processing Af 4 T 7 11 E T T T Nil 1 T T N N71 f T f T periodic signal make signal periodic LOCKl N DETECTION detect amp measure very small AC signals as small as nanovolts buried in 60dB larger noise phasesensitive detection detect signal of exact frequency amp phase reject any other as noise EX 10nV signal at 10kHz into a low noise amp w input noise SnVde BW100kHz gain 60dB output signal 10pV output noise San 105 x1000 16mV SNR 1160 use a BPF of Q 100 centered 10kHzieBW 100Hz output noise San 10Z x1000 50pV SNR 15 use a phasesensitive detector w effective BW 001 Hz output noise SnVXsIIO Z x1000 051V SNR 201 Phase Detector inverting amp low pass filter Vm Kcoswt wa signcos wt RC gtgtT 27ra Signal Processing Znn nm 7 K sin wt w Vow V sin 501 m j isinzpisin p 7sinp 5mm 73V5 sinzp 7 VM K sinwAwt Add another lowpass lter of time constant 1 V 2 V A A A N1 Aw lt 11 777 5m wt 7 ltlt1 Awgt1r mt Lockin Detection low noise 10W Pass slow scan amp filter output to meter Vsig phase EXPT gt detect chart rec computer etc V f phase re shift Ex Measurement of absorption spectra chopper sample detector Lock In Amplifier Vref adjust phase shift L4 for maximum signa Any noise outside bandwidth Aw 1 r set by lter will be eliminated Move signal away from DC large 1f noise to higher frequency Signal Processing Modulation Methods Sguare wave modulation of stimulus to experiment eg square wave modulation oflaser intensI y Reference me signsin wt 0 710 Vm A signcos wt zp 1 a 7 7 a V A 7 7 7 A 2 2 w 2 wjl w l OH mt 0 nZ q 3n2 ip 2n abs Vcu A A Sine wave modulation of the scanned parameter eg sine wave modulation of laser wavelength Kn AAcoswt p VD izMsinzp iz A sinzp 7t 7 d abs AA I Vou g A A A Signal Processing PHASESENSITIVE DETECTION 0 Reference vR t VR cos th o Signal vStVScoswStp vR tvst VRVS cosztcoswSt p VRVS cos wk wSt w coswR 7 wSt7 1 0 LowpassFilter VPSDtVRVqcoswR7wStip VRVSCOSp o Mixer slgnal I LPF Analog vs Digital PSD o harmonic rejection 39 reference signal can have many harmonics which mixes with signal digital direct digital synthesis DDS of reference sine wave harmonic content 120dB 0 output offset analog DC output of analog LPF is subject to all DC noise eg zero drift di ital numericcal output of digital signal processor DSP 0 dynamic reserve max noisemin signal analog 60dB digital limited only by quality of ADC 100dB Reference Signal 0 External Reference extems 31 9 sq clock 1 Iquot 39039 ref m I E I o lntemal Reference trlg 51g Ecpenment ref out Signal Processing Time Constant of LPF 4 A o A angular freq of 3dB point of LPF Long time constant 0 narrow bandwidth amp better noise rejection 0 longer settling time Analog vs Digital Filters 0 2 stages 0 12 dboct 24 dboct 0 space amp expense all numerical EX A 1kHz signal buried in noise component 105kHz 80dB above signal To attenuate noise to 1 40dB of signal need 120dB reduction of noise 50Hz away from signal 12 dBoct need 10 octave separation 502m 005 Hz or 3 sec 24 dBoct need 5 octave separation 5025 16 Hz or 01 sec GC dB 3 20dBdec 102101 100 101 102 mm Signal Processing Quadrature Measurement Signal vStVS cosw3t Ref l VRtVRcosaRt I Ref2 VRtVR costhiVRsinaRt PSD l X VS cosqp inphase component PSD2 Y VS sinqp quadrature component signal amplitude R X2 Y2 71 Y Low Naise 5060 Hz 001120 Hz phase angle a tan iii ii Vanage A a c Q Cum vscosqz a v om PSDl 2 R a 0 Relevance In Sine or YTL a X Out Discriminator Phase Locke a Sine Du m cm SRBSO FUNCTIONAL BLOCK DIAGRAM Discriminaim SPECTRUM ANALYSIS SweptLO Spectrum Analyzer low pass filtei image rejection 3 Signal input 200MHz fixed IF amp bandpass i ii ler at l F frequency Cetec 8 log conv 10MHZ 4 1 J Incal DEC V lVCO one 210MHz Digital FFT Acoustooptic Spectrometer ANALOG DIGITAL INTERFACE W max representater elf anamg s1gnax DA nnversmn AD nnversmn DIGITAL H mm 1 am w m NdmretevaME e g e 4 to 2 quot1 and currespundmg number emenages Egtlt Venage smax m the range 75v 5v usmg arm uffset bmary Dr T nmphment demma uffsetbma 2seem hment vena e 127 1111 1111 D111 1111 4sa1v 126 1111 111a u111 111m 4922v 125 1111 1111 u111 11u1 4ee3v 2 1m mum Dunn mum DD7Ev 1 1m uuu1 Dunn uuu1 nn39v u 1m Dunn Dunn Dunn uuuuv 1 u111 1111 1111 1111 emuasv 2 u111 111m 1111 111a eumev Dunn mum 1m mum 419221 Dunn uuu1 1m uuu1 419511 Dunn Dunn 1m Dunn Dunv Scaled Resistors into Summing Junction fast uvvrpremsmn unvener Scaled Resistors into Summing Junction 1 ADC R2R Ladder DAC tVrei V151 KV0 10 VmOilR I 8i1i 9i10015i V mfg21111611 i quot1 16R V Va iglR9W j 16 Digital input analog output me 5V 0000 0000V 0001 O313V 0010 O625V 0011 O938V 1116 43 1 11 74 Switching is done by FET or BJT ADC Curre ntSwitched DAC WM M35 MSE l N334 MSBi aLsB i l I i l l l l l if I l L V 7 AV 0 Each transistor is a current source 16 z IE BR W E o All the bases and therefore the emitters are at the same potential 0 Collector currents are i 2i 4i 8i for QD QC QB QA Multiplying DAC 0 analog output scaled proportional to reference voltage Ratiometric Measurements 0 use the same reference voltage for DAC reference and for powering the sensor 0 measurement amp control with accuracy greater than stability of voltage suplly FVC FrequencytoVoltage Conversion Schmitt trigger for fixedlength pulse per each cycle average by low pass filter output is proportional to frequency direct conversion of frequency to analog voltage Without counter ADC ANALOGTODIGITAL CONVERSION ADC Parallel Encoder ADC Flash Encoder 5000v comparators binary output priority encoder detect highest comparator oN 5 output binary code 0 very fast 30 ns but dif cult to make very high resolution HalfFlash Encoder eg for 8bit conversion 4 bit ash encoding with 16 comparators DAC convert the result and subtract from input 4 bit ash encoding of the error total 32 comparators instead of 256 in onlytwice the time mm y su Hniiiiiam ADC ADC Countdown ADC analog in stop digital out 0 simple and good resolution but can be slow 0 Tracking ADC count up or down from current value depending on the change in input voltage Successive Approximation ADC Vin 0 I r I Vmax 1 2 3 digital outp 11011 0 Digitally generate successive approximation gt DAC gt comparator eg for 8bit conversion start from 0000 0000 set MSBto 1 1000 0000 DAC and compare with input keep 1 or reset to 0 repeat for lower bits it is a binary search w 8 comparisons Figurn 9 5 Sumnivraupmximanun ADC o alternate method for gnerating binary search V 2 1 f SingleSlope Integrating ADCs 0 Charge up a capacitor by a current source and measure the time it takes to reach refemce level analog in Vref converter start digital out Figure 9 54 singlesiupc AL DualSlope Integration 0 charge capacitor with current proportional to input voltage 0 discharge with constant curren 0 measure discharge time with counter 0 accuracy depends only on time base not capacitor or comparator DeltaSigma Converter 0 count number of cancellation current pulses to maintain fixed eg zero voltage from integrator ie zero charge on capacitor ADC VFC VoltagetoFreq uency Conversion TIME amp FREQUENCY MEASUREMENTS counting with FF frequency measurements time interval measurements time amp frequency standards COUNTING WITH FF DividebyZ 5 5 420 nnnnnnnn Q g g g 421 W 0 0 0 0 Q2 mm 0 0 0 1 0 0 1 0 93 l l l l 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 Time amp Frequency DivedbyThree Synchronous Counter Pulse Train Synchronizer 0 using SR FF and D register yuchmmm myquot 5 Figure 862 1335 Time amp Frequency Counters binary counter 74393 BCD counter modulo10 counter 74390 modulon counter cascadin ripple counter synchronous counter 60163 4bit synchronous 74590592 8bitsynchronous updown counter 74191 74193 74569 74579 load amp clear counter latch latched data can be displayed while counting continues threestate output 4 7 740925928 counter latch 7seg decoder driver TlL3067 counter with displa lntersil 7216 8bit 10M Hz universal counter w dispaly FREQUENCY MEASUREMENTS Digital Frequency Counter o Schmitt trigger 0 local oscillator o a e BCD counter latch Microwave Counting o GaAs ripple counters up to 3GHz o heterodyne to lower frequen 0 transfer oscillator PLL nth harmonic of VCO Time amp Frequency PLL Resolution Multiplication o for low frequency counting o PLL frequency multiplier oflow frequency input which is then counted mp1 signal m frequenw momm caumer Period Reciprocal Counting o for low frequency counting 0 count high freq local clock gated by low freq input input signal Scllmlll nigger HighResolution Frequency Comparison eg measurement of1 MHz signal to 1 sz precision 1 part in 10 2 stable 1MHz local oscillator PLL generate 1 000 001 Hz mix with 1MHz signal to get 1Hz heterodyne signal measure 1Hz signal s period to 1 ps balanced T mixer 2000001MH and IHZ Time amp Frequency TIME INTERVAL MEASUREMENTS TDC TimetoDigital Converter Linear Interpolation in Time Interval Measurement a o for interpolation of runt intervals shorter than clock period charge up a capacitor during runt period and discharge at slower rate 11000 say 0 count during discharge a b F71 41 srart slop cuincidcnce coincidence an 2zi i no m i W imp 21 2 3 relerence clock a n r 5n in Illllllilllllillllldlll quot i ragi i 5 i i quotWm I I I sum triggered In mks i as 15x13 us i my i 395 73944 i inxemuiamr H mm a k 739 mi iI W i stuv Iringered I mks 5 x E i W W ET EBA inlafholamr mm 4 1 1 7 V I i T T T3 7 72 an Innm 1 mm w e c j 3 anl ismora quot2770 J quotu swpmiclpve 739 n n in 1L FMUJJLt n o I z sJ rm m r r x gt 7 7 7 quot limo moo Vernier Interpolation b o clocks of period Tu and TD11n 0 start amp stop the second clock with the time interval being measured 0 find vernier coincidence Time Interval Averaging 0 measure the recurring interval many times and average 0 recurrence should not be commensurate with master clock Time amp Frequency TIME amp FREQUENCY STANDARDS Quartz Crystal Oscillators o stbility a few ppm a few ppb 0 TCXO temperaturecompensated crystal oscillator o ovenized crystals Atomic Clocks o rubidium 68GHz parts per 1011 o cesium 92GHz hyperfine transistion parts per 1012 international standard of second 0 hydrogen 1420 MHz maser o methane 339 pm infrared laser methanestabilized HeNe Calibration of Clock 0 LoranC o WWVB 0 Omega 0 GOES 0 GPS Global Positioning System Resources for Time amp Frequency 0 NIST Time amp Freqeuncy Division wwwboudernistgovtimefreq o NIST Measurement Systems Tutorial wwwbouldernistgovtimefreqphasePropertiesmainhtm USNO tychousnonavymigpshtm GPS primer by Aerospace Corporation GPS primer by Garmin ARRL Amateur Radio Relay League wwwarrorg WAVEFORM amp SIGNAL PROCESSING o waveforms o waveform operations 0 waveform file lO o waveform measurements 0 waveform generation 0 waveform conditioning o waveform monitoring WAVEFORMS Waveforms 0 start time t0 0 delta t dt 0 waveform data Y o Waveform terminals can be wired directly to the data Y Build Waveform Get Waveform Components Add Subtract Multiply Divide Waveformsvi o elementwise operations on waveforms A amp B new to is that of A dt must be identical in A amp B otherwise error waveform out error in amp out WAVEFORM OPERATIONS Index Waveform Arrayvi Align Waveform Timestampsvi Waveform Scale and Offsetvi Normalize Waveformvi Scale Delta tvi Get Waveform Subsetvi Append Waveformsvi Copy Waveform dtvi Waveform Min Maxvi Waveforms Waveform Scalar Limit Comparisonvi Get Final Time Valuevi Waveform Durationvi Number of Waveform Samplesvi Search Waveformvi Get Y Valuevi Get Waveform Time Arrayvi Waveform to XY Pairsvi WAVEFORM FILE IIO Write Waveforms to Filevi Read Waveforms from Filevi Export Waveform to Spreadsheet Filevi WAVEFORM MEASUREMENTS Basic Averaged DCRMSvi Averaged DCRMSvi Cycle Average and RMSvi Transition Measurementsvi Pulse Measurementsvi Amplitude and Levelsvi Extract Single Tone lnformationvi Harmonic Distortion Analyzervi SINAD Analyzervi FFT Power Spectrumvi FFT Power Spectral Densityvi FFT Spectrum MagPhase Reallmvi Waveforms Frequency Response Function MagPhase Reallmvi Cross Spectrum MagPhase Reallmvi WAVEFORM GENERATION Basic Function Generatorvi Formula Waveformvi Sine Waveformvi Square Waveformvi Triangle Waveformvi Sawtooth Waveformvi Basic Multitonevi Basic Multitone with Amplitudesvi Multitone Generatorvi Uniform White Noise Waveformvi Gaussian White Noise Waveformvi Periodic Random Noise Waveformvi WAVEFORM CONDITIONING Digital FIR Filtervi Digital IIR Filtervi Scalecl Winclowvi WAVEFORM MONITORING Limit Testingvi Limit Specificationvi Limit Specification by Formulavi Waveform Peak Detectionvi Waveforms Basic Level Trigger Detectionvi Waveforms EXERCISES EX 301 EX 302 waveform basics Generate a sine wave and a cosine wave with various parameters appropriately set with controls Plot waveforms on a waveform graph Form sinquot2 cosquot2 and plot it also Save sine and cosine to a waveform file and read back Save sine and cosine to a text spreadsheet file Open waveform file and text file using text editor and examine signal averaging Generate a sine waveform and a uniform white noise waveform and add the two Provide appropriate controls for various parameters Repeat this in a loop and display running average of the noisy sine wave to observe the signal rising from the noise OSCILLATORS 555 oscillator relaxation o cillators VCO v t econtrolled oscillators quadrature oscillators RF oscillators Q OSCILLATORS igudback nuLpuL w xtu ad mmml he uul rt nlncrwmc n l Loan Gain gt1 m Milan 5 rskuris but mp mmquot until clipping mm A pa39lecl inaurabccl mm walla 539 need a pusnrsm Chulluhr SK ng on sun Gciiuuhxl Noise Fig 145 An oscillalnr with nolss Realworld ampliiierg no matter how quiet Oscillators OSCILLATOR WITH 555 VFVHVCC me 2 OUHH Charge through RA RE discharge through RE T 0693RA 2RBC R R o duty cycle 5 2 50 RA 2R5 Sawtooth Generator Oscillators RELAXATION OSCILLATOR OpAmp circuit with saturation St t39 KKgtV39 V aura ionlf K K Va JCC VB V always Vcc If Vm Vm initially YC CCH Capacitor charges toward Vcc B 391 o vccz When VA reaches Vet2 V gt K VD chc Yam2 Capacitor discharges toward Vcc Y 22RC 7 gt 5 2 cc Vcc When VA reaches VCC2 V lt K gt V Repeat from beginning A cc vout Vcc 045 f7 RC CMOS Relaxation Oscillator 1 o R1ltltRz fe 0 very low noise Oscillators VOLTAGE CONTROLLED OSCILLATOR VCO 005pF c1 V 100k R Vin 2 499k 4 499klt Q1 ICi Integrator A If Qi is not conducting Vuut 0 Vst R2 OSVW R2 V 7V 05V 1 7 m 1 m SpAVWW R1 100k 5uAV If n 44730514 w05m100m 005 If Qi is conducting Vuut V V 0 1 n m 21 R4 499k 1IH 1 Vb V 05V 100er I 0 Schmitt Trigger 2 V V T 150Hz 3100 f V Vb WKZ3V 13v v Vout 0 0 VCO s can also be made from 555 timers H 0ng g2V715V Function Generator 0 VCO wave shaping o integrate square wave gt triagular wave 0 integrate triangular wave gt low pass lter gt good approx of sine wave VCO ICs 8038 2206 74L86249 20MHZ 1648 200MHz VFC voltagetofrequency converters LM331 AD650 PLL VCOphase detector 4046 74HC4046 Oscillators QUADRATURE OSCILLATORS Generation of sinmt and cosmt o switched capacitor resonator o analog trigonometric function generator lookup table statevariable oscillator phase sequence filters quadrature square waves start from twice the frequency digital square pulse 0 radiofrequency quadrature Sine wave of arbitrary phase 0 Asin mt a asinmt b cosmt sine out cos ne out ll AAA I II Vquot II RADIOFREQUENCY OSCILLATOR CIRCUITS Wien Bridge 0 low distortion sine wave LC OScillators 0 high frequency sine wave 0 varactor voltagevariable capacitance of reversebiased pn junction 0 Voltagetuned LC oscillator with varactor Varactor o voltage controlled capacitor 0 reversebiased pn junction 0 junction capacitance depends on bias voltage sz look 1 l mf qi Figure 545 Voltagetuned LC oscillator th MW 21 tunlnn Oscillators Quartz Crystal Oscillator o quartz is piezoelectric o highQ stable oscillator o 10kHz 10MHz o few ppm 39equency stability VCXO voltagecontrolled crystal oscillator o pull quartz crystal oscillator 39equency using varactor o 10 1000 ppm tunability TCXO temperaturecompensated crystal oscillator o s 1 ppm Ovenstabilized quartz oscillator art in 10 Atomic Clocks A Fiona oscillator DIGITAL SIGNAL PROCESSING W DIGITAL SAMPLING SIngaI x0 samphngIntENaI At samphngfrequency fmyh1At sampIEdsIgnaI Xx0xAtxZAtx3At Am grimw m m Aliasing aIIaSI Nyq Hg uIst frequency maXImum SIgnaI frequency that can be accuratEIy represented fur a gIvErI samphng ma 7 WA 2 many fW WWWWW Nahum 5mm ng PWNMWWI Ahased sum mam Undersamnhnq gtgt samphng VI Aha frequency Agu m fWII mnEarEst Integer Dwgwta Swgna Preeessmg 1 2 3 o 25 Hz m Hz 15D Hz 3m Hz Fwequenny 1s 7 u fsmu sea Mums Frawenw Samvhng Frkwenw renews Adua SHMa FrEIwzHCyCumDunems sum Arrmvs Aclum Frmusncy g H m Dashed Arm Ahzvs an Hz E1 2 vhas e 4 aha 1 I 2 a 4 mu 2 Hz AI DH 7DHZ 15m Hz 5mm 4 Fwequemy ls iszmu sun mum requnne Samvhnq reeuenw mee WE S una Frelweucy Cumvunems and Ahases Errors in Digital Sampling ahasmg undersamphng quanuzatmn Errur msu ap nure m Dith jErA en39n an u 5L e n remuves effem mpruved resu usefu m a ea mment b t resuhmun DC mng Errur m n m Pr mn uf quanuzatmn e measurement nmse un bratmn Dwgwta Swgna Prunessmg wage n Tune 2 Dc Level of a signal fur urmnuus swgna fur mgmzed swgna RMS Level of a signal furmnunuusswgna y furdwgmzedswgna y Dwgwta Swgna Prunessmg mm m quotequeno 5st m Fourier Transform N4 N4 Xk z xn2 1quot39 z xn cos 7 M N Am maxwmum frequency FM 7 windowing frequency resumtmn A T Am N Digitai signai Prunessing Spectral Averaging RMS averaging r FFT spenmm 2 dz 7 puvver spenmm 2 X 7 cross spenmm grY Vemuraveraging r FFT spenmm X r puvver spenmm X X 7 cross spenmm X Y Y 7 frequency Ll Harmonic Distortion Vin V Vuut Digital Signal Processing o THD total harmonic distortion THD 11422AAj A1 0 THDN total harmonic distortion noise J 2 2 N2 THDN L JAIZ 1422 1432 N2 o SINAD signal in noise and distortion 1 SINAD THDN LABVIEW PROGRAMMING structures strings arrays clusters local variables graphs amp charts file IO waveforms STRUCTURES FOR Loop counterterminal N iteration terminal i For loop executes N times input and output tunnels enabledisable auto indexing of array wait amp wait until WHILE Loop 0 conditional terminal continuestop if true 0 iteration terminal i 0 While loop executes at least once then checks condition Shift Register 0 add shift register 0 initialization 0 add element CASE Structure 0 Boolean cases True False o numeric cases single value list of values 137 range of values 28 0 default case add case etc 0 string cases 0 error cluster cases 0 output tunnel has to be wired from every case use default if unwired Sequence Structure 0 frames 0 add frame etc 0 sequence local Expressinn Nude Fnrmulande STRINGS pnmab e Munepnmame ASCH chavac evs Haylepevchavactev A NUL String Fundinns 51Hquot ength cuncatenate s1wvgs 51mg subset vep ace s ubsmng seavch and vep ace subsmng match panem StringNumber Cnn 39 numbe numbenu engmeevmg demmaxsmngm n mbev vacuumaVexpunenuaVengmeevmg 51mg m numbev uvmawame can va ue Format Specifier Examples The underhne char cter r 252m Spa25 m the mutant The 55 yeee Wm We The heuee e W m Me Me speemee e m We a 2W three enmes are exemmes w uh entrv shaws the output when the MM the want um LabVIEW Programming Table 0 2D array of strings ARRAYS Array 0 dimensions 1D 2D 3D add dimension 0 index 0 elements numeric string boolean etc empty array cut data copy data paste data 0 array control 0 array indicator 0 array constant Array Functions 0 array size 0 index array 0 initialize array 0 build array 0 array subset 0 insert into array 0 delete from array 0 replace array subset o rotate 1D array 0 reverse 1D array 0 transpose 2D array 0 reshape array 0 array max amp min CLUSTERS grouping of elements of various types for convenience bundle unbundle bundle by name unbundle by name array to cluster amp cluster to array points cluster of numeric elements numeric functions can be applied reorder cluster elements autosizing LOCAL VARIABLES LabVlEW Programming Access controls and indicators from more than one location in block diagram Pass data between structures that cannot be wired directly create local variable find terminal find controlindicator find local variable select item change to read change to write GRAPHS amp CHARTS waveform chart 0 Input to a singleplot waveform chart is a data point 0 plot legend common plots color line style line width point style 0 scale legend 0 graph palette 0 digital display 0 scrollbar o X amp Y scales format 0 chart history length 0 clear chart 0 chart update mode strip chart scope chart sweep chart 0 multiplot waveform chart bundle data points stacked or overlaid waveform graph 0 Input to a singleplot waveform graph is a 1D array 0 cursor legend 0 multiplot waveform graph 2D array of size M plots x N points xy graph 0 Input to a singleplot xy graph is a cluster of two 1D arrays xarray and yarray o multiplot xy graph array of singleplot clusters LabVIEW Programming examplesgeneralgraphgengraph Ilb intensity gra h Input to intensity graph is a 2D array representing zxy marker color interpolate color transpose array ar graph o cle Input Array Column Resulting Plot tlk veil II I il blue yellow green uk Isl yum WM pmi l Figurellr IIIIensIIyCIIaIICUIoI Map examplesgeneralgraphintgraph Ilb FILE IIO Text Files 0 Expected to contains ASCII characters only 0 Numerical data are rst converted to strings before writing 0 String representation ofnumerical data must be converted back to numerics alter reading 0 Can be opened in any text editing programs 0 Easier to program and to access but not ef cient with storage space and speed Binary Files Can contain any kind of data or patterns of bits and bytes 0 The application accessing the le has to knowhowto interpret the bit and byte patterns 0 In LabVIEW numerical data are written to a binary le the same way they are stored in memory 2 bytes for I16 8 bytes for double precision et 0 Needs more care in programming and accessing but more ef cient with storage space and speed General File IIO Process 0 open or create le is generates a refnum which is used in all subsequent le access LabVlEW Programming 0 read orwrite 0 close file Write to Spreadsheet Filevi 0 1D or 2D array of numeric data 0 file path dialog if empty 0 new file path 0 format 3f 0 append o transpose o delimiter Read from Spreadsheet Filevi 0 file path amp new file path 0 number of rows 0 format 0 all rows or first row 0 mark after read 0 EOF 0 start of read offset 0 max charactersrow o transpose o delimiter Write Characters to Filevi 0 file path amp new file path 0 character string 0 append Read Characters from Filevi file path amp new file path number of characters character string start of read offset mark after read EOF Read Lines from Filevi OpenlCreateReplace Filevi o prompt file path start path function 0 open 1 open or create 2 create or replace 3 create 4 open read only error in default name LabVIEW Programming refnum new file path file size error out Write File refnum amp duplicate refnum position mode start end current position offset data any type of data can be written offset error in amp error out Read File 0 count 0 data data is read into a string it is up to the program to interpret it properly Close File 0 refnum o path 0 error in amp error out Format into File 0 input file path or refnum o refnum out o format string 0 inputs 0 error in amp error out Scan from File 0 input file path or refnum o refnum out o format string 0 outputs 0 error in amp error out File Constants o path constant 0 empty path 0 not a path 0 not a refnum 0 current Vl s path File IIO Remarks 0 disk streaming 0 flow through parameters 0 error handling LabVIEW Programming 8 EXERCISES EX 201 Is this a prime number Take an input integer I32 greater than two In a WHILE loop divide it by integers 2 3 4 N2 Use QuotientandRemainder instead of ordinary divide Turn on or off an LED depending on raminder is nonzero or zero Exit WHILE loop as soon as there is a divisor with zero remainder or when the divisor has reached N2 EX 202 slot machine Generate a set of three random integers between 0 and 9 random 9999999 round down then convert to I32 Repeat until the three numbers come out as 777 Display the number of repetition Slow down the loop to make it look more realistic EX 203 addition quiz Generate two random integers between 0 and 100 and display them in indicators Wait in a while loop for the correct answer to be entered in a control The score starts from 100 and decreases by one point every second until the correct answer is entered EX 204 binary addition quiz More appropriately for this course write a VI that tests binary addition You can slightly modify EX 203 by changing Format amp Precision EX 205 binary quiz Write a VI that tests binary to decimal conversion EX 206 summation of series Add all integers from 1 to N Use FORloop and shift register EX 207 calculate factorial Start from 1 and multiply to it the numbers 2 through N Use shift register How large can N be EX 208 calculate factorial of larger numbers A 32bit unsigned integer can hold a number up to about 4G Note that 13 is already 6G Extend the factorial calculation to handle larger numbers Use two or more digital indicators and set up carries between them Have each indicator hold an integer up to 1000000000 1 EX 209 average of an array Generate an array of N random numbers simply by using autoindexing in a FOR loop Then calculate the average of the array Do this in another FOR loop using autoindexing and shift register LabVlEW Programming 9 EX 211 fake signal source So that we can use it as a fake signal source until we have real signal input from DAQ set up a subVl that outputs a simulated signal Every time it is called it returns a number that is sum of a dc level A and a noise that is a random number between B and 8 Use a FOR loop with N1 and a shift register without initialization The shift register adds a random number between B to 8 to the last output value Note that the subVl retains all the data including the shift register values between calls Provide input controls for B noise level and A dc level EX 212 waveform chart Temperature monitor Use the fake signal source subVl set A and B to mimic temperature fluctuation of about 2 degC around dc level of 25 degC Clear the chart each time before starting the loop using property node EX 213 multiplot chart Generate fake voltage signal with A 0V and B 10V Plot voltage and power assuming 10k 2 resistance Stack plots EX 214 waveform graph Generate a N 200 point 1D array of sinx with x ranging from O to xmax 10 and wavelength lambda 5 Provide input controls for these numbers Plot the array in a waveform graph Set the x scale using property node XScaleMultiplier EX 215 multiplot waveform graph Modify the diagram to display three plots sinx cosx and tanx EX 216 XY graph cos 9 sing Generate a spiral In the form of x 6 y 6 With approprIate constant a and e rangIng from a a O to 2m1T Generate a twoplot xygraph by building an array of two clusters one from the part a and the other the negative of a Send this twoelement array to the xygraph EX 217 Lissajous curve Draw Lissajous curves with various parameters input from controls EX 218 loaded dice Roll a die repeatedly and display histogram of values EX 219 function generator output forms sine square triangle use arcsin for triangle Use menu ring Provide controls for amplitude frequency phase offset Do not use waveform functions for this exercise EX 220 intensity graph LabVlEW Programming 10 2 Plot a 3D function such as Z 40057 r eXpK L r sz y2 with appropriately defined a range and parameters 2 Also try 2 Aexp r 2 cos 9 a EX 221 lowpass filter The lowpass RC filter action can be simulated by V ltrmgt1 nltrgtv r V IRV RVm Rc m 611 611 At AVG Kn V7ut Set up connectors for function generator exercise and use it as a subVI here to generate input signal Calculate the output according to the above expression Plot input and output on a p Provide various controls to be able to change the parameters while continuously running EX 222 string exercises Two controls one for item name eg apple and one for price eg 123 Generate a statement eg The price of apple is 123quot Express 12345678 in various string formats decimal fractional exponential and engineering using width 15 and precision 5 EX 223 character ASCII converter Type in a character and display its ASCII code in decimal hex and binary Conversely type in an ASCII code in decimal and display the corresponding character EX 224 representtion Wire a constant 258 to a U8 indicator Explain your observation Wire a constant 250 to an l8 indicator Explain your observation EX 225 text file IIO File dialog Write string to file Read string from file Write a number as string Read string into a number Try various formats amp other options EX 226 spreadsheet data IIO Set up a 361 x 4 numerical array First column goes 0 360 degrees Next three columns are sinx cosx and tanx Write this trig table as a spreadsheet to a text file Read the file into indicator array Open the text file using text editor or Excel Make certain it is in an expected and readable form Modify the VI to add column and row headings LabVIEW Programming EX EX 227 binary llO Write the trig table into SGL binary file Read the file and verify that the data is correct Open the binary file as if it is a text Can you recognize the data Compare the size of the text and binary files 228 general file llO Opencreatereplace file Write good morningquot Write 50 random numbers as strings delimited with commas Write another 50 random numbers directly as real numbers without any delimiters Write good nightquot Close file Open the file in a text editor and examine Timing Circuits 11 PLL PHASELOCKED LOOP fsig Af out 3 phase 1 low pass IA AV VCO detector b V l fref llllllllllll input may be sine square etc plus may have noise locks on to signal frequency regenerates clean output signal output may be functiongenerated as sine square etc AMFM demodulation frequency synthesis pulse synchronization etc PHASE DETECTOR Phase detector output is a function of phase difference between the signal and reference Detect phase error signal amp integrate average for gtgt 1 f sig lf sig amp ref are same frequency then PD output is DC lf sig amp ref are different frequency then PD output has the difference frequency Type Digital sig ID MWT VPD ref VPD VPD l l 0 2n 0 271 50 duty cycle of both sig amp ref othenNise Timing Circuits 12 Type Linear fourquadrant multiplier balanced mixer 2V gt VPD 7 cosgp VSg 2 V0 sin wt me 2 Sign sin wt 0 LOW PASS FILTER limit the response bandwidth reduces capture range and increases capture time act as flywheel smooth out noise or fluctuation in input signal prevent oscillation VCO VOLTAGECONTROLLED OSCILLATOR OpAmp VCOs VFC VoltagetoFrequency Converters digital output VCO RF VCOs LC oscillator with varactor varactor reversebiased pn junction used as voltage variable capacitor klystron microwave ode Depletion or i or Region T Reversed Biased Silicon Junction Diode Junction v Cathode Fig 1437 Modern VCOs use the voltagevariable characteristic of diode PN junctions for tuning Timing Circuits 13 APPLICATIONS tone decoding AMFM demodulation frequency multiplication frequency synthesis pulse synchronization regeneration of clean signals generation of sine wave locked to pulse freuqncy Frequency Multiplier f nf MI PD H LM Minn FM Detection phase Intitctor Figure 9J7 PLL FM discriminator AM Detection AM detection by signal rectification amp low pass filter r H I low pass filtev I detach urnplnucle Signal rnmlu ILI r ml C l39l39lEZF Figure 979 AM detection homodyne detection Pulse Synchronization CleanSignal Regeneration