Slide 1EE100 Summer 2008 Bharathwaj MuthuswamyEE100Su08 Lecture #14 (July 28th2008)• Outline– MultiSim licenses: trying to get new licenses– HW #2: regrade deadline: Monday, 07/28, 5:00 pm PST.– Midterm #1 regrades: DONE!– QUESTIONS?– Bode plots– Diodes: Introduction• Reading– Appendix E* (skip second-order resonance bode plots), Chapter 1 from your reader (skip second-order resonance bode plots)– Chapter 2 from your reader (Diode Circuits)Slide 2EE100 Summer 2008 Bharathwaj MuthuswamyExample Circuit)1()/1)/1(22CRjACjRjwCAINOUTωω+=+=VVINOUTnctionTransferFuVV=−+AVTR2R1+VT+VOUTCVIN+cRcINOUTZZAZ+=VVA = 100R1= 100,000 OhmsR2= 1000 OhmsC = 10 uFSlide 3EE100 Summer 2008 Bharathwaj MuthuswamyExample Circuit−+AVTR2R1+VT+VOUTCVIN+A = 100R1= 100,000 OhmsR2= 1000 OhmsC = 10 uFSlide 4EE100 Summer 2008 Bharathwaj MuthuswamyExample Circuit−+AVTR2R1+VT+VOUTCVIN+A = 100R1= 100,000 OhmsR2= 1000 OhmsC = 10 uFSlide 5EE100 Summer 2008 Bharathwaj MuthuswamySlide 6EE100 Summer 2008 Bharathwaj MuthuswamyBode Plot: Label as dB0204060-201010010001Radian Frequency)1(2CRjAINOUTω+=VVA = 100R2= 1000 OhmsC = 10 uFwp= 1/(R2C) = 100AMagnitude in dBNote: Magnitude in dB = 20 log10(VOUT/VIN)Slide 7EE100 Summer 2008 Bharathwaj MuthuswamySlide 8EE100 Summer 2008 Bharathwaj MuthuswamyExample: Phase plot)1(2CRjAINOUTω+=VV-90090180-1801010010001RadianFrequency-45oA = 100R2= 1000 OhmsC = 10 uFPhaseActual value is 45450}4520100{}|1|0100{ −=−=∠∠=+∠PhasejPhaseSlide 9EE100 Summer 2008 Bharathwaj MuthuswamyTransfer Function• Transfer function is a function of frequency– Complex quantity– Both magnitude and phase are function of frequencyTwo Port filter networkVinVout()()()outout ininVfVHfθθθ==∠−=∠outinVHVH(f)Slide 10EE100 Summer 2008 Bharathwaj MuthuswamyFilters• Circuit designed to retain a certain frequency range and discard othersLow-pass: pass low frequencies and reject high frequenciesHigh-pass: pass high frequencies and reject low frequenciesBand-pass: pass some particular range of frequencies, reject other frequencies outside that bandNotch: reject a range of frequencies and pass all other frequenciesSlide 11EE100 Summer 2008 Bharathwaj MuthuswamyCommon Filter Transfer Function vs. Freq(Magnitude Plots shown)()HfFrequencyHigh Pass()HfFrequencyLow Pass()HfFrequencyBand PassFrequencyBand Reject()HfSlide 12EE100 Summer 2008 Bharathwaj MuthuswamyFirst-Order Lowpass Filter()()12121( ) 1 1tan1( ) 11112()1() , tan1BBBBjCRCjC R jRCRCLet and fRC RCHffHffffωωωωωωπθθ−−=== ∠−+++===∠⎛⎞==−⎜⎟⎝⎠⎛⎞+⎜⎟⎝⎠CVH(f) =VH(f)R+-CVVC+-1/210 101() 22()120log 20( )log 2 3(0) 2BBHfHfdBH−===− =−Slide 13EE100 Summer 2008 Bharathwaj MuthuswamySlide 14EE100 Summer 2008 Bharathwaj MuthuswamySlide 15EE100 Summer 2008 Bharathwaj MuthuswamySlide 16EE100 Summer 2008 Bharathwaj MuthuswamyFirst-Order Highpass Filter()()()1212tan1( ) 1 21() , tan21RBBBRCRjRCRCjC R jRCRCfffHffffωωπωωωωπθ−−⎡⎤=== ∠−⎢⎥++⎣⎦+⎛⎞⎜⎟⎛⎞⎝⎠==−⎜⎟⎝⎠⎛⎞+⎜⎟⎝⎠VH(f) =VR+-CVVC+-1/210 101() 22()120log 20( )log 2 3(0) 2BBHfHfdBH−===− =−VRSlide 17EE100 Summer 2008 Bharathwaj MuthuswamyFirst-Order Lowpass Filter121211tan112()1() , tan1RBBBBLjLRLRRRRLet and fLLHffHffffωωωωπθθ−−⎛⎞== ∠−⎜⎟⎝⎠⎛⎞++⎜⎟⎝⎠===∠⎛⎞==−⎜⎟⎝⎠⎛⎞+⎜⎟⎝⎠VH(f) =VH(f)R+-LVVL+-VRSlide 18EE100 Summer 2008 Bharathwaj MuthuswamyFirst-Order Highpass Filter1212tan2112()() , tan21LBBBBBjL LLRRjLRLRRRRLet and fLLHffffHffffωωπωωωωπθπθ−−⎡⎤⎛⎞== ∠−⎜⎟⎢⎥⎝⎠⎣⎦⎛⎞++⎜⎟⎝⎠===∠⎛⎞⎜⎟⎛⎞⎝⎠==−⎜⎟⎝⎠⎛⎞+⎜⎟⎝⎠VH(f) =VH(f)R+-LVVL+-VRSlide 19EE100 Summer 2008 Bharathwaj MuthuswamyFirst-Order Filter CircuitsL+–VSCRLow PassHigh PassHR= R / (R + jωL)HL= jωL/ (R + jωL)+–VSRHigh PassLow PassHR= R / (R + 1/jωC)HC= (1/jωC) / (R + 1/jωC)Slide 20EE100 Summer 2008 Bharathwaj MuthuswamySlide 21EE100 Summer 2008 Bharathwaj MuthuswamyDiodes• OUTLINE– Diode Model(s)– Circuit Analysis with Diodes– Diode Logic Gates– Load Line Analysis– Zener Diodes– Diode Peak Detector• Reading– Reader: Chapter 2Slide 22EE100 Summer 2008 Bharathwaj MuthuswamyDiode Physical Behavior and EquationNtypePtypeSchematic Device+−VIISymbol+−VQualitative I-V characteristics:IVV positive, easy conductionV negative, no conductionQuantitative I-V characteristics:)1e(IIkTqV0−=In which kT/q is 0.026V and IOis a constant depending on diode area. Typical values: 10-12to 10-16A. Interestingly, the graph of this equation looks just like the figure to the left.A non-ideality factor n times kT/q is often included.Slide 23EE100 Summer 2008 Bharathwaj MuthuswamyDiode Ideal (Perfect Rectifier) ModelThe equationis graphed below for 1)kTqVexp(II0−=A10I150−=The characteristic is described as a “rectifier” – that is, a device that permits current to pass in only one direction. (The hydraulic analog is a “check value”.) Hence the symbol:+−VISimple “Perfect Rectifier” ModelIf we can ignore the small forward-bias voltage drop of a diode, a simple effective model is the “perfect rectifier,” whose I-V characteristic is given below:VIReverse bias0Vany ,0I<≅Forward bias0Iany ,0V >≅A perfect rectifier0246810-5 0 5 10Current in mAForward Voltage in VSlide 24EE100 Summer 2008 Bharathwaj MuthuswamyI-V CharacteristicsIn forward bias (+ on p-side) we have almost unlimited flow (very low resistance). Qualitatively, the I-V characteristics must look like:VFIcurrent increases rapidly with VVFIThe current is close to zero for any negative biasIn reverse bias (+ on n-side) almost no current can flow. Qualitatively, the I-V characteristics must look like:Slide 25EE100 Summer 2008 Bharathwaj Muthuswamypn-Junction Reverse Breakdown• As the reverse bias voltage increases, the peak electric field in the depletion region increases. When the electric field exceeds a critical value (Ecrit≅ 2x105V/cm), the reverse current shows a dramatic increase:ID(A)VD(V)reverse (leakage) currentforward currentbreakdown voltageVBDSlide 26EE100 Summer 2008 Bharathwaj MuthuswamyThe pn Junction I vs. V EquationIn EECS 105, 130, and other courses you will learn why the I vs. V relationship for PN junctions is of the form)1e(IIkTqV0−=where I0is a constant proportional to junction area and depending on doping in P and N regions, k is Boltzman constant, and T is
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