1Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38Lecture 38: Frequency responseProf J. S. SmithDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithContextNext week is the last week of lecture, and we will spend those three lectures reviewing the material of the course, and looking at applications of the material.Today and Friday, we will look at a device matching, and then the basics of differential amplifiers.2Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithReadingzChapter 10, Frequency analysis of active circuitsDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithLecture OutlinezDevice matching in current mirrors zIntroduction to differential amplifiers3Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithDevice MatchingzOne of the things that we depend on in the design of analog integrated circuits is device matching. For example, if we make a current mirror, we are depending on the reference and the mirror device behaving is a very similar fashion. When a gate-source voltage is developed on the reference device, passing a given current, the same voltage appearing across the gate to source on the mirror device will allow the same drain current.Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithVariationszThe transistors will generally vary due to several causes:zTemperature→very similar for devices on the same substratezImplant variations→important for small deviceszVariations in width→important for narrow deviceszVariations in length→important for short channel deviceszLayout variationsOften, analog devices will not be minimum sized devices, so that output resistances will be lower, short channel effects will be smaller, and the effect of variations is reduced.4Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithCurrent mirrorzLet’s look at the two transistors of a current mirrorV+V−The drain currents are given by:()2111121tGSoxnDVVLWCI −⎟⎟⎠⎞⎜⎜⎝⎛=µ()2222221tGSoxnDVVLWCI −⎟⎟⎠⎞⎜⎜⎝⎛=µDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithInduced errorzLet’s now define all the parameters in terms of their average values, and their variations.2/2/21212/2/212121ttavetttavetaveaveaveDaveDVVVVVVLWLWLWLWLWLWIIIIII∆−=∆+=⎟⎠⎞⎜⎝⎛∆−⎟⎠⎞⎜⎝⎛=⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛∆+⎟⎠⎞⎜⎝⎛=⎟⎠⎞⎜⎝⎛∆−=∆+=5Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithSmall variationszIf the variations are small, we can put these into our equation for the drain current, expand, and neglect the higher order terms:zFirst, we will write all of these in the formWhere x is small→()22/21212/ttaveGSaveoxnaveVVVLWLWCII∆±−⎟⎟⎠⎞⎜⎜⎝⎛⎟⎠⎞⎜⎝⎛∆±⎟⎠⎞⎜⎝⎛=∆±µ()x±1()()()xxyxyx2111112±≈±±±≈±±Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithzSo we have:zThe first terms each make a term of our original equation, but for the average values()222/1211212/12/ ⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛−∆±−⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛∆±⎟⎠⎞⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛∆±=∆±taveGSttaveGSaveaveoxnaveaveaveVVVVVLWLWLWCIIIIIµ6Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. Smith()222/1211212/1 ⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛−∆±⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛∆±−⎟⎠⎞⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛∆±taveGStavetaveGSaveoxnaveaveVVVLWLWVVLWCIIIµDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. Smith22/12112/1 ⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛−∆±⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛∆±=⎟⎟⎠⎞⎜⎜⎝⎛∆±taveGStaveaveVVVLWLWII⎟⎟⎠⎞⎜⎜⎝⎛−∆±⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛∆±=∆±taveGStaveaveVVVLWLWII2/2212/ ⎟⎟⎠⎞⎜⎜⎝⎛−∆+⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛∆=∆taveGStaveaveVVVLWLWII27Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithzIf we look at this result, we see that the proportional error in current is equal to the proportional error in the width to length ratio:zSo for a given accuracy in our photolithography, if we make our devices wide and long, they will be more accurately matched (but also consume more area)aveaveLWLWII⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛∆=∆ Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithzThe variation in the drain current due to threshold voltage variation is proportional to the variation of the threshold voltage with respect to the amount by which the gate voltage exceeds threshold. zSo if we run our devices significantly above threshold, they will match better. (but they will use more power, and dissipate more heat)⎟⎟⎠⎞⎜⎜⎝⎛−∆=∆taveGStaveVVVII28Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithzLayout is also important: If we need to lay out three transistors, and we put them in a row, the middle one may vary from the ones on the ends.zIf matchin is critical, you might put dummy devices on either side of all three transistors:zWatching the edge of the well is important too.Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithVoltage RoutingzAnother interesting consideration is how to get the currents that you create to where you want them.zYou can create the g-s voltages, and then run wires to the points where you need the current sink or source. This is called voltage routing:V+V−9Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 38 Prof. J. S. SmithCurrent RoutingzOr you can generate the current sink and then run a wire which is passing the current over to where you need the current sink, which is called current
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