OPAMP APPLICATIONSOPAMP APPLICATIONSEE122D. W. ParentD. W. ParentThe inverting integrator a good place lk b lto start talking about signal processing.∫+−=initialinoutVdtVVIt acts like a low pass filter with a pole at ω=0.∫initialoutRCp pIntegrate Vin=1, AssumeVinitial=0Integrate Vin 1, Assume Vinitial0)(101tVdtV∫−+Linear function m=‐1/RC b=0)(0tVRCdtRCVinout∫=+−=Linear function, m=‐1/RC, b=0R=10kΩ, C=0.01uF, m=‐10kV/sWe should get a ramp with a 0.1mV/s slope.10kV1secondCan we really go 10kV?What happened?What happened?What happened?What happened?Vinitial was not set to zero. Spice needs initial conditions and realneeds initial conditions and real integrators need a reset mechanism. To set an initial condition in spice add d()a spice directive .ic V(OUT)=0• It is under edit and has a little .op symbol in the p ypull down menu.What happened?Another simple integrator test is to set Vin=0. We should get zero Volts out overVin 0. We should get zero Volts out over time.•We do!We do!•Whathappens in a device with a real VOS?•Whathappens in a device with a real VOS?VOS is a DC quantity and is integrated over time.1 second might seem like a lot of time but these systems are supposed to work right for years!Adding a feed back resistor can provide a “leakage”path for the DC terms caused byleakage path for the DC terms caused by VOS.Voltage goes to 6mV over timeVoltage goes to 6mV over time.The smaller RF the more the eff ect of VOS i ddis reduced. The larger RF the more ideal the integrator.The larger RF the more ideal the integrator.You need to trade off idealness vs VOS. If you know your signal has no DC, it is easier!There are many other “industry standard” wa ys to do integrationwa ys to do integration.This is a first pass at an artificial quadratic integrate and fire neuron.Deboo i ntegratorhttp://www maximic com/appnotes/index mvp/id/1155http://www.maxim‐ic.com/app‐notes/index.mvp/id/1155Lore nz AttractorLore nz AttractorLore nzAttractorLore nz AttractorCommunications encryptionAbsolute ValueAbsolute ValueAbsolute ValueAbsolute ValueLog amplifierLog amplifier⎟⎟⎠⎞⎜⎜⎝⎛−=RIVVVinToutln⎟⎠⎜⎝RIsToutHow would you turn this circuit into V2?How would you turn this circuit into
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