Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer Science6.002 – Circuits & ElectronicsSpring 2004Problem Set #5Issued 3/3/04 – Due 3/10/04Exercise 5.1: This problem studies the MOSFET amplifier shown below. A saturation-regionmodel for the MOSFET is also given below. Assuming that the MOSFET operates in its saturationregion, determine vOUTas a function of vIN. Also, determine the range of vINand the correspondingrange of vOUTover which the MOSFET operates in its saturation region.+_VS+_vIN+_vOUTRSaturation:0 < (vGS - VT) < vDSiD = K(vGS-VT)2/2Exercise 5.2: A “linear” MOSFET amplifier may be constructed using two MOSFETs asshown below. Note that the transconductances KAand KB, and the threshold voltages VTAandVTB, of the two MOSFETs are different. Assuming that both MOSFETs operate in their saturationregions, determine vOUTas a function of vIN. Also, determine the range of vINand the correspondingrange of vOUTover which both MOSFETs operate in their saturation region.+_VS+_vIN+_vOUTSaturation:0 < (vGSA - VTA) < vDSAiDA = KA(vGSA-VTA)2/20 < (vGSB - VTB) < vDSBiDB = KB(vGSB-VTB)2/2(A)(B)Problem 5.1: So far we have studied MOSFET amplifiers that have no load. That is, thecurrent circulating through the output port of each amplifier was zero. For example, in Problem4.3 the current out of the fist amplifier and into the second amplifier was zero because iG=0forthe second MOSFET. In this problem, which studies the amplifier shown below, the output currentis no longer zero. The load below is a resistor that does draw current from the amplifier. Hint, inanalyzing this amplifier, consider the use of both Thevenin equivalence and load line analysis tosimplify the problem. Also, review your solution to Problem 4.3.Once again, use a simplified model for the MOSFET as shown below. The simplification is againthat the triode region of operation is compressed onto the curve iD= Kv2DS/2, which becomes acommon curve of operation for vGS− VT>vDS.(A) Determine the range of vINover which the MOSFET operates in cutoff. Also, determine vOUTfor this operating range.(B) Assuming that the MOSFET operates in its saturation region, determine vOUTas a function ofvIN. Also, determine the range of vOUTand the range of vINthat correspond to the saturatedoperation of the MOSFET.(C) For values of vINthat are above the range found in Part (B), the MOSFET operates in itstriode region, which in the model below is compressed onto the curve iD= Kv2DS/2. DeterminevOUTfor vINin this range of operation.vINRVS+_vOUTiDvDSCutoffiD = 0 vGS - VT < 0}SaturationiD = K(vGS-VT)2/20<vGS-VT<vDSTriodeiD = KvDS2/2vGS -VT > vDSRLProblem 5.2: This problem continues to study the two-stage amplifier studied first in Prob-lem 4.3. In this problem, let vIN= VIN+ vinand vOUT= VOUT+ vout, where VINand VOUTarethe large-signal components of vINand vOUT, respectively, and vinand voutare the small-signalcomponents of vINand vOUT, respectively.(A) Assume that both MOSFETs are biased so that they operate in their saturation regions.Develop a small-signal circuit model for the amplifier that can be used to determine voutasa function of vin. In doing so, assume that VINdefines the operating point around which thesmall-signal model is constructed, and evaluate all small-signal model parameters in terms ofVINas necessary.(B) Use the small-signal model to determine voutas a function of vin.(C) Compare the small-signal gain found in Part (B), defined as vout/vin, to that found in Part (F)of Problem 4.3. Explain any differences.(D) Determine the small-signal Thevenin equivalent of the amplifier when it is viewed through itsoutput port.Problem 5.3: Consider again the amplifier described in Exercise 5.1. In this problem, letvIN= VIN+ vinand vOUT= VOUT+ vout, where VINand VOUTare the large-signal componentsof vINand vOUT, respectively, and vinand voutare the small-signal components of vINand vOUT,respectively.(A) Using your result from Exercise 5.1, determine the small signal gain of the amplifier as afunction of the input bias voltage vIN. That is, determine vout/vin= dvOUT/dvINevaluated atVIN.(B) Again assume that the MOSFET is biased so that it operates in its saturation region. Developa small-signal circuit model for the amplifier that can be used to determine voutas a functionof vin. In doing so, assume that VINdefines the operating point around which the small-signal model is constructed, and evaluate all small-signal model parameters in terms of VINasnecessary.(C) Use the small-signal model to determine the small-signal gain vout/vin. Compare this small-signal gain to that found in Part (A) and explain any differences.(D) Determine the small-signal Thevenin equivalent of the
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