EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONSUniversity of CaliforniaBerkeleyCollege of EngineeringDepartment of Electrical Engineeringand Computer ScienceRobert W. BrodersenEECS140Analog Circuit Design LecturesonAPPLICATIONSEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-011.01V0.99VtRISEtFALL1VEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-02Telephone FilterA/D ConverterPCM Codec15-20 Years AgoEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-0360Hz 800Hz 3.4kHz 5.8kHz0dBH ω()40dB–EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONSPole - Zero DiagramsA convenient way of visualizing transfer functions, HS()νOUTs()νINs()----------------sz1–()sz1∗–()⋅sp1–()sp1∗–()⋅-------------------------------------------==p120– j 30π⋅+=z1j 10π⋅=S σ j ω⋅+=z1∗j 10π⋅–=S - PLANEp1∗20– j 30π⋅–σ APP-04the Laplace Transform :XXOOj ω⋅EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-05Often what we are really interested in is ,i.e. theH ω()ω.H ω() Hs()Sjω⋅==H ω()j ω⋅ z1–()j ω⋅ z1∗–()⋅j ω⋅ p1–()j ω⋅ p1∗–()⋅----------------------------------------------------------=Poles - Zero Diagrams (Cont.)magnitude and phase at frequency, To find the magnitude use the fact that magnitude of the products equals the product of the magnitudes , so that :H ω()j ω⋅ z1–()j ω⋅ z1∗–()⋅j ω⋅ p1–()j ω⋅ p1∗–()⋅----------------------------------------------------------j ω⋅ z1–()j ω⋅ z1∗–()⋅j ω⋅ p1–()j ω⋅ p1∗–()⋅----------------------------------------------------------------==EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-06Poles - Zero Diagrams (Cont.)S σ j ω⋅+=S - PLANEσXXOOj ω⋅j ω⋅ p1∗–()j ω⋅ p1–()j ω⋅ z1∗–()j ω⋅ z1–()Lets graphically evaluateH ω()here at jωOj40π=The magnitude is the product of the lengths of vectors product of the lengths of vectors 1 & 2.H ω()3 & 4 divided by theEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-07Poles - Zero Diagrams (Cont.)σXXOOωZ60Hz 800Hz 3.4kHz 5.8kHz0dBH ω()40dB–jωEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-08σXXOOjω60Hz 800Hz 3.4kHz 5.8kHz0dBH ω()40dB–Xp3p3Poles - Zero Diagrams (Cont.)EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-09Poles - Zero Diagrams (Cont.)fO∆f3dBQfO∆f-----=EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-10Chose an “Equivalent” discrete time structure.Use appropriate cont. Discrete Transformation (i.e. Bilinear, Mapping differentials)Σz1–αSimulate Disirete Timeinplementation and compare with original spec.(DINAP)Filter DesignSpecificationAMPLBdFREQLC PrototypesContinuous Time Factorization into 2-Pole,2-Zero sections(Biquadratic)EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-11Active RC Filter(Continuous Time)Switched Capacitor Circuits(Sampled Data any Amplitude)Digital Filter(Sampled Data, Quantized Amplitude)EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-12A/DDigital FilterEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-13Typical Filter SpecificationsAMPLBd()FREQνOUTω()νINω()------------------H ω() H ω()ej θω()⋅⋅==H ω()2Amplitude (Magnitude in dB) =10 H ω()H∗ω()⋅[]logContinuous time specificationsof transfer function |H(ω)|EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-14Typical Filter Specifications (Cont.)Group Delay ω∂∂θω()=GroupFREQDelay(msec.)Group DelayEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-15Types of 2-Pole Transfer FunctionsLowpass :Hs()ωo2s2ωoQ----- s⋅ωo2++-----------------------------------=s1s1∗,ωoQ-----ωoQ-----24 ωo2⋅–+−–=j ωPωPQ-----–jωPσPXXEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-16Types of 2-Pole Transfer Functions (Cont.)( Lowpass )ωoωoQ-----+ωoωoQ-----–H ω()ωo1QQωosP≡ sP2ωP2+=QsP2 sP⋅--------------≡12---1ωPsP-----2+⋅=EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-17Types of 2-Pole Transfer Functions (Cont.)Bandpass :Hs()ωoQ----- s⋅s2ωoQ----- s⋅ωo2++-----------------------------------=ωoωoQ-----+H ω()ωo0.7071jωPσPXXOEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-18Types of 2-Pole Transfer Functions (Cont.)Highpass :H ω()ωoHighpass 1 Lowpass()Bandpass()––=11ωo2-----ωoQ----- s⋅+s2ωoQ----- s⋅ωo2++-----------------------------------–s2s2ωoQ----- s⋅ωo2++-----------------------------------==QjωPσPXXOEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-19Types of 2-Pole Transfer Functions (Cont.)Bandstop (or Notch) :H ω()ωoBandstop 1-sωoQ-----⋅s2ωoQ----- s⋅ωo2++-----------------------------------s2ωo2+s2ωoQ----- s⋅ωo2++-----------------------------------==ωjωPσPXXOOEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-20Types of 2-Pole Transfer Functions (Cont.)All Pass (Delay Equalizer) :H ω()ωo12 Bandpass()––=Hs() 12 sωoQ-----⋅⋅s2ωoQ----- s⋅ωo2++-----------------------------------–s2ωoQ-----– s⋅ωo2+s2ωoQ----- s⋅ωo2++-----------------------------------==ωH ω()ωGroupDelayjωPσ–PXXOOσPEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-21Lowpass & Bandpass :-+CΣ-+-+CRQVLPVINRRVBPState Variable Active RC FilterEECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-22ν1ν2RFR1R2 +-νOUTνOUTν1RFR1----- ν2RFR2-----+=State Variable Active RC Filter (Cont.)EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-231s---1RC--------–VBPRRQ-----ΣΣVLP-VIN1s---1RC--------–+++VLPVIN-------1RC--------2s21RCC⋅-------------- s⋅1RC-----++-------------------------------------------------ωo2s2ωoQ----- s ωo2++-------------------------------==ωo∴1RC--------= QRQR-----=State Variable Active RC Filter (Cont.)EECS140 ANALOG CIRCUIT DESIGN LECTURES ON APPLICATIONS APP-24State Variable Active RC Filter (Cont.)VBPVIN-------1RC--------– S⋅S1RCC⋅-------------- S⋅1RC-----2++----------------------------------------------------ωoS⋅–SωoQ----- S⋅ωo2++--------------------------------------==(Note GAIN is at instead of 1 as required for a canonical bandpass.) Q–ωoHighpass : Using a 3RD OP AMP we form the sum,VHIGHPASSVINVLP–1Q---- VBP⋅+=Highpass 1
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