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# ELEC INSTRU & MEASUREMNT PHY 402G

UK

GPA 3.82

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This 14 page Class Notes was uploaded by Alda Roberts on Friday October 23, 2015. The Class Notes belongs to PHY 402G at University of Kentucky taught by Kwokwai Ng in Fall. Since its upload, it has received 16 views. For similar materials see /class/228261/phy-402g-university-of-kentucky in Physics 2 at University of Kentucky.

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Date Created: 10/23/15

clc and ac Vt Vt V A sin wtd ac Ammum I w2nf and f1T phase l quotdc is a particular case of ac with Jo gt0 T gtoo Example Neutral white Live black Ground Green vpp156v 156V Capacitor in an ac circuit Capacitor is insulating to clc but it is conducting to ac We can think it like a membrane in a water pipe 4 gt dc no water can flow through the ac no water can flow through the membrane and no current membrane but there is water current Pressure lt gt voltage water flow lt gt current Note phase difference between I and V is leadingV by TLZ t If W v0 sin wt vt Then lt we V0 sin um TE7 Example Note phase difference between I and V l is leading V by TLZ Kt A fVt V0 sin wt Vlt Then l t 00C V0 sin wt TZE w0 for dc signal O for dc signal The capacitor does not conduct for dc signal Just think and believe 1 The higher the frequency the quoteasierquot to displace a current through the capacitor 2 The larger the capacitor the quotsofterquot it is the quoteasierquot to displace a current through the capacitor Impedance of a capacitor Since Vt 2 V0 sin a t I wCV mMM In complex numbers V W m 7r wt j 1t a C V0 e1E 2 i wCV0 elme2 a Ceizj V0 em w Ceizj Vt wc va l or Vt H 0 imC 0 De ne ImpedanceXC 2 1 39 109C Ohm s Law VU Ht XC Units for XC Q Example 100 VC 41 10 V0 IXC 00S Ve 497 05J Vei I V Z V Z V i RXc 1mg 10101 41 j 1U3 Ve 4 V 10 101 i1 45 Va 101013910 101 6 2Mk5Ve 4 V1020101 ZQVJ v 2 T V005 005i 0055 V 647 Phase difference between I and V Phase difference between VC and V Impedance of a capacitor Remember The larger the C the smaller the impedance The smaller the w the larger the impedance think about dc case So the impedance of a capacitor must be in the form Note that the impedance is a function of w Example Consider a capacitance of lnF Impedance XC at f 60Hz is XC 42653 x1069 12653MQ 127rgtlt601gtlt1039 f 600Hz is XC 12653gtlt1050210653MQ 127rgtlt6001gtlt1039 f 6kHz is XC 1 9 2 12653x104g22 12653k9 127rx60001gtlt1039 f 6MHzis XC 1 2426539 i27rgtlt6gtlt1061gtlt10399 Low pass filter R This is a potentiometer At low frequency impedance of C will be greater and hence the voltage difference V across C will be larger At low frequency more voltage C if out Signal WI appear across C In other words less hIgh frequency signals will appear across C 50 this is a low frequency pass filter 1 C icoC 1 Vin 2 Vin i0in Vout RXC R 1 1a2 CZRZ icoC 1 V icoC 102C2R2 iquot 1imCR 1UJZC2R2 V IX V 1aC 1 C 1icoCR icoC 1 zvm 1 xla2C2R2 11mCR 1 1 1im CR Vout lags Vin by a phase angle of tan39 0 RC V quot1icoCRj1 icoCRj 1 icoCR V lquot1co2 CZRZJ Example At f 60Hz 1272 gtlt 6O1gtlt10396 c 1000 127r gtlt 601gtlt1039 265361 1000 265361 26536 Vout 10002265362 26536 R1kQ 2 dB V OUT dB 2 20 Log 10 0 dB if VoutNin1 Adding 20dB corresponds to multiplying 10 times eg X 1000 X 10300 20dB 20dB 20dB 60dB Important X dB V i multiplication addition 3dBgt OUTNIOZO 141 2 Vin 10 20dB V 6dB gt 5 22 2 6dB Example C Vout V out 1 Vin 12C2R2 Attenuation of the lter is 3dB at a RC is known as the time constant T of the filter Properties of low pass filter CDtan391oRC AtwOAVLut1or0dB A in 900 Vout Atw oo Av T O 45 Am i A i 3013 RC3 V J 1 0 0 Athi hfre enc agtgti V0 RC g q y RC Vin J1w2C2R2 1 1 When to increases 2 times 1 k m octave AV decreases by 2 times Viquot IQZCZR2 a CR This filter has a roll off rate of 1 6dB per octave 1 3dBorf 6dB per octave means AV quot Linear scale When 00 increases 2 times 1 h octave Av decreases by 2 times Viquot This filter has a roll off rate of 1 6dB per octave 1 3dB0rT 2 6dB per octave means AV quot n E Log scale Log VOUT 1 Log VOUT 1 A Vin w Vin w Logo 0 0 RC 1 3dB or 5 Approximate model

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