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# MSU PHSX 262 - Phsx262 Lecture 2

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Based with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 1Today1/25/11 Physics 262 Lecture 2• Filters– Basics: Analog versus Digital; Passive versus Active– Basic concepts and types of filters– Passband, Stopband, Cut-off, Slope, Knee, Decibels, and Bode plots• Active Components and Filters– Review basics of OpAmps– First Order Active Filters • OpAmps with complex analysis• Transfer Functions • Bode Plot of Active Filters• Homework– Reading 175-180 (up to 4.07) and 263-268 by 2/1/11– 1.21 (p. 38), 1.22 (p. 39), 1.24(p.40, don’t need phasors), and 1.26 (page 42) and problems on next slide• Lab 2 this week– Lab 1 and Lab 2a notebooks due Friday 2/4/11 at 10am.– Work on lab 1a experiment (not PSpice) and Lab 2a meeting– Do Lab 2a pre-lab BEFORE lab meeting on Thursday 1/27/11Based with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 2Homework 2• Passive RC Filter–Write an expression for the complex transfer function (Vout(f)/Vin(f)) in terms of R, C, and f.–Write an expression for the magnitude of the transfer function in terms of R and C. Draw a sketch of it with axis label with numbers for key values.–Write an expression for the phase of the transfer function. –What are values of the magnitude and phase of the transfer function at the cutoff frequency? –Select a value for C so the cutoff frequency is 3.0kHz.• Passive RL Filter–Repeat but substitute an inductor L for the capacitor C –Find value of L for a cutoff frequency of 1600 Hz.• First-Order Active RC filter–Repeat steps for RC Filter above, but for active filter circuit to the right.Write expressions in terms of C, R1, and R2.–Select a value for C so the cutoff frequency is 6.0kHz.R15.0kR210k+-VoutVinCC0V17Vac0Vdc5.0k0V17Vac0VdcRVoutVinBased with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 3Filters• Filters: An electrical filter is a device designed to pass a certain group of signals or suppress other groups of signals from a collection of signals.• Analog versus Digital Filters– Analog Filters: Process real continuous, analog signals.– Digital Filters: Numerically process signals that have been discretely sampled and digitized.• Passive versus Active Analog Filters– Passive Filters: Filters implemented with resistors, capacitors, and inductors. Gain is less than or equal to one.– Active Filters: Filters implemented with resistors, capacitors, inductors, and active devices such as operational amplifiers or transistors. Can have gain greater than one.Based with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 4Basic Filter Concepts• Frequency dependent impedancesLow Frequencies: C-> infinity circuit => R2High Frequencies: C->0 circuit => R1|| R2 ( Z < R2 ) R1R2CR1R2LLow Frequencies: L-> 0 circuit => R1|| R2 ( Z < R2 ) High Frequencies: L->infinity circuit =>R 2Based with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 5Types of Ideal Filters• Transfer Functions of Ideal FiltersPassband(s): Frequency that pass weakly attenuated or have gain. Stopband(s): Frequencies that are “strongly” attenuated.Real World Filters: No sharp cutoffs; gain rolls off, stopband G>0.T(f)T(f)T(f)T(f)Based with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 6Passive Filter: Generalized Voltage Divider212()() ()() ()out sZVVZZVVs01()Z2()Z212() ()()() () ()outsVZGVZZGain (or attenuation)212()() /(2)() ()ZfTf fZf ZfTransfer Function()sV()outVBased with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 7Passive RC Filter Analysis2ZRC0VoutVin1Z1221(1 / ( )) 1()(1 / ( )) 11exp tan1()1()exp( ())1()1(/ )() tan /ccjCTfRjC jRCRCjRCTf j fMagTfffPhasefff12CfRC2fCut-off frequencyBased with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 8Filter Gain CharacterizationKneePass Band “40 dB” Stop Band33order = slope = 1PBGGain-Frequency plot (log-log) of the Bode DiagramBand Widthfc0V11Vac0VdcR110kC10.1uTransitionRippleBased with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 9Logarithmic NomenclatureDefine Decibel:10 100020log 10logVPdBVPFactor dB21210301001212110130110030620304036203040Multipliers on a Log AxisName RatioOctave 2:1Decade 10:1T(f)Based with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 10Bode DiagramsBode gain diagram: – Log-Log plot of |T(f)| vs f– Log(f) = x-axis– Log(|T(f)|) = y-axis Bode phase diagram: – Log-Lin Plots of Phase(f) vs f– Log(f) = x-axis– Phase(f) = y-axis (Linear) Quick analysis of filter behavior:– Filter type– Pass band gain– Cut-off frequency, aka;• Corner or Knee frequency• 3dB down point (|T(f)| =1/sqrt(2) – Stop band (“skirt”) slope (order)– Phase shiftVs14.5VppR10kC0.05u0Based with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 11Bode Diagram: PhaseVs14.5VppR10kC0.05u0outvCAs 0, Z(in phase)out SvvCAs , Z 0 Since ,RR SviRvand is in phase with CR Sii vBut, is -90 out of phase with So, is -90 out of phase with .CCout SvivvBased with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 120V11Vac0VdcR11kC10.1uR21kC20.1uR31kC30.1uVVV Frequency10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHzV(R2:1) V(R2:2) V(R3:2)10uV100uV1.0mV10mV100mV1.0VMultiple-Order (Passive) Filterm=1m=33dBdown0V11Vac0VdcR11kC10.1uR21kC20.1uR31kC30.1uVVVBased with permission on lectures by John GettyPhysics 262: Laboratory Electronics II Spring 2011 Lect 2 Page 13Cascaded

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