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MEMS1082MechatronicsChapter 5-4 Operational amplifierInstrumentation amplifierVery high input impedanceLarge common mode rejection ratio (CMRR)Capability to amplify low level signalsConsistent bandwidthIntegratordtvRCVtoinO1Lossless capacitordttxkdttxRCtytoto1Differentiation and integrationdtvRCVtoinO1Improved IntegratorLossy capacitorRs is shunt resistorRs=10R1The use of shunt resistor is to limit the low frequency gain of the circuit.Otherwise, a small DC offset at the input would be integrated over time, eventually saturating the op amp.DC offset due to the input bias current can be minimized by R2. Choose:ssRRRRR112IntegratorExampleVtuevts215Vvo100Find vo(t) for t>0Summing Integrator2211221121RtxRtxRtvRtvtititicdttiCtvtocc1tdRtvRtvCtvtc022111tdCRtxCRtxtyt02211tdtxktxktyt02211DifferentiatorDifferentiator The input signal to the differentiator is applied to the capacitor. The capacitor blocks any DC content so there is no current flow to the amplifier summing point, resulting in zero output voltage. The capacitor only allows AC type input voltage changes to pass through and whose frequency is dependant on the rate of change of the input signal. At low frequencies the reactance of the capacitor is "High" resulting in a low gain (Rf/Xc) and low output voltage from the op-amp. At higher frequencies the reactance of the capacitor is much lower resulting in a higher gain and higher output voltage from the differentiator amplifier.DifferentiatorImproved Differentiator AmplifierExample: Integrator and Switch An integrator and a voltage-controlled switch─ An integrator is a circuit that can perform the mathematical operation of integration. The output voltage, vo(t), is related the input of the integrator, vs(t).1021tvdttvKtvotts─ Integrators have many applications. One is to measure a time interval t2-t1. 11220tvVttKtvosExample: Integrator and SwitchVoltage controlled switch- Switch can be controlled electronically. The node voltage, vc(t), is called the control voltage.Example: Integrator and SwitchTo design an integrator circuit12220010ttmsVtvo1122tvVttKtvosomsVVKs20010sK110ExampleKRCdtvRCvttso1121kFsVRFC10011011150 tttvoOp-Amp Open Loop GainIn Op-amp, practically, the gain is so high that the output will be driven to +Vccor –Vccfor any appreciable difference between V1and V2.This is useful in the comparator. For practical applications other than the comparator, negative feedback is used to control the device gain.Comparator The extremely large open-loop gain of an op-amp makes it an extremely sensitive device for comparing its input with zero.  For practical purposes, if V2>V1, the output is driven to the positive supply voltage; If V2<V1 it is driven to the negative supply voltage. The switching time for - to + is limited by the slew rate of the op-amp.Comparator The basic comparator will swing its output to at the slightest difference between its inputs. But there are many variations where the output is designed to switch between two other voltage values VHand VL. Also, the input may be tailored to make a comparison to an input voltage VTother than zero.Comparator: application Often it is desirable that switching occurs at prescribed voltage . Comparator can be used for this purpose. vvifVvvifVtvLHo VHand VLare the only two values that vo(t) can have.Comparator: ExampleTcLTcHoVtvifVVtvifVtv For the following circuit, suppose VA>VT> vc(0), VTis a threshold voltage; and the input voltages for the comparator areTcVvtvv The output voltage The capacitor voltageRCtAcAceVvVtv 0 At t1, the comparator voltage switches from VLto VHRCtAcATeVvVV10ATAcVVVvRCt0ln1Comparator: Example For the shown circuit, the initial value of the capacitor voltage is vc(0) =1.667V. What value of the resistance, R, is required if the comparator is to switch from VLto VHat time t1=1ms?Comparator: Example For the shown circuit, the comparator is used to compare the resistor voltage vR(t) with a threshold voltage VT. Suppose VA>VT> RiL(0). At time t1, the comparator output voltage switches from VLto VHtLRALALeRViRVti 010tLRALALTeVRiVtRiVATALVVVRiRLt0ln1Comparator: Example For the shown circuit, the initial value of the inductor is iL(0) =1mA. What value of the inductance, L, is required if the comparator is to switch from VLto VHat time t1=10ms?The Sample and Hold circuit  When The Sample and Hold circuit uses two buffers to keep a voltage level stored in a capacitor. Pressing Ssamplewill charge the capacitor to the present signal level, while the input buffer ensures the signal won't be changed by the charging process. From there, the output buffer will make sure that the voltage level across the storage cap won't decrease over time.  Pressing Sclearwill short out the storage cap, discharging it and setting the output to 0V. We can build the Sample and Hold circuit with mechanical pushbutton switches to see it in action. In actual practice, the switches used are various forms of transistor switch, which provides cleaner switching and also allows another circuit to control the sample and clearing operations.Uses of Linear Op-Amp Circuits Amplifiers– Making signals bigger! Summing Amp– Mixing (e.g. audio applications)– Analogue arithmetic Integrator– Analogue computing– Active filter design Difference Amp– Balanced line receiversIdeal Op-Amp Linear Circuit Analysis When negative feedback is applied, the use of these assumptions makes design/analysis much easier (although not necessarily simple!). Of course, they aren’t really true! anything .3 .20 and 0


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Pitt MEMS 1082 - Mechatronics

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