Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits Electronics Spring 2004 Problem Set 5 Issued 3 3 04 Due 3 10 04 Exercise 5 1 This problem studies the MOSFET ampli er shown below A saturation region model for the MOSFET is also given below Assuming that the MOSFET operates in its saturation region determine vOUT as a function of vIN Also determine the range of vIN and the corresponding range of vOUT over which the MOSFET operates in its saturation region Saturation 0 vGS VT vDS VS vIN vOUT R iD K vGS VT 2 2 Exercise 5 2 A linear MOSFET ampli er may be constructed using two MOSFETs as shown below Note that the transconductances KA and KB and the threshold voltages VTA and VTB of the two MOSFETs are di erent Assuming that both MOSFETs operate in their saturation regions determine vOUT as a function of vIN Also determine the range of vIN and the corresponding range of vOUT over which both MOSFETs operate in their saturation region Saturation A B VS vIN 0 vGSA VTA vDSA iDA KA vGSA VTA 2 2 vOUT 0 vGSB VTB vDSB iDB KB vGSB VTB 2 2 Problem 5 1 So far we have studied MOSFET ampli ers that have no load That is the current circulating through the output port of each ampli er was zero For example in Problem 4 3 the current out of the st ampli er and into the second ampli er was zero because iG 0 for the second MOSFET In this problem which studies the ampli er shown below the output current is no longer zero The load below is a resistor that does draw current from the ampli er Hint in analyzing this ampli er consider the use of both Thevenin equivalence and load line analysis to simplify the problem Also review your solution to Problem 4 3 Once again use a simpli ed model for the MOSFET as shown below The simpli cation is again 2 2 which becomes a that the triode region of operation is compressed onto the curve iD KvDS common curve of operation for vGS VT vDS A Determine the range of vIN over which the MOSFET operates in cuto Also determine vOUT for this operating range B Assuming that the MOSFET operates in its saturation region determine vOUT as a function of vIN Also determine the range of vOUT and the range of vIN that correspond to the saturated operation of the MOSFET C For values of vIN that are above the range found in Part B the MOSFET operates in its 2 2 Determine triode region which in the model below is compressed onto the curve iD KvDS vOUT for vIN in this range of operation iD R VS vIN vOUT RL Triode iD KvDS2 2 vGS VT vDS Saturation iD K vGS VT 2 2 0 vGS VT vDS vDS Cutoff iD 0 vGS VT 0 Problem 5 2 This problem continues to study the two stage ampli er studied rst in Problem 4 3 In this problem let vIN VIN vin and vOUT VOUT vout where VIN and VOUT are the large signal components of vIN and vOUT respectively and vin and vout are the small signal components of vIN and 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 ampli er that can be used to determine vout as a function of vin In doing so assume that VIN de nes the operating point around which the small signal model is constructed and evaluate all small signal model parameters in terms of VIN as necessary B Use the small signal model to determine vout as a function of vin C Compare the small signal gain found in Part B de ned as vout vin to that found in Part F of Problem 4 3 Explain any di erences D Determine the small signal Thevenin equivalent of the ampli er when it is viewed through its output port Problem 5 3 Consider again the ampli er described in Exercise 5 1 In this problem let vIN VIN vin and vOUT VOUT vout where VIN and VOUT are the large signal components of vIN and vOUT respectively and vin and vout are the small signal components of vIN and vOUT respectively A Using your result from Exercise 5 1 determine the small signal gain of the ampli er as a function of the input bias voltage vIN That is determine vout vin dvOUT dvIN evaluated at VIN B Again assume that the MOSFET is biased so that it operates in its saturation region Develop a small signal circuit model for the ampli er that can be used to determine vout as a function of vin In doing so assume that VIN de nes the operating point around which the smallsignal model is constructed and evaluate all small signal model parameters in terms of VIN as necessary C Use the small signal model to determine the small signal gain vout vin Compare this smallsignal gain to that found in Part A and explain any di erences D Determine the small signal Thevenin equivalent of the ampli er
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