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Berkeley ELENG 140 - Lecture on Feedback

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EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 27 University of CaliforniaBerkeleyCollege of EngineeringDepartment of Electrical Engineeringand Computer ScienceRobert W. BrodersenEECS140Analog Circuit Design LecturesonFEEDBACKEECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 27 FB-1FeedbackΣaf+-νinνενofbνoBasic AmplifierFeedback AmplifierError SignalFeedback Signalf = gain of feedback amplifiera = gain of basic amplifierEECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 27 FB-2Feedback (Cont.)νενinνofb–=νofbf νo⋅=νενinf ν⋅o–=νoa νε⋅=Aννoνin⁄a1 af⋅+()-----------------------1f---T1 T+------------ Closed loop gain←⋅===T Loop Gain≡ af⋅=Aνa ∞→1f---=f Feedback Factor=a Open Loop Gain=T 1»EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 27 FB-5Feedback (Cont.) There are 4 basic kinds of Feedback Circuits : (Type of Feedback) (Type of Sensing) 1) Series (Voltage) - Shunt (Voltage) 2) Shunt (Current) - Shunt (Voltage) 3) Shunt (Current) - Series (Current) 4) Series (Voltage) - Series (Current)EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 27 FB-6Series-Shunt (νout/νin) +-νGνinR2νfbνoR1+-This is a voltage amplifier, a typical example is the wellknown configuration shown below :EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 27 FB-7Series-Shunt (Cont.) +-+-+-+-+++-- -νενoνoνfbf νo⋅=νinrinaννε⋅rofR1R1R2+-----------------=EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 27 FB-8Series-Shunt (Cont.) Gain Calculation : νoaννε⋅=νfbfννo⋅=νinνενfb+νoaν----fννo⋅+==νoνin-----1fν---T1 T+------------⋅ Aν Closed Loop Gain==νoνinaν⋅1 aνfν⋅+---------------------=νinνε1 aνfν⋅+()⋅=EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 27 FB-9Series-Shunt (Cont.) Rout Calculation (Closed Loop Output Resistance) : Drive output with νt, measure it+-+-roitνt Routνin0=νtit----=aννεitνtaννε⋅–ro-----------------------=νεfννt⋅+ νin0 ; νεfννt⋅–===itνtaνfννt⋅⋅+ro-------------------------------=νtit----Routro1 aνfν⋅+---------------------ro1 T+------------===νin0=Aν10= fν0.1= aν50000,=T 0.150000,⋅ 5000==ro100Ω=ROUTro1 T+------------0.02Ω==EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 28 FB-10Series-Shunt (Cont.) Rin Calculation : Rinνiniin-----=νin1 T+()νε⋅=iinνεrin----νin1 T+()rin⋅--------------------------==Rinνiniin-----1 T+()rin⋅==EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 28 FB-11Shunt-Shunt (Transresistance νout/iin)+-++--iεifbfGνo⋅=aRiε⋅rorinνενoνoiinEECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 28 FB-13Shunt-Shunt (Cont.)ifbfGνo⋅=νoaRiε⋅=iεiinifb–=fGifbνo----=aR has units of resistanceGain Calculation :νoaRiinfGνo⋅–()⋅=ifbνoiin----1fG---T1 T+------------⋅=EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 28 FB-14Shunt-Shunt (Cont.)∑iinRSEECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 28 FB-15Rin Calculation : Shunt-Shunt (Cont.)RINνεiin----=RINνεiin----rin1 T+------------==iε∴iin1 aRf⋅+--------------------=iεiinfGνo⋅– iinaRfGiε⋅⋅–==EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 28 FB-16Rout Calculation (Closed Loop Output Resistance) : Shunt-Shunt (Cont.)ROUTνtit----iin0==νoνt=()iin0 itifb+==νoitro⋅ aRiε⋅+ itro⋅ aRfGνo⋅⋅–==νoit----ro1 T+------------ROUT==iεifb– fG– νo⋅==EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 28 FB-17Shunt-Series (Current Amp iout/iin)+-iεifbfiνo⋅=aiiε⋅rorinνεioiinioEECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 28 FB-18Shunt-Series (Cont.)fiifbio----=ioiin----1fi---T1 T+------------⋅=RINrin1 T+------------=ROUTro1 T+()⋅=Taifi⋅=Rout Calculation (Closed Loop Output Resistance) : Rin Calculation : Gain Calculation :EECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN LECTURE 28 FB-19Series-Series (Transconductance iout/νin)+-ifbfRνo⋅=νενinrin+-+-aGνε⋅roioioEECS140 ANALOG CIRCUIT DESIGN LECTURES ON FEEDBACKROBERT W. BRODERSEN


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