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Analog Electronics Tutorial Series Operational Amplifiers. _. +. Kristin Ackerson, Virginia Tech EE Spring 2002. Table of Contents. The Operational Amplifier______________________________slides 3-4 The Four Amplifier Types______________________________slide 5 - PowerPoint PPT Presentation

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  • Kristin Ackerson, Virginia Tech EESpring 2002_+

  • Table of ContentsKristin Ackerson, Virginia Tech EESpring 2002The Operational Amplifier______________________________slides 3-4The Four Amplifier Types______________________________slide 5VCVS(Voltage Amplifier) Summary:Noninverting Configuration____________slides 6-9Inverting Configuration________________slides 10-12ICIC(Current Amplifier) Summary________________________slide 13 VCIS (Transconductance Amplifier) Summary_____________slides 14-15ICVS (Transresistance Amplifier) Summary_______________slides 16-18Power Bandwidth_____________________________________slide 19Slew Rate____________________________________________slide 20Slew Rate Output Distortion____________________________ slide 21Noise Gain___________________________________________slide 22Gain-Bandwidth Product_______________________________slide 23Cascaded Amplifiers - Bandwidth________________________slide 24Common Mode Rejection Ratio__________________________slides 25-26Power Supply Rejection Ratio___________________________slide 27Sources_____________________________________________slide 28

  • The Operational AmplifierKristin Ackerson, Virginia Tech EESpring 2002Usually Called Op AmpsAn amplifier is a device that accepts a varying input signal and produces a similar output signal with a larger amplitude.Usually connected so part of the output is fed back to the input. (Feedback Loop)Most Op Amps behave like voltage amplifiers. They take an input voltage and output a scaled version.They are the basic components used to build analog circuits.The name operational amplifier comes from the fact that they were originally used to perform mathematical operations such as integration and differentiation.Integrated circuit fabrication techniques have made high-performance operational amplifiers very inexpensive in comparison to older discrete devices.

  • i(+), i(-) : Currents into the amplifier on the inverting and noninverting lines respectivelyvid : The input voltage from inverting to non-inverting inputs+VS , -VS : DC source voltages, usually +15V and 15VRi : The input resistance, ideally infinityA : The gain of the amplifier. Ideally very high, in the 1x1010 range.RO: The output resistance, ideally zerovO: The output voltage; vO = AOLvid where AOL is the open-loop voltage gainThe Operational AmplifierKristin Ackerson, Virginia Tech EESpring 2002+VS-VSvidInvertingNoninvertingOutput+_i(-)i(+)vO = AdvidROARi

  • The Four Amplifier TypesKristin Ackerson, Virginia Tech EESpring 2002

    DescriptionGain SymbolTransfer FunctionVoltage Amplifieror Voltage Controlled Voltage Source (VCVS)Avvo/vinCurrent Amplifieror Current Controlled Current Source (ICIS)Aiio/iinTransconductance AmplifierorVoltage Controlled Current Source (VCIS)gm(siemens)io/vinTransresistance AmplifierorCurrent Controlled Voltage Source (ICVS)rm(ohms)vo/iin

  • VCVS (Voltage Amplifier) SummaryKristin Ackerson, Virginia Tech EESpring 2002Noninverting Configuration+_vin++-vOvidi(+)i(-)iOiFRFRLR1i1vid = vo/AOLAssuming AOL vid =0Also, with the assumption that Rin = i(+) = i(-) = 0_vF+_v1+_vL+_iLApplying KVL the following equations can be found:v1 = vinvO = v1 + vF = vin+ iFRFThis means that, iF = i1Therefore: iF = vin/R1Using the equation to the left the output voltage becomes:vo = vin + vinRF = vin RF + 1R1 R1

  • Kristin Ackerson, Virginia Tech EESpring 2002VCVS (Voltage Amplifier) SummaryNoninverting Configuration ContinuedThe closed-loop voltage gain is symbolized by Av and is found to be:Av = vo = RF + 1 vin R1The original closed loop gain equation is:Av = AF = AOL 1 + AOL

    Ideally AOL , Therefore Av = 1 Note: The actual value of AOL is given for the specific device and usually ranges from 50k 500k. is the feedback factor and by assuming open-loop gain is infinite: = R1 R1 + RF

    AF is the amplifier gain with feedback

  • Kristin Ackerson, Virginia Tech EESpring 2002VCVS (Voltage Amplifier) SummaryNoninverting Configuration ContinuedInput and Output ResistanceIdeally, the input resistance for this configuration is infinity, but the a closer prediction of the actual input resistance can be found with the following formula:RinF = Rin (1 + AOL)Where Rin is given for the specified device. Usually Rin is in the M range.Ideally, the output resistance is zero, but the formula below gives a more accurate value:RoF = RoWhere Ro is given for the AOL + 1specified device. Usually Ro is in the 10s of s range.

  • Kristin Ackerson, Virginia Tech EESpring 2002VCVS (Voltage Amplifier)Noninverting Configuration ExampleGiven:vin = 0.6V, RF = 200 k R1 = 2 k , AOL = 400kRin = 8 M , Ro = 60 Find: vo , iF , Av , , RinF and RoFSolution:vo = vin + vinRF = 0.6 + 0.6*2x105 = 60.6 V iF = vin = 0.6 = 0.3 mA R1 2000 R1 2000Av = RF + 1 = 2x105 + 1 = 101 = 1 = 1 = 9.9x10-3 R12000 AOL 101RinF = Rin (1 + AOL) = 8x106 (1 + 9.9x10-3*4x105) = 3.1688x1010 RoF = Ro = 60= 0.015 AOL + 1 9.9x10-3*4x105 + 1

  • Kristin Ackerson, Virginia Tech EESpring 2002VCVS (Voltage Amplifier) SummaryInverting Configuration+_RLvO+-vin+_R1i1RFiFThe same assumptions used to find the equations for the noninverting configuration are also used for the inverting configuration.General Equations:i1 = vin/R1iF = i1vo = -iFRF = -vinRF/R1Av = RF/R1 = R1/RF

  • Input and Output ResistanceIdeally, the input resistance for this configuration is equivalent to R1. However, the actual value of the input resistance is given by the following formula:Rin = R1 + RF 1 + AOLIdeally, the output resistance is zero, but the formula below gives a more accurate value:RoF = Ro 1 + AOL Note: = R1This is different from the equation used R1 + RFon the previous slide, which can be confusing.Kristin Ackerson, Virginia Tech EESpring 2002VCVS (Voltage Amplifier) SummaryInverting Configuration Continued

  • Kristin Ackerson, Virginia Tech EESpring 2002VCVS (Voltage Amplifier)Inverting Configuration Example+_RL+-vin+_R1i1RFiFGiven:vin = 0.6 V, RF = 20 k R1 = 2 k , AOL = 400kRin = 8 M , Ro = 60 Find: vo , iF , Av , , RinF and RoFvOSolution:vo = -iFRF = -vinRF/R1 = -(0.6*20,000)/2000 = 12 ViF = i1 = vin/R1 = 1 / 2000 = 0.5 mAAv = RF/R1 = 20,000 / 2000 = 10 = R1/RF = 2000 / 20,000 = 0.1Rin = R1 + RF = 2000 + 20,000 = 2,000.05 1 + AOL 1 + 400,000RoF = Ro= 60 = 1.67 m 1 + AOL 1 + 0.09*400,000

    Note: is 0.09 because using different formula than above

  • ICIS (Current Amplifier) SummaryKristin Ackerson, Virginia Tech EESpring 2002 Not commonly done using operational amplifiers+_LoadiiniLSimilar to the voltage follower shown below:Both these amplifiers have unity gain:Av = Ai = 1+_iin = iLvin = vovin+_+-vOVoltage Follower1 Possible ICIS Operational Amplifier Application

  • VCIS (Transconductance Amplifier) SummaryKristin Ackerson, Virginia Tech EESpring 2002Voltage to Current Converter+_LoadiLR1i1vin+_OR+_LoadiLR1i1vin+_vin+_General Equations:iL = i1 = v1/R1v1 = vin The transconductance, gm = io/vin = 1/R1Therefore, iL = i1 = vin/R1 = gmvinThe maximum load resistance is determined by:RL(max) = vo(max)/iL

  • Kristin Ackerson, Virginia Tech EESpring 2002VCIS (Transconductance Amplifier)Voltage to Current Converter Example+_LoadiLR1i1vin+_Given: vin = 2 V, R1 = 2 k vo(max) = 10 VFind: iL , gm and RL(max)Solution:iL = i1 = vin/R1 = 2 / 2000 = 1 mAgm = io/vin = 1/R1 = 1 / 2000 = 0.5 mSRL(max) = vo(max)/iL = 10 V / 1 mA = 10 k

    Note: If RL > RL(max) the op amp will saturateThe output current, iL is independent of the load resistance.

  • Kristin Ackerson, Virginia Tech EESpring 2002VCIS (Transresistance Amplifier) SummaryCurrent to Voltage ConverterGeneral Equations:iF = iinvo = -iFRFrm = vo/iin = RF+_iFiinRFvO+-

  • VCIS (Transresistance Amplifier) SummaryCurrent to Voltage ConverterKristin Ackerson, Virginia Tech EESpring 2002Transresistance Amplifiers are used for low-power applications to produce an output voltage proportional to the input current.Photodiodes and Phototransistors, which are used in the production of solar power are commonly modeled as current sources.Current to Voltage Converters can be used to convert these current sources to more commonly used voltage sources.

  • Kristin Ackerson, Virginia Tech EESpring 2002VCIS (Transresistance Amplifier)Current to Voltage Converter Example+_iFiinRFvO+-Given: iin = 10 mA RF = 200 Find: iF , vo and rmSolution:iF = iin = 10 mAvo = -iFRF = 10 mA * 200 = 2 Vrm = vo/iin = RF = 200

  • Power BandwidthKristin Ackerson, Virginia Tech EESpring 2002The maximum frequency at which a sinusoidal output signal can be produced without causing distortion in the signal.The power bandwidth, BWp is determined using the desired output signal amplitude and the the slew rate (see next slide) specifications of the op amp.BWp = SR 2Vo(max)SR = 2fVo(max) where SR is the slew rate

    Example:Given: Vo(max) = 12 V and SR = 500 kV/sFind: BWpSolution: BWp = 500 kV/s = 6.63 kHz 2 * 12 V

  • Slew RateKristin Ackerson, Virginia Tech EESpring 2002A limitation of the maximum possible rate of change of the output of an operational amplifier.As seen on the previous slide, This is derived from:SR = 2fVo(max)SR = vo/tmax

    Slew Rate is independent of the closed-loop gain of the op amp.

    Example:Given: SR = 500 kV/s and vo = 12 V (Vo(max) = 12V)Find: The t and f.Solution: t = vo / SR = (10 V) / (5x105 V/s) = 2x10-5 s f = SR / 2Vo(max) = (5x105 V/s) / (2 * 12) = 6,630 Hz f