Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits Electronics Spring 2006 Problem Set 5 Issued 3 8 06 Due 3 15 05 Exercise 5 1 This problem studies the MOSFET ampli er shown below Assuming that the MOSFET operates in its saturation region de ned by iD 0 5K vGS VT 2 and 0 vGS VT vDS 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 VS vIN R vOUT Problem 5 1 Both ampli ers shown below are constructed with a non quadratic MOSFET having the vDS iD characteristics shown graphically below The characteristics are plotted for vGS 0 5 V 0 55 V 0 6 V 0 65 V 0 7 V 0 8 V 1 5 V For vGS 0 5 V the MOSFET is cut o Note that the last page of this problem set contains a larger graph of the MOSFET characteristics It may be turned in with your problem set solutions Ampli er B 10 k R1 Ampli er A 10 k 5V R2 vOUT 5V vOUT vGS vIN MOSFET Characteristics 1 v 0 9 GS 1 1 V v GS 1 0 V v 0 8 GS 0 9 V 0 7 v GS 0 8 V 0 5 D i mA 0 6 v 0 4 v 0 3 v 0 2 v 0 1 0 GS GS GS GS 0 7 V 0 65 V 0 6 V 0 55 V vGS 0 5 V 0 0 5 1 1 5 2 2 5 vDS V 3 3 5 4 4 5 5 A Consider Ampli er A Using graphical analysis plot vOUT as a function of vGS for 0 V vGS 1 5 V B Using your results from Part A determine the range of vGS and the corresponding range of vOUT over which the small signal voltage gain of Ampli er A from vGS to vOUT is reasonably constant at its largest value use engineering judgment It is over this range that the ampli er provides its largest voltage gain with little distortion What is the corresponding small signal voltage gain Also what is the small signal voltage gain near vGS 0 Your answer to the last question explains why small signals can not be input directly at vGS if they are to be ampli ed C Consider Ampli er B This ampli er builds on Ampli er A and uses the resistor network comprising R1 and R2 to bias vGS and vOUT In this way the ampli er will be designed to amplify vIN when it is centered around 0 V Determine vGS in terms of R1 R2 vIN and the power supply voltage of 5 V D Let R1 10 k Using your results from Parts A B and C determine R2 so that the performance of Ampli er B satis es the following two criteria For vIN 0 V resistors R1 and R2 establish the bias value of vOUT As vIN varies around 0 V vOUT varies around its bias value With this in mind the rst criterion is that vOUT must be allowed to vary within 1 V of its bias value while remaining within the range identi ed in Part B That is Ampli er B must be designed to provide voltage gain with little distortion over a 2 V range of vOUT Note that the range for vOUT found in Part B is wider than 2 V and so this criterion does not uniquely specify R2 The second criterion is that the small signal voltage gain of Ampli er B from vIN to vOUT should be maximized when vOUT is within the range established by the rst criterion With this additional criterion R2 is uniquely speci ed E Given your design of R1 and R2 found in Part D what is the small signal voltage gain of Ampli er B for values of vIN near 0 V F The small signal voltage gain found in Part E should be smaller than that found in Part B Why 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 voltage 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 voltage 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 voltage gain vout vin Compare this small signal gain to that found in Part A and explain any di erences D Determine the small signal Thevenin equivalent of the ampli er when it is viewed through its output port Figure For Problem 5 1 MOSFET Characteristics 1 vGS 1 1 V 0 9 v GS 1 0 V vGS 0 9 V 0 8 0 7 vGS 0 8 V iD mA 0 6 0 5 v GS 0 4 vGS 0 65 V 0 3 vGS 0 6 V 0 2 vGS 0 55 V 0 1 0 0 7 V vGS 0 5 V 0 0 5 1 1 5 2 2 5 vDS V 3 3 5 4 4 5 5
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